Design and Testing of a
by
B.S., Massachusetts Institute of Technology (1988)
Submitted in Partial Fulfillment of the Requirements for the Degree of
at the
Aine 1990
© Massachusetts Institute of Technology, 1990
Signature of Author
Certified by
Accepted by
I
V _I
Depatfieat of Aeronautics and Astronautics
May 11, 1990
JUN 19 1990
LOBRARO
ARC-AVE S
Professor David L. Akin
Thesis Supervisor
Department of Aeronautics and Astronautics
-- ---- -
:W
WProfessor Harold Y. Wachman
Chairman, Departmental Graduate Committee
Department of Aeronautics and Astronautics

by
Submitted to the Department of Aeronautics and Astronautics on May 11, 1990 in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics
An innovative nine degree-of-freedom robotic manipulator intended for neutral buoyancy space simulation research has been developed. The manipulator design specifications were driven by two primary goals; to duplicate and surpass the operational characteristics of the Shuttle Remote Manipulator System (SRMS) and to serve as a robust, neutral-buoyancy positioning system. The ability to provide fine tip positioning as well as large force production capability was realized by decoupling the system design into a three degree-of-freedom, revolute joint, manipulator arm augmented by a six degree-of-freedom, parallel-link, micromanipulator. Hybrid pneumatic/hydraulic actuators were developed to overcome neutral buoyancy constraints and to satisfy safety considerations. Finally, a variety of joint-based control schemes and Cartesian trajectory planning methods were implemented and studied.
This research was funded by the NASA Office
Technology (NASA Grant NAGW-21).
of Aeronautics and Space
Thesis Supervisor: Professor David L. Akin
Rockwell Assistant Professor of Aeronautics and Astronautics

Two years ago as a fledgeling graduate student, I approached Dave and asked
"What would be a really neat thing to build?" He replied, "Ummm, well, I've got an idea for a pneumatic positioning arm. It would be like the big arm down at Marshall [Space
Flight Center] but much stronger. And I figure that we can make it strong enough to use in
one-g, so we can take it to freshman open houses and tap people on the shoulder with it."
At the time I had no idea what to call the arm. A long string of attempts at naming ensued with such dubious acronyms as Big Large Arm Hopefully (BLAH) and
SSL, I finally decided the "big arm" would be called the Stewart Platform Augmented
Manipulator, and thus, SPAM was born. Where the inspiration for SPAM came from, I am uncertain. Of course there is the processed meat product of the same name to consider. But
I doubt that. There is alternatively my dear friend Cindy Shen, who picked up the nickname
"SPAM" when she was a freshman. But I have my doubts about this also. Lastly, there is the skit by Monty Python ("Spam, spam, spam...") involving a restaurant that only serves
There are a great number of people that I feel deserve my expressed appreciation and gratitude. First and foremost, I would like to thank Professor David Akin for his encouragement, support, and timely advice over the past few years. I am convinced that the prospect of working with Dave was the primary factor which drove me to pursue another degree at MIT. All that I have learned and gained during the past two years, I feel I owe to him. It is my sincere hope that we will be able to work together again in future days.
Second, I am indebted to all the undergraduates who worked on SPAM. Paul
"Jello" Duncan, deserves endless acclamations since he toiled long hours building most of the hardware and being the "SPAM Diver". I could not have asked for a more capable
"right-hand man". Cecelia "Too Tall" Park should be given an award for the amazing amount of foam and fiberglassing she had to endure under my dubious guidance. I cannot thank her enough for her unwavering commitment and dedication. Paul "Moonbeam" Stach will hopefully realize his ambition of"going to the moon on a craft of his own design", but until then, I hope he will take pride in the most excellent parts of SPAM (especially the
"Stach Wrench") that he built. It was great fun and a tremendous pleasure to have worked with a fellow Illini! Additionally, I owe thanks (and probably several apologies for waking
3

her) to Beth "Starlight" Kader, the "Bonus UROPer". I had no idea that hiring
"Moonbeam" was a package deal, but I appreciate all of Beth's help at Pool Tests. Finally, gratitude is also due to Wisdom Franchot Coleman, Ronke Olabisi and Jen Tran.
To Professor Harold "Sandy" Alexander, I extend my heartfelt appreciation for his constructive suggestions, weekend shop supervision, and for introducing me to the
Advanced Missions Group at NASA-Ames. To Ping Lee, I apologize profusely for the stream of inundating purchase orders and receipts that I constantly poured on her desk.
Acknowledgement must additionally be given to Al Shaw, Earle Wassmouth, and Don
Weiner for having the courtesy to deal with myself and everyone associated with SPAM.
To the community that is the "SSL family", my thanks go: to Rich Patten for teaching me everything about pneumatics; to Karl "Killer" Kowalski for always being amusing and wanting a good argument; to Jud "Cowardly Lion" Hedgecock for his friendship since Unified; to Ender St. John-Olcayto "Smythe" for being a great roommate, friend and confidant; to Ella "Mrs. Smith" Atkins for just being Ella (even though she decided my name should be "Fong Unit") and for always telling me "that's nice, dear"; to
Rob Sanner-Blah for his invaluable advice in computer science and fabulous cookies; to
Sayan "Interview-Man" Chakraborty for being an active member in the "Sleep 'Til Noon or
Preferably Later Club" (may he always have a "birdhouse in his soul"); to Sam
"Zonmmnrrrtech" Druker for lending me Young M.C.'s Stone Cold Rhvmin' and for sharing my disgust of Microsoft products; to Kurt "Smut-Man" Eberly for always amusing me with his "Hans and Franz" imitation; to Matt "Mattress" Machlis for throwing a frisbee
(and for splattering me all over the slopes at Cannon Mt.); and to Russ "Fluffy" Howard for having the reference books on anything and everything I needed.
Finally, my thanks to my family and friends who have made the past two years the best years of my life. To my parents for always giving me the encouragement and support to do whatever I wanted to do my entire life, I will always be deeply ndebted. I only hope that they know how much their love has meant to me. To my brother Tim, and sister
Tammy, thanks for being silly and asking amusing questions. To Brian, Cindy, Ellen,
Eric, Mini, Ryo, and Tex, thanks for everything. To Eriko, for being my friend, fellow
"strobophobe" and for always amusing me. Most of all, thanks to Jessica for being the most wonderfully caring person in the world, for talking with me about anything and everything, and for giving me companionship and love.
This thesis is dedicated to my parents and Jessica.
4

"I didn't expect a kind of Spanish Inquisition."
"NOBODY EXPECTS THE SPANISH INQUISITION!!! Our chief weapon is surprise..
surprise and fear... fear and surprise... our two weapons are fear and surprise...
and ruthless efficiency. Our three weapons are fear and surprise and ruthless efficiency and an almost fanatical devotion to the Pope... Ourfour ... no... amongst our weapons are such elements as fear, surprise... (amrtgh) I'll come in again..."
Monty Python's Flying Circus
5

1.1 SSL Research Background
1.2 The SRMS Simulator
1.2.1 Summaryof the SRMS
1.2.2 SRMS Simulator Characteristics
1.3 Motivation for Research
System Design
2.1 Design Goals
2.2 The Stewart Platform Augmented Manipulator
2.2.1 SPAM Concept Development
2.2.2 3-DOF Manipulator Design Specifications
2.2.3 6-DOF Stewart Platform Specifications
3.1 Manipulator Kinematics
3.1.1. 2-Link Manipulator
3.1.1.1. Forward Kinematics
3.1.1.2. Inverse Kinematics
3.1.2. 3-Link Manipulator
3.1.2.1. Forward Kinematics
3.1.2.2. Inverse Kinematics
3.2. Manipulator Control Schemes
3.2.1. Open-Loop Position
3.2.2. Open-Loop Resolved Motion Rate
3.2.3. Closed-Loop Position
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3.2.4. Closed-Loop Tip Control
3.2.5. Inverse Jacobian Controller
3.3. Revolute Joint Design & Testing
3.3.1. Development of Neutral Buoyancy Actuators
3.3.2. Revolute PHAD-A
3.3.3. Revolute PHAD-B
3.3.4. Position Sensor
3.3.5. Joint Servo Control
3.3.5.1. Position Servo Design & Testing
3.3.5.2. Velocity Servo Design & Testing
3.4. SPAM Manipulator Hardware
3.4.1. Neutrally Buoyant Arm Booms
3.4.2. Joint/Arm Boom Interface
3.4.3. R-PHAD-A Power System
3.4.4. Electronic Control System
3.5. 2-link Manipulator Testing & Results
3.5.1 Open-Loop Control Testing
3.5.2 Closed-Loop Position Control Testing
4.1 The Stewart Platform
4.1.1 Geometric Analysis
4.1.2 Kinematics
4.1.2.1 Inverse Kinematics
4.1.2.2 Forward Kinematics
4.1.2.3 Kinematic Constraints
4.2 Stewart Platform Control
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4.2.1 Joint-Based Control
4.2.2 Cartesian-Based Control
4.3 Joint Design & Testing
4.3.1 PHAD Revisited
4.3.2 Universal Joint
4.3.3 Spherical Joint
4.3.4 JELLO Sensor
4.3.5 L-PHAD Servo Control
4.4 SPAM Stewart Platform Design
4.5 SPAM Stewart Platform Hardware
4.5.1 Assembled Hardware
4.5.2 Pneumatic System
4.5.3 Electronic Control System
5.1 Hardware Integration
5.2 Distributed Systems
5.3 Operation of SPAM
5.3.1 User Interface and SPAM Control
5.3.2 Operational Issues
6.1 Current SPAM Hardware
6.2 SPAM Development Observations
6.3 Recommendations for Future Studies
6.3.1 Implementation Specific Issues
6.3.2 Manipulator Arm
6.3.3 Stewart Platform
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6.3.4 Space Research Topics
6.4 Research Summary
References
Appendix A: SPAM Electronics
Appendix B: SPAM Hardware
Appendix C: SPAM Software
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Figure 1.2.1:
Figure 2.2.1:
Figure 2.2.2:
Figure 3.1.1:
Figure 3.1.2:
Figure 3.1.3:
Figure 3.1.4:
Figure 3.2.1:
Figure 3.2.2:
Figure 3.2.3:
Figure 3.2.4:
Figure 3.2.5:
Figure 3.2.6:
Figure 3.3.1:
Figure 3.3.2:
Figure 3.3.3:
Figure 3.3.4 (a):
Figure 3.3.4 (b):
Figure 3.3.4 (c):
Figure 3.3.5:
Figure 3.3.6:
Figure 3.3.7:
Figure 3.3.8:
Figure 3.3.9 (a):
Figure 3.3.9 (b):
SRMS Configuration
A Stewart Platform
Stewart Platform Augmented Manipulator (SPAM)
2-link planar manipulator
Frame assignments for 2-link planar arm
3-link anthropomorphic manipulator
Frame assignments for 3-link arm
Open-Loop Position Control
Resolved Motion Rate Control
Closed-loop Position Control
Augmented Closed-Loop Position Control
Closed-loop Tip Controller
Inverse-Jacobian Controller.
Pneumatic and Hydraulic Actuating Device (PHAD)
Diagonally-driven 5-bar linkage
5-bar linkage motion with diagonal drive
Characteristic curve of 5-bar linkage
Characteristic curve of 5-bar linkage
Characteristic curve of 5-bar linkage
Revolute PHAD-A
Neutrally-buoyant R-PHAD-A
Pivoting 2-bar crank
2-bar cranking motion
Characteristic curve of 2-bar crank
Characteristic curve of 2-bar crank
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Figure 3.3.9 (c):
Figure 3.3.10:
Figure 3.3.11:
Figure 3.3.12:
Figure 3.3.13 (a):
Figure 3.3.13 (b):
Figure 3.3.14:
Figure 3.3.15:
Figure 3.3.16:
Figure 3.3.17 (a):
Characteristic curve of 2-bar crank
R-PHAD-B schematic
R-PHAD-A Optical Encoder Mounting
P-D Joint Position Servo
P-D Position Servo (Kp = 1.0, Kd = 0.1)
P-D Position Servo (Kp = 2.0, Kd = 0.1)
BLAH Controller Logic
BLAH Velocity Servo
Proportional Velocity Servo
P Velocity Servo (Kp = 1.0)
Figure 3.3.17 (b):
Figure 3.3.18:
Figure 3.4.1:
Figure 3.4.2 (a):
Figure 3.4.3:
Figure 3.4.4:
P Velocity Servo (Kp = 1.0)
Proportional-plus-derivative Velocity Servo
Figure 3.3.19 (a):
Figure 3.3.19 (b)
P-D Velocity Servo (Kp = 1.0, Kd = 0.1)
P-D Velocity Servo (Kp = 1.0, Kd = 0.1)
Figure 3.3.20 (a): P-D Velocity Servo (Kp = 1.0, Kd = 0.1)
Figure 3.3.20 (b): P-D Velocity Servo (Kp = 1.0, Kd = 0.1)
Arm Boom Tube Configuration
End plug with Koganei solenoids
Joint Collar
Joint/Arm Tube Interface
R-PHAD-A Power System
Manipulator Hookup Board (MHB)
Figure 3.4.5:
Figure 3.4.6:
Figure 3.4.7:
Figure 3.5.1.
Figure 3.5.2:
Figure 3.5.2:
SPAM Electronic Control System (schematic)
2-link arm frames (vertical test mounting)
SPAM 2-link planar arm
2-link arm geometry for {L2, 0, LO+L1 })
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Figure 3.5.3: Joint angles resulting from {L2, 0, LO+L1 } command
Figure 3.5.4:
Figure 3.5.4:
Figure 4.1.1:
Figure 4.1.2:
Figure 4.1.3:
Figure 4.1.4:
Figure 4.1.5:
Figure 4.2.1:
2-link arm geometry for {L2+0.707L1, 0,
LO+0.707L command
Joint angles from {L2+0.707L1, 0, LO+0.707L1 } command
Common Stewart Platform Implementation
General Stewart Platform
Symmetrical Stewart Platform Geometry
Frame and Vector Assignments
Actuator Vector Relationships
Stewart Platform Joint Based Control
Figure 4.2.2:
Figure 4.3.1:
Figure 4.3.2:
Stewart Platform Cartesian Based Controller
L-PHAD Design Schematic
Assembled L-PHAD
Universal Joint Design Figure 4.3.3:
Figure 4.3.4:
Figure 4.3.5:
Figure 4.3.6:
Assembled Universal Joint Design
Universal Joint Workspace
"Spherical" (U-Joint-plus-Swivel) Design
Assembled U-Joint-plus-Swivel Joint Design Figure 4.3.7:
Figure 4.3.8:
Figure 4.3.9:
U-Joint-plus-Swivel Workspace
Joint Encoder with Localized Linear Optics (JELLO) schematic
Figure 4.3.10:
Figure 4.3.11:
Figure 4.3.12 (a):
Joint Encoder with Localized Linear Optics (JELLO)
P-D Position Servo
P-D Position Servo (Kp = 0.05, Kd = 0.01)
Figure 4.3.12 (b): P-D Position Servo (Kp = 0.05, Kd = 0.01)
Figure 4.3.12 (c): P-D Position Servo (Kp = 0.05, Kd = 0.01)
Figure 4.3.13 (a): P-D Position Servo (Kp = 0.05, Kd = 0.01)
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Figure 4.3.13 (b):
Figure 4.4. l:
P-D Position Servo (Kp = 0.05, Kd = 0.01)
Excel CAD model of Stewart Platform
Figure 4.4.2: SPAM Stewart Platform Mounting Points
SPAM Stewart Platform schematic Figure 4.5.1:
Figure 4.5.2:
Figure 4.5.3:
Assembled SPAM Stewart Platform
SPAM Stewart Platform pneumatic system
Figure 4.5.4: NMIS-0001 and NMIS-0021
Stewart Platform Electronics Control System Figure 4.5.5:
Figure 5.1.1:
Figure 5.2.1:
Figure 6.1.1:
Figure 6.1.2:
Adjustable Hinge Coupling
SPAM Distributed Processing Network
SPAM Elbow-to-Stewart Platform (elbow view)
SPAM Elbow-to-Stewart Platform (tip view)
Figure 6.3.1: SPAM Stewart Platform Base Frames
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i -- i
1.1 SSL Research Background
During the past decade, the MIT Space Systems Laboratory (SSL) has been engaged in the study of orbital productivity. Specifically, this research has been directed towards qualifying and quantifying methods of increasing the productivity of activities in space. In 1982, the Automation, Robotics, and Machine Intelligence Systems (ARAMIS) study was conducted for NASA to determine the feasibility of introducing man-machine systems and methods to space operations. The results of this study theorized that significant cost savings and increased productivity of specific activities could be achieved by augmenting humans with automation and machine intelligence (Miller et al., 1983).
In the years following ARAMIS, the SSL has focused its efforts in the areas of teleoperation and expert systems. Recent activities have included research into the development of teleoperators for structural assembly, multiple sensor/control loop fusion techniques, autonomous docking and proximity operations, wurksite integration of multiple humans and robots, and intelligent control systems. The vast majority of this research has been performed in neutral buoyancy simulations. A neutrally buoyant research environment was selected since it offered the capability to perform full-scale testing of man/m.chine
operations. Furthermore, unlike other environments, neutral buoyancy does not restrict translational or rotational degrees of freedom, and thus offers a high degree of space simulation fidelity.
SSL's neutral buoyancy research has been conducted at two primary research sites, the MIT Alumni Swimming Pool and the NASA / Marshall Space Flight Center Neutral
Buoyancy Simulator (MSFC-NBS). The MIT Alumni Swimming Pool, measuring 40 by
75 feet with a maximum depth of 13 feet, offers limited space for large scale activities.
Research in this facility has been focused on localized activities such as assembly of structural nodes, proximity operations, and anthropometrics. The MSFC-NBS, on the other hand, is a 70 foot diameter by 40 foot deep tank, which allows for large space operation testing. Included at the MSFC-NBS are high-fidelity mockups of the STS
14

payload bay and the Hubble Space Telescope, pressure suits and support facilities, and a
Shuttle Remote Manipulator System (SRMS) simulator.
The SRMS simulator at the MSFC-NBS is a full scale kinematic simulation of the
SRMS. To understand its capabilities and deficiencies, it is first necessary to understand the mechanism it mimics, the Shuttle Remote Manipulator System (SRMS).
1.2.1 Summary of the SRMS
The SRMS was conceived as part of a cooperative development effort between
NASA and the National Research Council of Canada. Built by Spar Aerospace
(CANADA), the SRMS is intended to provide a controlled means of cargo deployment and retrieval during on-orbit STS missions. It is essentially a six degree-of-freedom manipulator system comprised of a large, three degree-of-freedom anthropomorphic manipulator augmented by a three degree-of-freedom end-effector. The SRMS configuration is shown in diagrammatic form in Figure 1.2.1.
Figure 1.2.1: SRMS Configuration
(Ussher, T.H., and Doetsch, K. H., An Overview of the Shuttle
Remote Manipulator System, NASA N85-16964, 1985).
o

The SRMS delivered to NASA, and currently used on the STS, is 50 ft. in length and weighs 950 lb. It is designed to maneuver a nominal payload of 32,000 lb. and to retrieve a maximum payload weight of 65,000 lb. The operational characteristics of the
SRMS are summarized below in Table 1.1 (Ussher, T. H. 1985).
Table 1.1: SRMS Operational Parameters
Degrees-of-freedom
Max. tip extension
Min. tip force (straight-arm)
Arm stiffness (straight-arm)
Joint rate hold accuracy
Tip position hold accuracy
Max. tip translation rate
6
50 ft
15 lb.
8.4 lb./in.
±1 deg./sec.
+2 in.
2 ft./sec.
(15.24 m)
(81.96 N)
(1,471 N-m)
(-0.025 m)
(0.61 m/sec)
The SRMS is controllable in any one of four standard, switch-selectable modes.
These modes are (1) Manual Augmented, in essence open-loop tip control with translational and rotational hand controller (THC & RHC) Cartesian rate commands resolved into joint rates; (2) Single Joint, which controls an individual joint rate while freezing the other five joints; (3) Direct Drive, whereby fixed rate commands are sent to switch-selected joints; and (4) Automatic Mode, where preprogrammed end-effector position trajectories are used to generate joint rate command sequences. All of these modes except for Direct Drive utilize the General Purpose Computer (GPC) onboard the STS for computation of joint rate commands.
SRMS Simulator Characteristics
The SRMS simulator was intended to provide the MSFC-NBS with the capability of simulating STS tasks involving the SRMS. At the time of the simulator's conception, two hardware simulations of the SRMS had been constructed elsewhere, at the Real-Time
Simulation Facility (SIMFAC) in Canada and at NASA's Johnson Space Center (JSC).
The SIMFAC simulator was constructed with an air-bearing system to simulate zero gravity. Due to space limitations and logistics, this simulator was useful only for verifying performance of SRMS components. Conversely the JSC simulator, used for training STS crews, was designed to operate in one-g. Although this simulator provided kinematic similarity, its dynamic characteristics were extremely different since it operated in full gravity instead of zero-g. To address the shortcomings of both of these simulators, it was proposed to construct a SRMS simulator at MSFC. Operating a SRMS simulator in the
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MSFC-NBS would theoretically be able to offer kinematic similarity as well as provide a high-fidelity simulation of on-orbit conditions.
Although the simulator eventually constructed at the MSFC-NBS is kinematically identical to the SRMS, it differs both from a physical and an operational standpoint. The simulator hardware (e.g. joints, boom structures, etc.) were assembled from surplus equipment at MSFC, waterproofed for operation in the NBS. Additionally, the four SRMS control modes were not implemented in the simulator, the only method being a direct mapping of translational and rotational hand controller offsets to joint rates. Moreover, no effort was made to compensate for the characteristics of a neutrally buoyant environment
(e.g. water drag and currents).
As a result of these factors, the SRMS simulator at MSFC-NBS exhibits three prominent differences from the actual SRMS. First, because of the water environment, the system is much less accurate and moves quite sluggishly. This makes precise positioning and deployment/retrieval of payloads significantly harder. Secondly, since the joint actuators were not originally designed for underwater use, the force available in the NBS is much lower. Tests have shown that the maximum tip force that the SRMS simulator can exert is on the order of one pound. This exacerbates the positioning problem because payloads with suboptimal neutral buoyancy cannot be moved. Finally, since the arm cannot be controlled in a closed-loop sense, it is extremely difficult to position the tip at desired positions and orientations. Taken collectively, these shortcomings mean that the SRMS simulator is not a very realistic simulation of the capabilities of the SRMS. Although the
SRMS simulator very closely matches the kinematics of the SRMS, in terms of reachable and dexterous workspace, it is severely deficient in its duplication of positioning and performance characteristics.
1.3 Motivation for Research
The current direction of SSL research indicates that future studies will focus to a greater and greater extent on enhancing man/machine system productivity. This may involve investigation of coordinating humans with multiple autonomous and teleoperated robots in performing activities in space. Some potential tasks for study include satellite servicing, structural assembly and maintenance. Additional research may entail quantifying worksite positioning requirements and finding means of reducing the expenditure of consumable supplies. To effect much of this research, however, a positioning system of some form will be required. Since SSL research is conducted primarily in neutral buoyancy, a logical choice to fulfill positioning needs would be a system similiar to the
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SRMS simulator at the MSFC-NBS. As discussed in the previous section, however, this simulator has shortcomings which tend to obviate its usefulness.
The problem at hand, therefore, is to develop a neutral buoyancy positioning system that corrects the deficiencies of the MSFC-NBS SRMS simulator. The fundamental requirements for such a system are threefold. First, it should be capable of duplicating the
SRMS workspace, in terms of reach and volume. Secondly, it should be designed for robust operation in a neutral buoyancy environment, able to generate large forces in the presence of water drag and currents. Finally, it should be operable by modem control methods and provide an efficient man/machine interface.
In the following chapters an innovative concept, the Stewart Platform Augmented
Manipulator (SPAM), is described which fulfills these requirements. The system is in essence a three degree-of-freedom anthropomorphic manipulator arm with revolute joints, augmented with a six degree-of-freedom parallel-link platform micro-manipulator. The
SPAM concept, as will be shown, is capable of simulating the SRMS with a high degree of fidelity in neutral buoyancy. Moreover, the system has the potential for higher performance and flexibility than even the actual SRMS can provide.
In Chapter 2 the SPAM concept is presented and a description of the system design specifications is given. Chapter 3 details the development of the anthropomorphic manipulator including the design of an underwater hybrid pneumatic/hydraulic rotary actuator, the implementation and testing of digital rate controllers, and the testing of revolute joints. Chapter 4 describes the design of a parallel-link platform micro-manipulator
(often referred to as a Stewart Platform), the development of linear pneumatic/hydraulic actuators, and parallel-link control issues. Chapter 5 presents planned systems integration and operational methods for the complete SPAM system, including a distributed processing system architecture. Finally, Chapter 6 summarizes the findings of this thesis and suggests avenues for future research.
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2.1 Design Goals
The development of a manipulator-type positioning system for neutral buoyancy was driven by two goals. First, the system had to be kinematically similar to the SRMS.
This indicated that the manipulator design should reflect dexterous and reachable workspaces that closely matched those of the SRMS. Secondly, the system had to operate in a robust manner in an underwater environment. This implied that the joint actuators be capable of producing large enough forces to compensate for water drag, and that link rigidity or joint controllability be sufficient to reject disturbing currents.
The design goals for the positioning system were initially based on the SRMS operational characteristics. During the early design phase, however, several modifications to these objectives were made. First, since the primary task is fine positioning, it was specified that the system be capable of fine tip control in six degrees-of-freedom. While the
SRMS has a total of six degrees-of-freedom at the tip, the three translational degrees are provided by the large manipulator arm section; making fine translation difficult.
Additionally, since the objects intended for positioning are humans and telerobots (which are much less massive than STS payloads), duplication of maximum SRMS tip force was not necessary. Finally, overall arm stiffness was determined not to be a critical design constraint. Although link flexing would have an impact on precise tip positioning, the conclusion was that micro-manipulator actions combined with active control would sufficiently compensate for lack of rigidity.
The easiest means of achieving SRMS react and workspace similarity is simply to duplicate the SRMS hardware arrangement of joints and links. In short, a large, three revolute joint (i.e. shoulder pitch, shoulder yaw, and elbow pitch) anthropomorphic arm augmented with a three revolute joint (wrist roll, pitch, and yaw) end-effector should be constructed. In this arrangement, the large arm provides large reach capability while the end-effector provides fine tip angular position control. This system is readily accomplished in neutral buoyancy, as demonstrated by the MSFC-NBS manipulator. Unfortunately
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though, this approach has a significant drawback since it utilizes a serial-link end-effector at the large arm's tip.
Serial-link mechanisms, though able to provide high positioning accuracy and positioning ease, typically are incapable of producing large forces. Generally speaking, this is not a problem since other devices or mechanisms can fulfill requirements for force. In an underwater environment, however, force production capability is a matter of concern since large water forces, such as drag and currents, are present.
In the case of the MSFC-NBS SRMS simulator, the serial-link end-effector attached to the large arm does not generate a large amount of force. Consequently, the large arm is relied upon to produce tip forces when positioning objects. Since this requires extremely minute joint control, which is difficult to achieve with long linkages, fine positioning is extremely hard to perform. In essence, any positioning advantages offered by the end-effector are totally offset by the inability to produce strong forces. As the
MSFC-NBS simulator demonstrates, a serial-link end-effector is not a viable solution for fine positioning in neutral buoyancy.
2.2.1 SPAM Concept Development
An elegant solution to the tip positioning problem is to replace the 3 jointed, seriallink wrist with a parallel-link mechanism. Parallel-link, or closed kinematic chain, devices are alternatives to traditional serial type mechanisms in which two or more linkages connect the base of the manipulator with the end-effector. The direct benefits of this arrangement are (Ismail; A., 1984):
* High strength and stiffness-to-weight ratios can be achieved since the links do not carry moment loads but act only in tension and compression.
* Positioning of the end-effector is performed by actuators acting in parallel, resulting in a total force and moment capability greater than each individual servomechanism.
* Moving only the end-effector in space rather than massive servomechanisms results in economy of power, excellent dynamic performance, and low manipulator inertia.
* High accuracy and precision is possible since actuator errors are not magnified by lengthy linkages.
20

Since all of these characteristics are advantageous for underwater mechanisms, it seems natural to implement a parallel-link mechanism in neutral buoyancy.
The design task, therefore, is to create a positioning system that combines a large manipulator arm with a six degree-of-freedom parallel-link micromanipulator. One concept that matches this description is the Stewart Platform Augmented Manipulator (SPAM). In this system, a three degree-of-freedom, anthropomorphic manipulator arm is augmented by a parallel-link mechanism called a Stewart Platform.
The Stewart Platform is a space truss comprised of six prismatic actuators, each mounted by a universal joint to the manipulator base and by a spherical joint to the top platform. Figure 2.2.1 depicts a typical Stewart Platform. This arrangement of actuators allows the platform to be placed in any position and orientation (i.e. with six degrees-offreedom) within a certain volume of space.
platform spherical
prismatic
Universal
base
Figure 2.2.1: A Stewart Platform
In the SPAM concept, the large, anthropomorphic manipulator arm provides coarse positioning and large reach capability with three revolute joints. The Stewart Platform, which augments the manipulator, offers fine tip positioning in six degrees-of-freedom.
Moreover, it has the characteristics (e.g. strength, stiffness, power, etc.) of parallel-link devices which are advantageous for underwater operation. The complete SPAM system is illustrated schematically in Figure 2.2.2.
21

e1form I/r
(pitch)
(yaw)
-'.
:'.":..,::::
::.':':
:.'''.:?'"
'/
Figure 2.2.2: Stewart Platform Augmented Manipulator (SPAM)
(schematic)
Detailed design specifications for the two main components of SPAM, the manipulator arm and the Stewart Platform, are presented in the following two sections.
2.2.2 3-DOF Manipulator Design Specifications
The preliminary design specifications for the large arm component of SPAM were derived from the SRMS. Three revolute joints arranged anthropomorphically (i.e. shoulder yaw, shoulder pitch, and elbow pitch) are connected by straight link sections. As with the
SRMS, the revolute joints should have a working range of 180 degrees. To complete the
22

SRMS kinematic simulation, therefore, simply requires a duplication of SRMS linkage lengths.
If the joints and linkages are modularly designed, however, mechanisms other than the SRMS may be simulated. As a result, linkage lengths were not specified as a fundamental design specification, but modularity was included in the baseline. Tip accuracy was assumed to be within one percent of the maximum manipulator translational reach. The
SRMS 15 lb. straight arm tip force (corresponding to a total linkage length of 50 ft.) resulted in a maximum shoulder joint torque specification of 750 ft-lb.
A summary of the baseline design specifications for the manipulator is presented in
Table 2.1.
Table 2.1: Manipulator Baseline Specifications
Degrees-of-freedom
Number of joints & type
Joint range of motion
Joint torque capability
Joint rate hold accuracy
Tip position accuracy
Tip position hold accuracy
Max. tip translation rate
3
3 revolute
180 degrees
750 ft-lb.
+ 1 deg./sec.
> 1 % max reach
+2 in.
2 ft./sec.
(1,017 N-m)
(±0.051 m)
(0.61 m/sec)
2.2.3 6-DOF Stewart Platform Specifications
The design specifications for the Stewart Platform component of SPAM were based on SRMS tip characteristics with consideration given for operation in an underwater environment. To match SRMS tip positioning, the Stewart Platform must have, at a minimum, +1 inch translational position accuracy. The translational workspace requirements were derived from the assumption that the large arm can position the endeffector to within one percent of the maximum translational reach. For a 50 ft arm, this indicates that the Stewart Platform should be capable of +6 inches movement in three translational axes.
The SRMS wrist provides only three degrees-of-freedom in the end-effector workspace. Since the Stewart Platform provides a total of six degrees-of-freedom, SPAM has three more degrees of tip freedom than the SRMS. To offer a large and flexible endeffector workspace for positioning, it was decided that ±45 degrees of rotational movement in 3 axes would prove to be sufficient. To overcome water forces and to provide 15 lbs of end-effector force (equivalent to SRMS minimum tip force), each actuator had to be capable of generating at least 15 lbs of force.
23

A summary of the baseline design specifications for the Stewart Platform is presented below in Table 2.2.
Table 2.2:
Degrees-of-freedom
Number of joints & type
Joint force capability
Translational accuracy
Translational range
Rotational range
Stewart Platform Baseline Specifications
6
6 prismatic
15 lbs. (66.7 N)
+1 inch (-0.025 m)
+6 inches (-0.15 m)
+45 degrees
24

Chapter 3
The task of constructing the manipulator arm component of SPAM was separated into several design and testing phases. In the first phase, a revolute joint was developed for underwater operation. This entailed actuator research and development, linkage design, fabrication, instrumentation, control systems design, and testing. For the second phase, a
2-link manipulator was assembled and operated in neutral-buoyancy. Control systems were implemented via computer and tests conducted to determine viability of various control schemes. The third and final phase involved the construction and operational testing of the full 3-link manipulator. At the present time, however, this phase has not been completed.
In this section, the kinematics for 2-link and 3-link serial-link manipulators are presented. A serial-link manipulator is essentially a series of rigid bodies connected in a chain structure. Such an arrangement is often referred to as an open kinematic chain
(Asada, 1986). Two mappings completely characterize serial-link manipulator geometry.
The forward kinematics mapping relates the natural coordinates of a manipulator to reference coordinates. Similarly, the inverse kinematics mapping transforms reference coordinates to natural coordinates. These two mappings are often used with respect to the end-effector. Given a description of natural coordinates (e.g. joint angles), for example, the forward kinematics are used to compute the end-effector position and orientation in some reference frame (e.g. Cartesian coordinates). Conversely, given position and orientation in a reference frame, the inverse kinematics are used to calculate the set of joint angles which will place the end-effector in the specified location.
The natural coordinates for a serial-link manipulator having n degrees-of-freedom is a set of n joint variables (Craig, 1986). If the manipulator is comprised only of revolute joints, for example, the set of joint variables is the set of all the joint angles. This may be expressed as a vector in joint space:
25

81
01
0= 0~~~~~1
The reference coordinates most frequently used are Cartesian coordinates, with an orthonormal frame to describe position and Euler angle rotations to describe orientation.
This may be expressed as a 6xl vector in Cartesian space (using Roll-Pitch-Yaw Euler angles): x
Y
X
(3.2)
8 where p
9, V, are right-handed rotations about the x, y, z axes respectively. The forward kinematics mapping, F, is then:
F: => X (3.3)
Similarly, the inverse kinematics mapping, G, is:
G: X = 0 (3.4)
For serial-link manipulators, frames are assigned to the manipulator base, to each joint in the chain, and to the end-effector (tip). The mapping of positions fiom frame A to frame B is then performed with a 4x4 homogeneous transform matrix, T: where:
[AP];{
BR]
[
1
] Tt ~~~1
AR APB
ORG
000 1 j
Ap is a 3x 1 Cartesian position vector in frame (A)
BPis a 3x1 Cartesian position vector in frame B)
APB ORG is the location of the origin of (B) in A)
BR is a 3x3 rotatior matrix describing the angular orientation of {B) in (A}
(3.5)
26

The forward kinematics of the manipulator is, therefore, the transformation from the manipulator base frame {0) to the end-effector frame {T}, T.
Determining manipulator inverse kinematics is problematic since the kinematic equations are highly non-linear and a general closed-form solution does not exist.
However, several approaches to solving the inverse kinematics problem are described in the literature for serial-link manipulators (i.e. algebraic manipulation, geometric decomposition, Pieper's method, etc.) which may result in the desired closed-form solution. It should be noted that a universal, numerical solution does exist for 6 degree-offreedom, serial-link manipulators composed of revolute and prismatic joints (Craig, 1986).
From an inverse kinematics applications perspective, however, a numerical method is considered to be suboptimal since it necessitates a significantly greater amount of iterative computation than a closed-form method, and because such a technique is not guaranteed to discover all the solutions of the problem.
The 2-link manipulator was designed to have two revolute joints, s -oulder pitch and elbow pitch. Since the two joint axes are parallel, the manipulator is an extremely simple planar arm as shown in Figure 3.1.1.
/
V777
Figure 3.1.1: 2-link planar manipulator
The frames assigned to the manipulator joints follow the convention in (Craig,
27

joint (shoulder) and aligns with { 0 when the shoulder angle is zero. Frame (2 } is attached to the second joint (elbow) and aligns with 1 } when the elbow angle is zero. Frame T), the tip frame, is located at the end of the elbow link. The 2-link arm with frame assignments is shown in Figure 3.1.2
A
A
V AT
'T
A y
1
A
X
2
Figure 3.1.2: Frame assignments for 2-link planar arm
3.1.1.1. Forward Kinematics
The frame transformations for the 2-link planar arm are:
C1
T = S
1 O
0
C2
T = S2
-Sl 0 0
Ci
0
0 0
1 0
0 0 1
-S2 0 L
1
C2 0 0
0 1 0
0 0 1
1
0
1 0 0 L2
2T= 0 0 1
010
1 [00 where cl is notational shorthand for cos(81).
(3.6)

Multiplying these matrices together, produces the desired forward kinematics transform:
C12 -S12 L+L
T
S2 C12 0 Lsl+L
2
C
1 2
2
S
2 l
(3.7a)
0 0 0 O where cl2 = cos(0l + 02).
The kinematic equations relating the joint angles to the tip location, referenced to frame {0), are found in column 4 of the above:
x = Llcl + L
2 y = Lls
1
+ L
2 s c
12
1 2
(3.7b
3.1.1.2. Inverse Kinematics
Following the algebraic solution method presented in (Craig, 1986) results in the desired inverse kinematics. The equations relating the tip position, referenced to frame ({0), to the joint angles are:
01 = Atan2(y, x) - Atan2(K
2
,K
1
)
02 = Atan2(s
2
, c2) where: c2
X2 + y2_ L
2
- L 2
2L
1
L
2
=
(3.9)
S2 =
(2) 2
K
K
2
1
= LI+L
-= L
2 s
2
2 c
2
(3.10)
(3.11)
There are several items to note in the preceding. First, the two argument arc tangent function is used in (3.8) to determine the quadrant containing the resulting angle. Secondly, for a solution to exist, the the right-hand side of (3.9) must be in the range [-1, 1]. If this constraint is not met, then the specified tip position is outside the reachable workspace.
Finally, the multiple solutions of (3.10) correspond to multiple geometric configurations of the arm that result in the same tip position.
The 3-link manipulator was designed to have three revolute joints in an anthropomorphic configuration; shoulder yaw, shoulder pitch and elbow pitch. The
29

shoulder yaw joint axis, located at the manipulator base, is normal to the shoulder joint pitch axis. Since the shoulder pitch joint and elbow joint axes are parallel, the shoulder pitch/elbow section is identical to the 2-link manipulator. The 3-link manipulator is shown in Figure 3.1.3.
/
Figure 3.1.3: 3-link anthropomorphic manipulator
The reference frame, frame (0), is affixed to the base. Frame{ 1 } is attached to the shoulder yaw joint and aligns with the reference frame when the joint angle is zero. Frame
(2) is attached to the shoulder pitch joint. Frame (3), attached to the elbow joint, aligns with frame 2) when the elbow angle is zero. The tip frame, frame (4) is located at the end of the elbow link. The frame assignments for the 3-link manipulator are shown in Figure
3.1.4
30

YT
A
A
~
S A
y I
A
Y
A
X
1
X
2 x
X
3
A
XT
Figure 3.1.4: Frame assignments for 3-link arm
31

3.1.2.1. Forward Kinematics
The frame transformations for the 3-link anthropomorphic arm are:
Cl -SI 0 O o
T
= sl ci 0 0
T 0 0 1 0
0 0 0 1 s2 C
2
0 0
'T=[0
2 C2 -s2 0 Li
0 0 0 0
C3 -S3 0 L2
2T S3 C3 0 0
0 0 0 1
1 0 L3
0100
00
1
0
001
1
Multiplying these matrices together, produces the desired forward kinematics:
(3.12)
C
1
S
23
CIC23 -S1 L
2
C
1
S
2
+ L
3 c
1 2 3
OT
SlS23 SIS23 cl L2ss2 + L3SIS23 i23 -s23 0 L1 + L22 + L323
0 0 0 1
(3.13a)
The kinematic equations relating the joint angles to the tip location, referenced to frame (0), are contained in column 4 of (3.13a): x = L
2 c
1 s
2
+ L
3
C
1
S
23
y = L
2 s
1 s
2
+ L
1
S
23 z = L
1
+ L
2 c
2
+ L
3
C
23
(3.13b)
3.1.2.2. Inverse Kinematics
Since the 3-link anthropomorphic manipulator is essentially the 2-link planar arm augmented with a revolute base joint, the inverse kinematic mapping is easy to obtain.
First, use the specified x, y tip position (in frame 0)) with the two argument arc-tangent to calculate the shoulder yaw angle. Next, rewrite the specified Cartesian tip position in cylindrical coordinates, accounting for the base to shoulder pitch joint separation distance.
32

Finally, apply the 2-link arm solution using the cylindrical coordinates. The complete inverse kinematic solution is given below:
01 = Atan2(x, y)
R= x 2 + y
(3.14)
(315)
02 = Atan2(R, H) - Atan2(K
2
,K
1
)
03 = Atan2(s3, c3)
(3.16) where: c3
=
R2 + H2 _ L2
2
- L32
2L
2
L
3
(3.17) s3 =+_ 1 -(cos 03
2
(3.18)
(3.19) K
K
1
2
= L
2
= L
3
+L s
3
3 3
Equations (3.14) to (3.19), of course, are subject to the same constraints on the 2-link solution given in section 3.1.1.2. As a result, only the shoulder yaw angle has a unique solution.
The control problem for serial-link manipulators is an inherently nonlinear one.
Since a serial-link manipulator is a chain of rigid bodies, mass and inertia parameters are dependent on the manipulator configuration and are therefore time varying. Additionally, actuator non-linearities such as friction contribute to the difficulty of accurately modeling a manipulator system. Model based controllers, therefore, must compensate for changing manipulator characteristics by providing some form of adaptive or non-linear control.
System linearization may be used to derive locally linear models if nonlinearities are not a significant factor about an operating point. This approach has limited usefulness, however, since it requires a changing linearized model as the manipulator moves from point to point.
For a manipulator operating in neutral buoyancy, modeling of the system is further complicated. Water forces (e.g. drag, damping and turbulence) are highly non-linear and strongly dependent on the velocity of moving components. As a result, it is even more difficult to derive a system model upon which to base a controller. Non-linear methods
33

such as sliding-surface offer the potential to alleviate this problem since such techniques are able to produce extremely robust controllers.
The following sections describe several methods for controlling serial-link manipulators. Specifically, techniques for position and velocity control of the end-effector are detailed. Sections 3.2.1 to 3.2.4 present joint-based controllers, in which controller errors are represented in joint-space. Such controllers are fairly easy to implement and are found on a vast number of current commercial systems. The final section (3.2.5) describes
a Cartesian-based controller which maps controller errors in Cariesian space rather than joint space.
It should be noted that in all of these methods the manipulator is controlled with simple, error-driven controllers. Furthermore, each joint of the manipulator is operated independently without regard to the other joints by a localized servo controller. A serious deficiency of this methodology is that no attempt is made to derive and utilize a system model. At first glance, such an approach would appear to be a poor choice since it is impossible to guarantee optimal, or even fair, performance of the arm in all configurations.
However, since derivation of a model structure is problematic and because determination of model parameters (e.g. inertia moments, center of mass, etc.) is difficult, the benefits offered by model-based control may be few. Moreover, such controllers are likely to be computationally intensive, requiring fairly powerful computer power. On the other hand, the individual joint approach based on simple control laws requires few calculations so that low computational power will suffice.
3.2.1. Open-Loop Position
In this control scheme, the manipulator tip is controlled open-loop since there is no direct feedback of tip position. As a result, this method has limited appeal for direct tip positioning control. During operation of the manipulator, joint position commands are fed directly on a joint-by-joint basis to position servocontrollers, which receive joint position feedback. This is illustrated by block diagram in Figure 3.2.1. The resulting tip location may be determined by applying manipulator forward kinematics to the joint positions.
I
Figure 3.2.1: Open-Loop Position Control
34

For a human operator, this control scheme is feasible if the proper user interface is chosen. With an anthropometric manipulator, for example, one possible approach is to utilize similarity between a scaled model and the controlled arm. By controlling the tip of the scaled, master arm, inverse kinematics are implicitly performed and provide joint position commands for the slave manipulator. This technique has been used extensively for teleoperation tasks in the nuclear industry as well as for structural assembly research in the
SSL.
Moreover, it is possible to "teach" a manipulator how to perform a specific task.
This is accomplished by first having a human operator guiding (i.e. operating) the manipulator through a desired set of motions and sequentially storing sets of joint positions. Later, a sequencer plays back the series of joint sets, effectively commanding the manipulator to duplicate human actions. The primary application of teaching by showing is for programming a manipulator to perform repetitive tasks, reducing human operator workload.
3.2.2. Open-Loop Resolved Motion Rate
A more useful tip control scheme than open-loop position is referred to as resolved
rate or resolved motion rate control and is attributed to D.E. Whitney. In resolved rate control, given desired manipulator tip velocities, joint rates are determined which will cause the manipulator tip to move at the desired velocities. One common approach is to utilize the inverse Jacobian mapping to resolve Cartesian velocities into joint rates:
Od = (J)- Xd (3.20) where the leading, superscripted zero indicates terms written with respect to the base frame.
However, since the Jacobian is dependent on manipulator configuration, it is possible for it to become singular. In this case, the inverse Jacobian does not exist, and a determination of joint rates via (3.20) is not possible. Furthermore, as the manipulator approaches a singular configuration, the denominator of (3.20) tends towards zero and may result in excessively large joint velocities.
During resolved rate control the operator, in essence, "flies" the tip of the manipulator. Cartesian tip velocity commands are passed through a rate resolver to joint rate servos. The controller is shown schematically in Figure 3.2.2. Since there is no explicit feedback of tip position, tip control is technically in an open-loop sense. However, resolved motion rate control allows the operator to directly control the tip velocity in a
35

Cartesian sense. This is a significant advantage over open-loop position control since manipulator operation is more intuitive and places fewer demands on a human operator.
)
Figure 3.2.2: Resolved Motion Rate Control
An alternative to Jacobian-based resolved rate control is joint space differencing. In this technique, given a planned path of desired Cartesian tip states, X = f(t), joint positions are found by applying manipulator inverse kinematics. Joint rates are then determined by differencing of joint positions and are passed to the joint rate servos. This approach is perhaps easier to implement since fewer calculations are required than computing the inverse Jacobian. Differencing effects, however, warrant careful consideration (i.e.
causality, sampling rate, noise, etc.) It should be noted that multiple solutions and singularities generated by inverse kinematics are also problems.
The simplest closed-loop scheme focuses on feedback of tip position. Desired
Cartesian manipulator location, typically tip position with respect to the base frame, are converted to joint positions via inverse-kinematics. These positions are then directed to joint position servos. Since the servos operate on joint position, control errors are reflected in joint-space. This system operates in a closed-loop sense since tip position, transformed into joint positions by inverse-kinematics, is reflected in the joint-space controller error.
Figure 3.2.3 shows a block diagram of closed-loop position control.
1b.
Figure 3.2.3: Closed-loop Position Control
In practice, this control scheme is generally augmented with a path planning module
(either Cartesian or joint-space) which generates trajectories between specified endpoints or from symbolic specifications. A path planner is necessitated by several concerns including
36

singularity handling, smoothness of trajectory (i.e. continuous first and second derivatives), and obstacle avoidance. The addition of a trajectory generator, however, dramatically increases computation demands on the manipulator controller and is not always feasible for real-time operations. The augmented closed-loop controller is shown below in Figure 3.2.4.
Figure 3.2.4: Augmented Closed-Loop Position Control
3.2.4. Closed-Loop Tip Control
Although the closed-loop controller described in the previous section has some usefulness, it cannot be used to explicitly control tip velocity. The only means of specifying velocities to this controller is through the augmented path planner (i.e. velocity transformed into trajectory positions). This approach is suboptimal, however, since the path planner must produce joint position commands closely spaced in time to achieve any degree of velocity precision. Moreover, there is no direct tracking of velocity error since the controller operates solely on joint position.
The preferred means of tip position and velocity control is to implement a multipleinput, multiple-output (MIMO) controller. In this scheme, desired cartesian position and velocities are resolved into joint angles and rates which are transformed into joint commands via some type of state-space control law structure. Transformation of position to joint angle is usually performed with inverse kinematics, while resolution of velocity to joint rate is accomplished by the inverse Jacobian. Since the controller is based in statespace, there is a vast assortment of possible control structure (e.g. pole-placement,
LQRLQG, etc.). Depending on the choice of control law, the low-level joint controller may be either a position or a velocity servo, though the latter is more common. A block diagram of this controller is shown in Figure 3.2.5.
Figure 3.2.5: Closed-loop Tip Controller
37

As the figure shows, tip position and velocity errors are reflected in joint-space, with the
MIMO controller inside the feedback loop.
The tip control schemes described in previous sections (3.2.2 to 3.2.4) operate on errors described in joint-space. Since operator commands are generally given in Cartesian space, all of these methods require conversion to compute joint-space parameters. The primary difficulty with this approach is that the conversion process is computationally expensive (e.g. inversion of the Jacobian and its derivatives), particularly if higher order path derivatives are specified. In practice, typical current systems only transform position commands to joint angles. Velocity, and any other higher derivative, is then computed using differencing techniques. Differencing, however, may introduce undesirable sideeffects such as lag and noise amplification. (Craig, 1986). Since commanding higher order derivatives (e.g. acceleration, jerk, etc.) is desirable, the problem is to suggest an alternative to joint-based control which requires fewer computations to obtain the required derivatives.
One approach to manipulator control which offers a potential solution is described in (Craig, 1986) as the Inverse Jacobian controller. In this scheme, controller errors are mapped to Cartesian space by introducing coordinate transformations directly into the servo loop. Cartesian errors (presumed to be small) may be mapped to joint-space displacements using the inverse Jacobian. These displacements are then converted to actuator commands which reduce the Cartesian errors. The structure of this control scheme is shown in Figure
3.2.6.
Figure 3.2.6: Inverse-Jacobian Controller.

3.3.
In order to realize the serial-link manipulators described in section 3.1 in a neutral buoyancy environment, it was necessary to create a revolute joint for underwater operation.
To implement the controllers detailed in section 3.2, it was additionally necessary to devise joint position and rate servocontrollers. Details of the development process and final design for both are given in the following.
3.3.1. Development of Neutral Buoyancy Actuators
The underwater setting associated with neutral buoyancy simulation is an extremely challenging environment for actuator design. Among the difficulties that must be considered in the design of such devices are corrosion, lubrication, and the electrical conductivity of water. The situation is further complicated when humans are introduced to the scene since consideration must be made for confinement of contaminants and safety factors. Moreover, since the baseline specifications for SPAM called for a high-torque revolute joint and a high-force linear actuator, it was mandated that any actuator design be capable of high power output. Taken collectively, these factors meant that the development of actuators for SPAM was not a trivial task.
Three fundamental criteria were selected to drive the actuator design. First, to minimize the deleterious effects of water, moving components and linkages were desired to be as mechanically simple as possible. Secondly, the means used to power the actuator had to be safe to submerged humans. Finally, the actuator was specified to be as cost-effective as possible.
To fulfill these requirements, a substantial research effort was made to determine the viability of various actuation schemes. Among the methods rejected after evaluation were electrical torque motors with gearing, pneumatically driven motors, and hydraulics.
The first approach, electrical torque motor with gearing, was abandoned because of potential high voltage/currents and due to the gear lubrication problems. Pneumatically driven motors, though offering high torque at a low cost, had to be rejected since the required lubricated air supply presented a potential contaminant problem. Finally, hydraulics involving oil was dismissed since absolute prevention of oil leakage and spillage is extremely troublesome.
After rejecting traditional actuation methods, research was focused on novel approaches to actuator design. One such approach is the "water over air" cylinder. In this scheme, compressed air is used to supply actuating force and water, assumed to be incompressible, is used for braking and control. Since compressed air is clean, and because
39

water is readily available in neutral buoyancy, it was decided to pursue development of a high-powered actuator using this concept.
efforts. The PHAD, shown schematically in Figure 3.3.1, is a parallel arrangement of three cylinders, two pneumatic and one hydraulic. Air and water flow control is provided by solenoid valves. The air cylinders and solenoid valves are sized to meet force and supply demands. The hydraulic cylinder and solenoids are chosen according to braking and control considerations. Three cylinders were used in the PHAD design to guarantee balanced applied and braking forces.
Cylinder
Water
Solenoid
Valve
Soleno
Valve
Figure 3.3.1: Pneumatic and Hydraulic Actuating Device (PHAD)
(schematic)
During PHAD operation, compressed air is supplied to one side of the pneumatic cylinders. Since the hydraulic cylinder is sealed and contains an incompressible fluid (i.e.
water), the PHAD pistons remain in a static position. Opening the water solenoid valves allows water flow, and hence, the pistons move. Moreover, if the period the water solenoids are open is regulated by some method (e.g. pulse-width modulation), precise linear actuation is possible. To illustrate this, consider the PHAD depicted in Figure 3.3.1.
Suppling air to the left side of the air cylinders drives the pistons to the right, extending the piston rods. Controlling the water solenoids, and hence water flow through the hydraulic cylinder, regulates the piston rod extension speed. It should be noted that because the water
40

solenoids are used as ON/OFF switches, and do not actually regulate flow volume, the
PHAD is essentially a linear stepper.
For all of the PHAD implementations, compressed air is supplied to the pneumatic cylinders from a first-stage scuba regulator mounted on a 72 cu. ft. air tank. The regulator used, Scubapro model MK100, delivers 125-140 p.s.i. high-pressure air depending on ambient pressure and flow rate demand. Air flow control is provided by Koganei 110-4E1-
F11 solenoid valves equipped with a 12 VDC coil. The supply of water is obtained directly from the surrounding environment. Laketown or KIP solenoids are used to control the intake and output flow of water from the hydraulic cylinders. The choice of Laketown or
KIP solenoids is implementation specific and is dependent on hydraulic braking force considerations.
Three implementations of the PHAD concept were constructed. First, a revolute variant was developed to provide the in-line pitching required by the serial-link manipulator shoulder and elbow pitch joints. Since the PHAD is a linear device, it was necessary to employ a 5-bar linkage to convert motion from translation to rotation. This variant is described in section 3.3.2. Secondly, a different revolute variant was designed to provide the rotation required by the manipulator base-mounted shoulder yaw joint. For this variation, 2escribed in section 3.3.3, a 2-bar pivot was used. Finally, a linear PHAD was constructed for actuation of the Stewart Platform. This implementation is discussed in detail in section 4.3.1.
To provide the pitching motion required by the SPAM manipulator shoulder pitch and elbow joints it is necessary to convert PHAD linear motion to rotation. Of the many potential means of performing this conversion, gearing and closed-chain linkages were studied. Gearing, using a toothed rack and gear system, is highly desirable since it produces constant rotation for constant linear motion and constant torque for constant linear force. Unfortunately, several problems (e.g. underwater lubrication, required gearing ratio, mounting location) made implementation unfeasible. Closed-chain linkages, on the other hand, are extremely simple mechanical devices and do not have these intrinsic difficulties.
The disadvantage is that all closed-chain linkages have a non-linear relationship between linear and rotational motion. The logistical simplicity for implementation, however, resulted in a decision to utilize a closed-chain linkage with the PHAD, regardless of non-linearities.
As a result, a diagonally-driven 5-bar linkage was used to convert PHAD linear motion to rotation. The 5-bar linkage was chosen since it is has few links, provides good
41

torque to force ratios, and is a compact spatial arrangement. As shown in Figure 3.3.2, the linkage is symmetrical with two upper link members and two lower link members joined by the diagonal drive.
upp pivot
L
I
Figure 3.3.2: Diagonally-driven 5-bar linkage
In this configuration, extension of the center (drive) bar diagonally drives the linkage, causing the link bars to rotate about four pivot points. The motion is illustrated below in Figure 3.3.3
.4
Figure 3.3.3: 5-bar linkage motion with diagonal drive left to right - increasing drive bar extension
The extension of the diagonal drive member, L, is related to ~, the linkage halfangle at the lower pivot point, by:
42

cos ~ =
D 2 + L 2
2D
- C 2
(3.21) where C and D are lengths of the upper and lower pivot to linkage point link members respectively.
Force input through the diagonal drive, F, is converted to torque, r, about the lower pivot point by:
T= CLDsina
F C 2 +L 2 _D 2
(3.22) where a is the angle between upper and lower link members.
For the design of the PHAD 5-bar linkage, it was assumed that the range of motion for the diagonal drive was 12 inches. This corresponds to the largest stroke length available for small, cost-efficient pneumatic cylinders. Sizing of the link members was performed by studying rotational range and torque/force output as a function of drive member length. In order to utilize as much of the drive member range as possible, the upper and lower link bars were constrained to always sum to 12 inches. Characteristic curves for various link members lengths are shown below in Figures 3.3.4 (a-c):
12
10
-8
W 4
'C.
0
0
.
r
20 40
Drive extension - Torque/Force
60 80 100
Angle (degrees)
I
.4
&
I .
0.6
0.4
0.2
120 140 160 180
0
1.4
1.2
1
0.8
I-
5
Figure 3.3.4 (a): Characteristic curve of 5-bar linkage

-
_ _
Drive extension - Torque/Frce j
12 0.5
0.3 w
0.2
0.1 E
0
0 20 40 60 80 100 120 140 160 180
0
Angle (degrees)
Figure 3.3.4 (b): Characteristic curve of 5-bar linkage
(C = 6.00", D = 6.00")
- Drive extension - Torque/Force
JL
1')
0.5
10
0.42
8
.g
6
°rll
4
2
0
0 20 40 60 80 100 120 140 160 180
0
Angle (degrees)
Figure 3.3.4 (c): Characteristic curve of 5-bar linkage
(C = 625",D = 5.75")
0.3
0
0.2
0.1 0
44

As a result of these studies, symmetrical 6 inch links were chosen for the nominal
5-bar linkage design. The characteristic curve is shown above in Figure 3.3.4 (b). The motivating factor for selecting these link sizes was that both the drive extension-to-link angle and the input force-to-output torque curves were smooth, monotonic, functions over the full drive member range. Moreover, the theoretical rotational range covered a full 180
° .
PHAD cylinder sizing was governed initially by an attempt to meet the baseline torque specification. For most of its rotational range, the 5-bar linkage offers a torque-toforce ratio of 0.167 or better, indicating that at a minimum 4,500 lbs. of force is needed to generate 750 ft-lb of torque. The scuba compressed air supply will deliver at least 125 p.s.i., so that 36 square inches of pneumatic cylinder bore area is required. Discussions with cylinder manufacturers revealed that 2 inch bore cylinders had the best costeffectiveness and logistics, as well as being readily obtainable. This meant, however, that a total of twelve, 2 inch bore, cylinders would be needed to provide the required bore area.
Since this number of cylinders would have been exceedingly difficult to integrate, a decision was made to forgo the torque specifications in favor of joint compactness. Sizing of hydraulic cylinders was performed in a similar manner, with the emphasis placed on producing 4,500 lbs. of braking force.
The final design of the revolute PHAD (R-PHAD-A) for in-line pitching utilizes 4
Clippard UDR-32-12 pneumatic cylinders and 2 Aurora SS-3 hydraulic cylinders. Each of these cylinders has a 2 inch bore with a 12 inch stroke. The Clippard cylinders, driven by
125 p.s.i. air, produce a total force of 1,570 lbs corresponding to a minimum joint torque of 262 ft-lbs. The Aurora cylinders are equipped with hydraulic piston and shaft seals and are capable of 2,000 lbs. maximum breaking force. Laketown solenoids were chosen for control water flow because of flow rate capability and pressure rating. A schematic of the
R-PHAD-A is shown in Figure 3.3.5. Detailed drawings are included in Appendix B.
There are a few items of note in the figure. First, the right view clearly illustrates the integrated five-bar, diagonally driven linkage. Secondly, the four Laketown solenoids are directly mounted on the Aurora cylinders. This allows instantaneous water flow control during joint operation. Finally, the joint/arm boom interface (labeled as "Joint Collar") is shown. This connector is described in section 3.4.2.
45

S-.
3
(a)
Laketown solenoid valhV
1 a oder rzzr
::Sr 555'5; j"`'-::::::i':::::'
55·:
2·555t s
"': ztt j i:
1
;-- t··;;r i rs·
,,
-,,
:s:-
·
/
I
)R-32-12
Cylinder s ss·
2S
X
.
U
:wi::: i··.
sS r·
(b)
Figure 3.3.5: Revolute PHAD-A
(a) schematic (b) assembled R-PHAD-A
46

Submerged, the R-PHAD-A joint weighs approximately forty pounds. To simulate zero-gravity, foam and fiberglass flotation panels were installed to help make the joint neutrally buoyant. The resulting joint is shown below:
Figure 3.3.6: Neutrally-buoyant R-PHAD-A
3.3.3. Revolute PHAD-B
The SPAM manipulator arm shoulder yaw joint is mounted at the base of the system. This base is intended to be mounted on a variety of surfaces such as a worksite platform, a STS payload bay mockup, and on telerobots. Additionally, the joint rotation axis is located normal to the link axis since the joint provides yaw motion. Considering these factors, the revolute PHAD design described in the previous section could not easily be used for this joint. As a result, it was necessary to design a different rotational PHAD implementation. The approach taken, however, attempted to utilize as much of the previous design as possible. Therefore, the same number and type of cylinders and solenoid valve used on the R-PHAD-A were targeted for use in the R-PHAD-B design. Similarly, a closed-chain linkage would be employed instead of gearing.
Since the R-PHAD-B joint had to provide yawing about the link axis rather than pitching through (as the R-PHAD-A does), a two-bar crank was chosen to convert linear motion to rotary motion. The crank configuration, shown in Figure 3.3.7, utilizes a cylinder piston rod as the drive member.
47

Figure 3.3.7: Pivoting 2-bar crank
For this closed-chain linkage, extension of the drive cylinder piston rod rotates the link bar about the pivot point. This motion is illustrated below in Figure 3.3.8
Figure 3.3.8: 2-bar cranking motion
top to bottom-increasing drive bar extension

The rotation produced by the 2-bar crank is related to the drive extension, D, by the following:
A 2 + B 2 _ C 2 -D 2
2AB
(3.23) where A is the cylinder mount to joint axis distance, B is the length of the link bar, and C is the length of the drive cylinder.
Force applied through the drive rod is converted to torque, r, through the link bar.
The torque-to-force ratio is:
- = BsinO
F
(3.24) where 0 is the exterior drive-to-link bar angle.
Characteristic curves of joint rotation and torque-to-force are presented below in
Figures 3.3.9 (a) to (c) for different actuator mount to joint axis and link bar lengths.
12 g
1 11
10
8
.
7
6 x c
3
2
1
0
Drive Extension Torque/Force
0.1
20 40 60 80 100
120 140 160 180
0
Figure 3.3.9 (a): Characteristic curve of
(A = 25, B =6)
2-bar crank
0.5
0.4
0.3
0.2l
49

12
1
0
3
2
11
10
9
8
7
6
5
4
0
-Drive Extension Torque/Force
0.6
0.5 =
0.4
20 40
Figure 3.3.9 (b):
60 80 100 120 140 160 180
0
Angie (degrees)
Characteristic curve
(A = 24, B =6) of 2-bar crank
0.3 o
0.2
=
O
0.1
-Drive Extension Torque/Force
C
C
el x a s
St
12
11
10
9
8
7
6
5
4
0
1
3
2
0 20 40
Figure 3.3.9 (c):
60 80 100 120 140 160 180
0
Characteristic curve
(A = 25, B =7) of 2-bar crank
0.6
0.5
0.4
0.3
0.2 =
0
50

The curves shown in Figure 3.3.9 (b) resulted in 2-bar crank linkage lengths of A=24 and
B=6 inches. Although Figures 3.3.9 (a) and (c) demonstrate higher average and peak torque output, the angular range is smaller than that of Figure 3.3.9 (c). Using the lengths from Figure 3.3.9 (b) gives a smooth torque curve over a theoretical 180 degrees.
Due to the yawing motion produced by the 2-bar crank, it was necessary to include a bearing in the R-PHAD-B design. Off-the-shelf bearings, however, could not be used because of lubrication and corrosion problems inherent with a water environment.
Moreover, since the bearing is mounted along the arm link axis, it had to be capable of carrying large loads. For a base-to-tip distance of 50 feet (similar to the SRMS) with a maximum dynamic tip load of 50 lbs., the approximate bearing loading is 50 lbs axial and
2,500 lbs radial.
The final R-PHAD-B design (Figure 3.3.10) utilizes a metallic-plug type bearing custom manufactured by the Spadone-Alfa Corp. This bearing contains a pattern of solidlubricant filled plugs covering the load carrying surfaces. The solid-lubricant used is
Metaline, a dry lubricant composed primarily of metallic oxides and graphite, which provides bearing lubrication in hostile environments including chlorinated water. Design drawings of the R-PHAD-B are given in Appendix B.
Cylip
'late
Cylinder Mount Piston Mou*
: J
/Block
Clippard UDR-32-12\
/ \
Aurora SS-3
Pnewnatic Cylinder Hydraulic Cylinder
Figure 3.3.10: R-PHAD-B schematic
Joint
.C olar sline ing
Base
Flange
51

To provide angular information from each joint, an optical encoder (Sumtak LEI-
037-2048) was waterproofed and mounted on each R-PHAD. Since this encoder is manufactured with "O"-ring casing and shaft seals, waterproofing involved simply the attachment of a low-pressure air line.
The Sumtak LEI-037-2048, produces 2048 pulses per revolution of quadrature output. Since the R-PHAD designs have a theoretical range of 180 degrees (0.5
revolutions), angular position covers a 12-bit range:
(2048 revolution pulse (3.251
.,
= 212 bits
The design of the R-PHAD-A prevented mounting of the optical encoder directly along the joint pivot axis. Instead, the encoder was mounted at the 5-bar linkage link bar pivot point as shown in Figure 3.3.11 and a trigonometric transformation used to derive joint angle from measured pivot angle.
upper pivot
_ _ n
0
Figure 3.3.11: R-PHAD-A Optical Encoder Mounting
Optical
Encoder
52

The transformation used is:
0 = r- 2tan[ Dsin ]
LC-Dcos
(3.26) where C and D are the lengths of the upper and lower link bars, and ~ is the angle between these bars measured by the optical encoder.
3.3.5.
The controllers discussed in this section provide the lowest level of control for the
SPAM manipulator arm. Since the control schemes attempt to minimize errors between commanded and actual joint states (i.e. angle and angular velocity), the controllers may be classified as servocontrollers. In particular, the following sections describe design and testing of simple discrete-time controllers; section 3.3.5.1 gives details of a proportionalplus-derivative position servo and section 3.3.5.2 lists a number of velocity servo schemes.
All of the servo schemes were tested with a R-PHAD-A joint using an IBM microcomputer. The controllers were implemented in software with the Microsoft C v5.1
optimizing compiler. A complete C code listing is provided in Appendix C. Joint position was obtained using the optical encoder described in section 3.3.4 via a Hewlett-Packard
HCTL-2000 quadrature decoder/counter. Joint rates were inferred from three step backwards differencing. All servo outputs were transformed into PHAD solenoid control signals via two methods. The Koganei air solenoids were sent binary signals specifying on/off air flow. The Laketown water solenoids received 4-bit pulse width modulated
(PWM) signals to control water flow rate.
Testing revealed that the Laketown solenoids used on the R-PHAD-A cannot be driven faster than 9 Hz. with a 4-bit PWM. Consequently, the servos described in the following sections were run at a 9 Hz. control loop rate.
3.3.5.1. Position Servo Design & Testing
Position servocontrollers have limited applicability to manipulator arms. This is not to say that position servos are not used, in fact most industrial robots utilize such controllers, simply that velocity servos have a wider range of usefulness for manipulator control schemes (see Section 3.2). Since overshoot of joint angle may place the arm in a singular configuration or cause collision with some obstacle, most position servos are
53

critically damped or overdamped. Consequently, these servos generally have long response times and poor overall response, though this typically is not a problem.
As was discussed in Section 3.2, the non-linearities inherent with manipulators and an underwater environment make accurate modelling a difficult task. Although non-linear model-based control has reasonable potential, model-based control in the linear sense is certainly of dubious merit. This does not mean, however, that linear control laws cannot be applied to SPAM joint control. In fact, if one considers that position servos need to be heavily damped, that slow response time is not problematic, and that an underwater environment tends to quickly damp out high frequency effects, then it is indeed feasible to attempt some form of linear control in the absence of system modelling. To this end a linear position servo, specifically proportional-plus-derivative (P-D), was been implemented for
SPAM joint position control.
The classical P-D controller is classified as having a phase-lead structure since it attempts to improve system stability and response by increasing the phase-lead angle.
Although the P-D does not have the steady-state accuracy of either a proportional-plusintegral (P-I) or proportional-plus-integral-plus-derivative (P-I-D) controller, it tends to produce better time response characteristics than purely proportional (P) control.
Additionally, from a digital perspective, a P-D controller is only slightly harder to implement than a P controller, and much less computationally expensive than a P-I-D.
The "textbook" P-D controller is expressed in continuous-time Laplace form as:
Gas) = U(S)
E(s)
(3.27) where U(s) is the Laplace transformed controller output and E(s) the Laplace transformed error signal. This may be expressed in the discrete-time domain by applying a backwardsdifference transformation: s = Z
- 1
(3.28) where T is the sampling period. This results in:
Gz) =
+ K (3.29)
Z-transforming results in the difference equation for control:
54

Uk = Kek + Tek - ek-1)
=
+ k-
2ek-l
(3.30)
For the joint position servo, the error signal is derived by minimizing differences between commanded angle and actual angle, so the P-D control law is:
Uk = Kl(Od-)k - K2(d-)k- I (3.31)
A block diagram of the complete P-D joint position servo is given in Figure 3.3.12:
Figure 3.3.12: P-D Joint Position Servo
Testing of the position servocontroller was performed in neutral-buoyancy using a
R-PHAD-A joint. Six foot arm booms were attached to either side of the joint, and the assembly vertically mounted by attaching one of the booms to a floor mount. To simulate loaded operation, a ten pound weight was placed at the tip of the moving arm boom. Step testing was performed by commanding the joint to move from zero to 90 degrees. Testing results for two sets of P-D gains are shown in Figure 3.3.13.
55

1.2
1.0
0.8
0.6
0.4
0.2
0.0
_-
0
O angle (unloaded)
+ angle (loaded)
* PWM Duty Cycle
2 4 6 time (seconds)
8 10 12
Figure 3.3.13
(a): P-D Position Servo (Kp = 1.0, Kd = 0.1)
90 degree step response (nonnalized)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
,
.~~~~~~~~~~~~~~~~~~~~~~~~~~
AD~~
--
O angle (unloaded)
+ angle (loaded)
* PWM Duty Cycle
2 4 6 time (seconds)
8 10
Figure 3.3.13 (b): P-D Position Servo (Kp = 2.0, Kd = 0.1)
90 degree step response (normalzed)
56

As the figures show, the P-D servo produces a smooth response to the step input.
For much of the step, the joint position changes linearly with time in response to the saturated actuator command. Near the desired angle, the position curve is nicely overdamped as a result of the low P-D gains and water damping effects.
3.3.5.2. Velocity Servo Design & Testing
The design of a joint angular velocity servo followed an approach similar to that of the position servo previously described. The fundamental assumption made was that the damping characteristic of an underwater environment tends to smooth response and maintain stability by limiting the system bandwidth to very low frequencies. In the absence of system modelling, therefore, velocity servos using simple control laws and/or heuristics would be sufficient to provide adequate joint control.
The first approach to velocity servo design was the Basic Linear Actuator Heuristic
(BLAH) controller. This controller utilized the simple heuristic:
If the joint is not moving at the desired rate, increment or decrement the actuator control signal by a fixed quantity.
The rationale for this heuristic is that at the lowest control level, the control signal output to the PHAD solenoids is coarsely discretized (a 4-bit PWM signal). If the controller and
PWM generator can operate at a higher frequency than the water damped system, therefore, it should be possible to regulate joint velocity simply by flipping PWM bits. One control law formulation is then:
Uk = Uk-1 + Sg4(0d- .)k] (3.32) where "sgn" is the sign of the error term. Figure 3.3.14 shows a block diagram of the complete BLAH controller.
ad
MAEc
1%
-
E(z) i _r
-- l
------ I
-r' I --
,\
U(z) I I
JLII V-I X
I _-.. I
Figure 3.3.14:
BLAH Controller Logic
57

In practice, however, the controller bandwidth is limited by the response time of the pulse-width modulated solenoids. Since the Laketown solenoids restrict the control loop to
9 Hz. sampling, the BLAH controller bandwidth is on the same order as the physical system. As a result, the controller exhibits large overshoot and severe chattering. Step response of the unloaded joint, for a 1 deg/sec command, is shown in Figure 3.3.15:
' velocity (unloaded)
PWM Duty Cycle
3
2
5
4
1
0
0 5 10 15 time (seconds)
Figure 3.3.15: BLAH Velocity Servo
1 deg/sec step response (normalized)
20 25
The second velocity servo was designed to be a simple proportional controller.
Error, defined as the difference between commanded and actual velocities, is multiplied by a proportional gain and combined with the current control signal. The effect of this is to drive the control output to a setpoint and produce the commanded velocity. The control law expressed as a difference equation is:
Uk = Kp(Od- ) + Uk-I (3.33)
Figure 3.3.16 shows a block diagram of the complete proportional velocity error servocontroller.
58

Figure 3.3.16: Proportional Velocity Servo
Step testing revealed that the proportional velocity error controller has better command tracking characteristics than the BLAH controller. Response time, however, is a bit slow taking approximately 25 sampling intervals. Additionally, overshoot is very high; on the order of 1,000 percent for the unloaded joint and 600 percent with ten pounds loading. Step responses (1 deg/sec step) of this controller, for both unloaded and loaded operation, are shown below in Figure 3.3.17.
velocity (unloaded)
PWM Duty Cycle
3
2
5
4
1
0
0 2 4 6 time (seconds)
8 10
Figure 3.3.17 (a): P Velocity Servo (Kp = 1.0)
1 deg/sec step response (normalized), unloaded operation
12
59

velocity (loaded)
PWM Duty Cycle
6
5
4
3
2
1
0
0 2 4 6 time (seconds)
8
Figure 3.3.17 (b): P Velocity Servo (Kp = 1.0)
1 deg/sec step response (normalized), loaded operation
10 12
The P-D velocity servo was the final controller implemented. It was designed as an attempt to improve the transient response characteristics of the P velocity servo by the addition of an error derivative term in the control law. Similar to the P velocity servo, the error to be minimized is defined as the difference between commanded and actual velocities. As expected, the P-D velocity servo has a control law identical to the P-D position servo except for the error term:
Uk K, - K2ek-1
=
- K2('Od-)k
(3.34)
Figure 3.3.18 shows a block diagram of the complete P-D servocontroller.
Figure 3.3.18: Proportional-plus-derivative Velocity Servo
60

Step testing revealed that the P-D controller has the best command tracking characteristics of all three velocity servos. Step responses of this controller are shown below in Figure 3.3.19 (1 deg/sec step) and Figure 3.3.20 (3 deg/sec step).
velocity
PWM Duty Cycle
4
3
2
4
3
1
0
0 2 4 6 8 10 12 time (seconds)
14 16
Figure 3.3.19 (a): P-D Velocity Servo (Kp = 1.0, Kd = 0.1)
1 deg/sec step response (normalized), unloaded operation
18 20
velocity (loaded)
PWM Duty Cycle
2
1
0
0 2 4 6 8 time (seconds)
10 12
Figure 3.3.19 (b) P-D Velocity Servo (Kp = 1.0, Kd = 0.1)
1 deg/sec step response (normalized), loaded operation
14 16
61

velocity (unloaded)
PWM Duty Cycle
4
3
2
1
0
0 2 4 6 time (seconds)
8
Figure 3.3.20 (a): P-D Velocity Servo (Kp = 1.0, Kd = 0.1)
3 deg/sec step response, unloaded operation
10 velocity (loaded) command
2
4
3
1
0
0 2 4 6 time (seconds)
8
Figure 3.3.20 (b): P-D Velocity Servo (Kp = 1.0,
3 deg/sec step response, loaded operation
Kd =0.1)
10
62

As the figures show, the P-D servo performs fairly well. Overshoot is much less than the P servo and response time is better than either of the two servos. A small amount of steady-state error, however, exists in the step responses. This may be attributed to limit cycling inherent in the 4-bit PWM signal.
Comparison of the three velocity servo schemes revealed that the P-D velocity servo exhibits the best performance characteristics. As a result, this controller was chosen to serve as the joint servocontroller for all manipulator control schemes requiring joint velocity control.
3.4.
This section describes the physical hardware of the SPAM manipulator arm. At the time of this writing, the two-link serial arm has been fully assembled and tested. Both arm joints, elbow pitch and shoulder pitch, were implemented using the R-PHAD-A design.
The three-link arm, however, has not been completed due to time constraints and incomplete construction of the shoulder yaw joint (R-PHAD-B design). The following sections detail the design of peripheral joint hardware, modular joint interfaces and manipulator power systems.
3.4.1. Neutrally Buoyant Arm Booms
The arm booms in the SPAM manipulator provide rigid, straight-line connections between adjacent revolute joints. Each boom, independent of length, is neutrally buoyant to meet space simulation requirements. Additionally, the booms contain electrical and pneumatic control circuitry to drive the PHAD joints.
Since the baseline specifications called for joint-to-joint connections of various distances, booms were built in lengths of 6, 12, and 25 feet. Each boom was fabricated using two seamless aluminum tubes (6061-T3) concentrically aligned. The inner tube in this design, which is thin-walled (0.03125") and pressurized, provides the flotation necessary to achieve neutral buoyancy. The outer tube, with a thicker wall (0.125") than the inner tube, provides boom rigidity and strength. A schematic of this configuration is shown below in Figure 3.4.1.

rii- '-
.WL- tt ...
-- II
-3ower tube loat tube
I \ end plug solenoid block tuespport tube support end plug v purge valve
Figure 3.4.1: Arm Boom Tube Configuration
The inner tube (referred to as the "float" tube) is sealed on both ends with a PVC plug and 'O'-rings. The tube contains two Koganei solenoids and electrical hookups for the four Laketown solenoids used by the R-PHAD joints. Pressure and electrical lines are fed through connectors mounted to one of the PVC end plugs. During joint operation, air purged from the R-PHAD cylinders is vented into the float tube via the Koganei solenoids.
Excess pressure is vented through a Plastomatic purge valve mounted in the other end plug.
Photographs of the two PVC end plugs are shown in Figure 3.4.2.
Figure 3.4.2 (a): End plug with Koganei solenoids
64

F11-'Ure
'.4.2 (h): End plug with purge valve
Approximate sizing of float tubes was based on buoyancy calulatlons,, usiln nec densities of air, water. and aluminum listed in Table 3.1. Althouuh each arm N otm houi> idealil have zero net buoyancy, conservative calculations resulted n positivC hLO',!rlncvn
fiLur.es. The resultrlng tux icngth.s and assiociated huovancies are sho, n in Table 3 2.
Air
Water
TabIle 3.
Material
Assumed materinal densities
I
Density (lh/cu in)
0.()()()(4
().()()
Table .2'
Bo(om Size ()uter Tube ft) ( ft
1
_I
--
2I
~ ~~I
Arm Boxrim Paramrters
Inner Tube
( ft )
Net Buo;aric%
( I )
1
1(
2() 14
1i

It should be noted that positive buoyancy was not considered to be a problem for neutral buoyancy operation since compensation is easily achieved with balancing weights.
To facilitate change out of arm booms and reconfiguration of the manipulator arm, the R-PHAD joint and arm boom interface was designed to be modular and uncomplicated.
Since the R-PHAD pneumatic and electric hookup is contained in the arm boom float tube, pressure and electrical lines were designed to utilize simple connector hardware.
Specifically, CPC quick disconnect pressure fittings, Amphenol 165 series connectors, and
ITT Cannon Sure-Seal connectors were used.
Mechanical coupling of the joint and arm boom was constructed as a slide fitting, with the arm boom outer tube sliding over a "joint collar" (shown in Figure 3.4.3). The coupling arrangement is shown in Figure 3.4.4.
,.
Figure 3.4.3: Joint Collar
Joint Collar Arm Boom
Figure 3.4.4: Joint/Arm Tube Interface
66

3.4.3. R-PHAD-A Power System
Each R-PHAD-A joint in the manipulator arm operates with a combination of electrical signals, compressed air, and water flow. Electrical signals generated by the
Electronic Control System (ECS), described in the following section, operate the PHAD solenoid valves. Opening an air solenoid valve supplies compressed air to the PHAD pneumatic cylinders. Toggling the water solenoids provides controlled flow of water (from the surrounding environment) through the PHAD hydraulic cylinders. The resulting PHAD piston rod extension drives the R-PHAD-A 5-bar linkage, producing rotary joint motion.
As discussed in section 3.3.1, the compressed air for the SPAM manipulator arm is supplied from scuba tanks regulated through a Scubapro MK100 first-stage regulator. The
125-140 p.s.i. high pressure air from the regulator is fed from the water surface through the primary supply line (Clippard 1/8" urethane tubing) to the solenoid block end plug contained in each arm boom's float tube. Passing through a bulkhead connector, the compressed air is routed to the two Koganei solenoid supply ports. A secondary line, tapped off the primary supply line, is reduced to +2 lbs. over ambient pressure with a Go,
Inc. regulator. This line is used to pressurize the sensor (optical encoder) on each joint.
When the Koganeis are opened, the high pressure output is channeled through CPC quick disconnect fittings, filling the PHAD air cylinders. Closing the Koganeis allows cylinder to purging, sending the compressed air back through the float tube and out a check valve.
A schematic of the R-PHAD-A power system is provided in Figure 3.4.5:
(over ambient)
Figure 3.4.5: R-PHAD-A Power System
67

3.4.4.
Actuator commands from joint servocontrollers are transformed into electric signals via the SPAM Electronic Control System (ECS). The ECS consists of two primary subsystems, computer input/output (1/O) and power switching. Computer I/O is handled through circuitry installed on a Prototype Expansion Card connected to the IBM PC bus.
Encoder quadrature signals are decoded with HP HCTL-2000 counter/decoder chips.
Solenoid commands, generated from software controllers, are output through an Intel 8255 and 4-bit PWM generator circuit A schematic of this circuitry is given Appendix A.
Power switching circuitry is implemented on the Manipulator Hookup Board
(MHB) shown in Figure 3.4.6. The MHB is wired to the computer I/O board and transforms switching commands from TITL levels to the 12 VDC level expected by R-
PHAD solenoids. The MHB circuitry utilizes TIP-31 and MJ11016 npn-type transistors and is shown schematically in Appendix A. LED's mounted on the MHB chassis provides visual indication of solenoid state.
The complete ECS is shown schematically in Figure 3.4.7.
Figure 3.4.6: Manipulator Hookup Board (MHB)
68

I
I
I
I
I,,
-
I
I
I
I
I
I
I i
I
I
I
I
Ekaronic
System
I l I l to solenoids
Figure 3.4.7: SPAM Electronic Control System (schematic)
69

3.5.
The 2-link manipulator was constructed by assembling two R-PHAD-A joints and two six foot arm booms together. All testing of the manipulator was conducted in neutral buoyancy. To facilitate ease of handling and assembly, the arm was mounted to a vertical support stand. Since the 2-link manipulator is a planar arm, all tip movement was constrained to the X-Z plane of the base frame. Figure 3.5.1 illustrates the vertically mounted 2-link arm with frames. The completed planar arm is shown in Figure 3.5.2.
A
XT
A
X
2
A xo?
A
A
C
1
^IIx
Y2
A
Lo ilk z
Ns base
A
YI veric stan twbase
Figure 3.5.1. 2-link arm frames (vertical test mounting)
YT
70

Figure 3.5.2: SPAM 2-link planar arm
In this configuration, tip commands specified in the base frame (B) must be transformed to the manipulator 0}) frame using the mapping:
0 10 0 1
000 1
3.5.1 Open-Loop Control Testing
Open-loop testing of the arm verified that two R-PHAD-A joints could be operated simultaneously. The forward kinematics mapping was validated by comparing calculated
71

tip position with measured (physical) quantities. Since this method of manipulator control has limited usefulness, open-loop operation was brief.
Closed-loop tip position control testing was performed using the 2-link manipulator inverse kinematics mapping to transform desired tip commands in (base) to joint positions.
P-D servos were used to control the position of each R-PHAD-A joint. For both tests described below, both shoulder and elbow joints started at zero degrees; so that the arm was initially colinear with the (base) Z-axis.
In the first test, the Cartesian tip command of L2, 0, L+LI) was specified.
Geometrically speaking, this tip position corresponds to an elbow angle of 900 and a shoulder angle of 0°:
L2 9 elbow tip
J
A jv,
.. .
.. i
Figure 3.5.2: 2-link arm geometry for L2, O, Lo+L ) command
Execution of this command resulted in the correct joint angles, and hence, the desired tip position was achieved. Figure 3.5.3 shows the action of the P-D joint servos on elbow and shoulder position:
72

elbow shoulder
90
75 to
60
1 -
45
W
W;
C
30
15
0
0
Figure 3.5.3:
2 4 time (seconds)
6 8
Joint angles resulting from (L2, 0, L+L1 ) command
10
For the second test, the Cartesian tip command of L2+0.707Ll, 0, L
0
+0.707L
1
}
.
L
2
+ 0.707L
1
-
I l
\x elbow
J shoulder
1
Ebase
A
7i
Figure 3.5.4: 2-link arm geometry for (L
2
+0.707L
1
, 0, L+0.707L
1
) command
73

From this command, both joints were correctly below in Figure 3.5.5: driven to 45 degrees as shown elbow shoulder
rD,
40
L.
30
U
20
10
0
Figure 3.5.4:
I
2
I
4 time (seconds)
.I
6
Joint angles from (L
2
+0.707L
1
, 0, Lo+0.707L1 } command
8
I
As a result of these tests, it was concluded that the closed-loop tip position control scheme could be operated successfully given tip commands in the reachable workspace.
74

The task of developing the SPAM Stewart Platform component was divided into three phases. In the first phase, research was focused on acquiring knowledge of general
Stewart Platform theory. This involved study of parallel-link chains, kinematics and control schemes. The second phase was concerned with the design of a Stewart Platform to meet baseline design specifications. Geometric design and kinematic modeling for this phase was performed with computer assistance. Finally, the Stewart Platform hardware was designed and constructed. This phase involved joint and linear actuator design, underwater sensor development, and implementation of a microprocessor system.
The Stewart Platform is fundamentally described as a platform mechanism with 6 degrees-of-freedom. It has been suggested for numerous applications including motion based flight simulation, machining, and most recently, robotic manipulation. Though the
Stewart Platform has been the subject of a great deal of analysis and study, the exact origin of the device remains unclear. A survey of literature reveals that the mechanism is most commonly attributed to D. Stewart's paper published by the Institution of Mechanical
Engineers (Stewart, 1965). In this paper, Stewart proposes a platform mechanism for use as a helicopter flight simulator. Stewart's platform, however, is remarkably similiar to at least two other devices: Peterson and Cappel's Hexapod system, which was patented in the
United States in 1965; and Gough's Universal tyre test machine, designed in 1949 and operational in 1954. In fact, the platform mechanism described in this chapter most closely resembles this latter device. The mechanism, however, is referred to as a "Stewart
Platform" to maintain consistency with recent papers.
A common Stewart Platform implementation is shown in Figure 4.1.1. The mechanism is a space truss with an upper and lower plate and six links in an octahedral arrangement. The six mounting points on both plates are arranged in semi-regular hexagons. The Stewart Platform is classified as a six-degree-of-freedom platform
75

mechanism of type 6-SPS, where S and P denote spherical and prismatic joints. (Yang,
D.C.H., and Lee, T.W., 1984).
spherical
base
Figure 4.1.1: Common Stewart Platform Implementation
The Stewart Platform is a parallel-link or closed kinematic chain device. As discussed in section 2.2.1, parallel-link devices offer numerous advantages over serial-link or open kinematic chain devices including higher strength, force capability, and positioning accuracy. There are, however, also several disadvantages inherent in parallel-link mechanisms (Ismail, 1984). Specifically,
· Workspace is restricted because of parallel-links. There is difficulty in reaching around corners and/or into small spaces.
* Maneuverability and range of motion is much smaller than an open kinematic chain, given equivalent amounts of hardware.
* Near singular points, manipulator loading may result in excessive tensile/compressive actuator stresses.
In spite of these difficulties, a Stewart Platform manipulator "would be particularly feasible in applications where dynamic loading is severe and yet the demand on workspace and maneuverability is low" (Yang, D.C.H., and Lee, T.W., 1984).
It is important to note, however, that there is a significant difference in the mathematics between open and closed chain manipulators. For the former, the forward kinematic transform (from joint space to Cartesian space) is straightforward and the inverse kinematics (from Cartesian space to joint space) solution is difficult. In the case of closed
76

chain manipulators, however, the exact converse is true; the forward kinematics transform is difficult and the inverse kinematics transform is straightforward. The difference between the manipulators lies in the degree of solution difficulty. While open chain inverse kinematics involves simultaneous non-linear equations, the problem is frequently solvable in closed-form. Solution of forward kinematics for closed-chain manipulators, however, is a different matter entirely since the mapping is not globally well-behaved and is ill-defined
(Ismail, 1984). As a result, a simple closed-form solution is not possible and numerical methods, discussed in section 4.1.2.2, must be used.
The general Stewart Platform has two bodies connected by six links which may vary in length. The lower body (in whatever coordinate system is used as reference) is called the base and the upper body the platform. The assignment of these names is, of course, completely arbitrary since the system is topologically symmetrical. Each of the six links has one end located in the base and the other end in the platform. Though the location of the six mounting points in either base or platform is not restricted, not all configurations result in controllable mechanisms. In each of the bodies, a coordinate frame is located; {B) denotes the base and {P) the platform. The location of mounting points in each body are then described as vectors to these coordinate frames. Figure 4.1.2 illustrates the general
Stewart Platform (Fichter, 1986).
Figure 4.1.2: General Stewart Platform
77

In practice, Stewart Platforms are not completely arbitrary arrangements, but rather are implemented as geometrically symmetrical mechanisms due to mechanical design constraints. As shown previously in Figure 4.1, the most common configuration uses six links mounted in semi-regular hexagons on two plates. The resulting symmetrical Stewart
Platform appears spatially as an octahedron. Moreover, since the vertices of the semiregular hexagons may be inscribed in a circle:, the geometry of both the base and platform plates can be described using only 4 parameters as shown in Figure 4.1.3. It should be understood that for this paper only this configuration is considered to be of interest and that all subsequent discussion implicitly refers to this particular type of Stewart Platform
YB YP
I i/
\ I win
A,:.e
VY
_
__ -
B6
(a) (b)
Figure 4.1.3: Symmetrical Stewart Platform Geometry
(a) Base Plate, (b) Platform Plate where: r b
= base plate radius rp = platform plate radius ab = base mounting angle ap = platform mounting angle
It is interesting to note that this mechanism configuration is exactly the same as Gough's
Universal Tyre Test Machine. The device presented in Stewart's paper, though similiar, uses a different arrangement of links.
A Stewart Platform with this octahedral arrangement has a large number of internal degrees-of-freedom. Each link contains a prismatic joint with one degree-of-freedom. This
78

linear joint is attached to the base plate with a two degree-of-freedom Universal joint and to the top platform with a three degree-of-freedom spherical joint. This gives six degrees-offreedom per link. Since there are six links connecting the base plate and top platform, the
Stewart Platform has a total of 36 internal degrees-of-freedom. Table 4.1 (Ismail, 1984) presents a summary of these degrees-of-freedom.
Table 4.1: Stewart Platform Internal Degrees-of-Freedom
prismatic
Universal spherical
1
2
3
6
6
6
1 18 total
6
12
18
36 total
The above appears to indicate that the Stewart Platform has an excessive number of degrees-of-freedom. In actuality, the free degrees-of-freedom are sharply limited by the base and platform plate. To demonstrate this, it is worthwhile to conduct a spatial mobility analysis of the joint structure. Grodzinski and M'Ewen's general mechanism degree-offreedom equation has the form: g
F = yn-1)- (6-f) (4.1) where:
F = effective degree-of-freedom of mechanism
A = degree-of-freedom of operational space (6 for spatial motion, 3 for planar)
n = number of members g = number ofjoints f = degrees-of-freedom in joints
The Stewart Platform operates spatially so that A is equal to 6. The base plate and top platform are each single members. Combined with six links, this gives a total of 8 members. If the six prismatic joints are locked in place, we have six Universal and six spherical free joints giving g = 12. Applying (4.1) gives:
79

)+ (62) + (6-3)
PRISMATIC
JOINTS
UNIVERSAL SPHERICAL
JOINTS JOINTS
(4.2)
=0
If the six prismatic joints are free to move we have six additional members, giving n=14.
Applying (4.1) in this case gives:
F=6(14-1)-- (6-1)+ (6-2) + (63)
PRISMATIC
JOINTS
UNIVERSAL SPHERICAL
JOINTS JOINTS
(4.3)
=6
In summation, if the six prismatic joints are locked in a fixed positon, then the Stewart
Platform will be fully constrained to a fixed location and orientation. More importantly though, if the six prismatic joints can be controlled it will be possible to position the
Stewart Platform in a full six degrees-of-freedom.
4.1.2 Kinematics
Due to semantical ambiguity of parallel-link device mappings, it is important to clariif the numencl, ture before discussing kinematic specifics. Many authors, for example, consider the transformation from given Cartesian coordinates to link extensions as forward kinematics since the mapping is well defined. The inverse kinematics problem, therefore, is concerned with the ill-defined task of determining Cartesian frame coordinates given a set of link extensions. This convention parallels serial-link manipulator nomenclature since the forward kinematics are straightforward and the inverse kinematics difficult for those mechanisms. This approach, however, is less than optimal because it makes the naming
(and direction) of mappings device dependent. An alternate approach is to always define forward kinematics as the mapping from joint space to reference coordinate space, and inverse kinematics as the converse. For this paper, this latter nomenclature has been adopted for two reasons. First, the direction of mappings is always well defined. For example, discussion of forward kinematics always implies a transformation from natural manipulator coordinates to imposed reference coordinates. Secondly, and more importantly, it is consistent since the convention operates independent of the device under consideration.
80

In the following two sections, the forward and inverse kinematics of the symmetrical Stewart Platform are presented. Since inverse kinematics is the natural mapping for the Stewart Platform, this transform is presented first. As will be shown, application of inverse kinematics is straightforward and algebraic. The associated forward kinematics mapping is discussed in section 4.1.2.2. Since this transformation is highly non-linear and cannot be solved in closed-form, an iterative numerical solution approach is utilized.
4.1.2.1 Inverse Kinematics
The natural coordinates for a parallel-link device having n links is the set of n joint variables. For the Stewart Platform, this is the set of six prismatic joint lengths. Expressed as a vector in joint space:
12
L= 13
4
15
16
(4.4)
The reference coordinate frame, as with the manipulator arm, is Cartesian and is composed of an orthonormal position frame and Roll-Pitch-Yaw Euler angles:
X
Y z
X (4.5)
The inverse kinematics mapping, G, is thus:
G: X L (4.6)
For the symmetric Stewart Platform (using conventions of section 4.1.1) the base frame (B) and platform frame (P) are located at the centers of the base plate and platform plate respectively. The location of the base mount points are then expressed as vectors in
( B) and are numbered in a counterclockwise fashion about the positive ZB axis. Similarly, the location of the platform mount points are expressed as vectors in P) and numbered
81

about the positive zP axis. Link vectors, representing actuator linkages, connect the base and platform mount points. Numbering is such that for actuator i, link vector Li connects base mount vector Bi to platform mount vector Pi. A summary of these frame and vector assignments is presented in Figure 4.1.4.
Figure 4.1.4: Frame and Vector Assignments
Symmetrical Stewart Platform
In terms of the symmetrical Stewart Platform parameters given in section 4.1.1, the base mount vectors in (B) are:
BT [ rbcos( )
0]r o T
4:2= [ rco02)
= [ -rcoOo+2)
rbsin(60 )
[ rbcos(60 )
B=
[
-rbcos(60. 2)
BT
rbsin(600 2)
[ rbcos(60 2 )
-rbsin(60°tA) o IT o
T o ]T o ]T
(4.7)
Similarly, the platform mount vectors in (P) are:
82

PT p pT [
-rpsin6o ) o
]T
= [
· 1
-rpsi 6P ) ]
[ rpcos(e2 2 ) rsir o
[ rpco460)
T
(4.8) p [
P6
=
[ -rpcos4 )
]OJ o 1 rpsi )
If the desired position of the platform frame is specified with respect to the base frame, BXPORG = (xd, Yd, zd), then the vector relationship for link vector i is:
Li = Pi + BXpORG- Bi
This relationship is illustrated in Figure 4.1.5.
(4.9)
Figure 4.1.5: Actuator Vector Relationships
Expressing (4.9) as vectors in (B) gives the desired inverse kinematics relationship for each actuator:
= BRPPi + BXpORG - BBi (4.10)
83

where R is the 3-2-1 (Yaw-Pitch-Roll) Euler rotation transformation using desired platform orientation (, 0, yO specified in the base frame: cyVO c*s¢ -sWc cyis&c + ss
1
R = syV0
(4.11)
-sO cOs c c
The actual prismatic joint extension, li, is simply the 2-norm of (4.10):
(4.12)
4
4.1.2.2 Forward Kinematics
The forward kinematic mapping, F, for the Stewart Platform maps the six prismatic joint lengths to Cartesian position and orientation of the platform. The mapping is thus:
F:L = X (4.13)
This map F is ill-defined and is not well behaved since multiple solutions for X may exist for a specified L. It has been shown, however, that locally F exists and is differentiable, provided that the local state is non-singular. (Ismail, 1984).
If one considers the forward kinematics mapping as purely the inverse of the mapping G (the inverse kinematics) then determination of F simply requires inverting
(4.10) or (4.12) simultaneously with all six prismatic joints. Typically, however, only li and not Li is known so that (4.12) must be used. Unfortunately, the inversion of (4.12) is quite difficult in a closed-form sense since the problem involves solving six simultaneous non-linear equations for the six unknown components of X (x, y, z, 0, , y4. One means of solving this problem is given in (Dieudonne, 1972) and involves the application of the iterative Newton-Raphson method.
To apply Newton-Raphson to the inverse kinematics problem, begin by defining a vector function as the difference between calculated and actual (measured) length of joint i: f(X) = LTLi - ILa
2 (4.14) where ILa
2 is the actual (measured) length of joint i. Substituting (4.10) into the above yields:
84

= (BRPi + BXORG BBiT(BPPi + BXPORG BB)-
Expanding (4.15) and taking partial derivatives with respect to components of X (x, y, z,
, , ) gives the following set of equations:
PPT +
1 2
13
) = 2(y ay
PP,T
2 2
+ PPT
23
BB,) afj(
= 42(Z + PPi.T
3
+ P 32 + PPiT
33 -
BBi,)
(4.16) af(X)
=
2
(x BBiXPPiTT13 + PPi.T
1 2 ao
2(y BBXPp T,
3
)
+ PPiT22)
+
33
+ PPT32) af(X) = 2(x- BBi.-PPi.sincos+ PPisincosOcosyr
+ 2(y -B i,X-Pi.sinBsin
+ PPiysingcos0sin+ 'PPi,coscos0sin)
- 2(z - BBiPPi
1 cosO + PPi,,sinosinO af(X) = _ BBiPPT
21
+ PT22+ PiT22 a +
+ PP.T
12
+ PPiT 3) where Rii are components of (4.11). The Newton-Raphson iteration formula for obtaining a solution for X is straightforward:
85

X
_ a~l fi l i afl afl ifax at' at
1 an a
1 a
1 af
2 ax af2
.a* fl y
Y f2
Z z f
3
(4.17) f
4
0 f
5
'1+1 -V P af
6
i f6 Pt
The complete forward kinematics solution is as follows:
1) Measure lengths of the joints (li).
2) Guess platform position and orientation (Xo).
3) Calculate (4.11), (4.15), and (4.16) for each joint.
4) Iterate on (4.17) until (Xn+l-Xn) meets a convergence criterion.
It should be noted that if forward kinematics has to be performed in real-time,
(4.17) will be the limiting factor for computational speed. Since Newton-Raphson is an iterative technique, convergence of (4.17) requires a variable number of iterations, depending on local state gradients. Consequently, if the local state is near a singularity, convergence (which is not guaranteed) may require a large number of iterations.
Furthermore, because (4.17) involves calculating the inverse of a 6x6 matrix, iteration speed will depend primarily on how efficiently the inversion operation can be performed.
From an implementation perspective, the complete 6x6 matrix inversion is not necessary since back substitution using LU factorization will suffice. Finally, nominal convergence of
(4.17) may be such that a small, fixed number of iterations will give sufficient accuracy for the platform state, X.
4.1.2.3 Kinematic Constraints
Forward and inverse kinematics aside, there is a topic which concerns all manipulators, but is particularly important to parallel-link manipulators. Specifically, this is the problem of kinematic constraints imposed by the manipulator hardware. For all
86

manipulators, the fundamental constraint is joint position limitations (i.e. angular range or extension). Parallel-link devices, however, have the additional constraint of link interference. As a result, the symmetrical Stewart Platform has three kinematic constraints which limit the range of operation.
First, prismatic joint extension is restricted to a minimum and maximum length. As a result, not all X generated by the forward map F can physically be reached since all 'i may not be achievable. During operation of the Stewart Platform, this implies that the forward kinematic outputs (prismatic joint extensions) must be checked for validity. This constraint may be expressed algebraically as:
- lmin)
<
Imu (4.18)
Secondly, the prismatic joints are connected to the base and platform plates with spherical joints. In practical terms, no "spherical" joint is truly spherical since there are always limitations on joint range-of-motion. A ball-and-socket joint, for example, offers unrestricted rotation about one axis but is limited to a maximum angle around the other two axes. Other implementations, moreover, may have non-uniformly shaped workspaces. A
Universal-joint attached to a swivel, for instance, has large angular capability, but only in specific orientations. In terms of the Stewart Platform, this means that not all platform X are achievable, even if the commanded prismatic joint extensions are physically possible.
Finally, the Stewart Platform is constrained by parallel-linkage interference.
Specifically, since the device is a space truss with six links, changes in position and orientation of the platform with respect to the base will result in changes for all the connecting links. Consequently, the possibility of link interference exists, which makes certain base/platform configurations unachievable. Calculation of such configurations during real-time operation is a difficult problem due to the complexity of the Stewart
Platform spatial geometry. One approach, which treats the links as solid cylinders and searches for spatial intersection, is given in (Stelman, 1988).
The problem of controlling the Stewart Platform offers many challenges to the control system engineer. Not only does the mechanism have six degrees of freedom requiring active control, but because of the parallel-linkage there are strong relationships between each link. Although it is possible to choose any subset of joints for control, providing that six degrees of platform freedom are maintained, the prismatic joint set is desirable for three reasons. First, this group contains the minimum number of joints 6)
87

which produces full spatial mobility (as demonstrated in section 4.1.1). Secondly, since the joints are physically separated from one another, independent servo control may be used for each joint. Lastly, both the forward and inverse kinematic maps are concerned with link length, which is naturally controlled by varying prismatic joint extensions.
During the past decade, there, have been a number of research efforts directed towards high-level control of a symmetrical Stewart Platform. Fichter of Oregon State
University, for example, has been developing force control methods by deriving models of actuator loading and force output (Fichter, 1986). Additionally, research into variable admittance techniques has been pursued at M.I.T. by Dubowsky's group (Fresko, 1986,
Ismail, 1988, and Stelman, 1988).
For both the O.S.U. and M.I.T. groups high-performance linear actuators were implemented for Stewart Platform operation. Zero-backlash lead screws driven by electric motors were chosen by the former and a fast hydraulic system by the latter. In the case of
SPAM, however, such actuator systems are unsuitable for use in neutral buoyancy.
Consequently, the linear actuator used for the SPAM Stewart Platform (described in section
4.3.3) is extremely modest from a performance perspective, especially in terms of achievable velocity and acceleration. The actuator, however, is capable of achieving fine positioning.
Due to this limitation on actuator performance, the decision was made to focus initial control system design efforts purely on position control. Though this simplifies the control task a great deal, the problem still involves controlling six degrees-of-freedom. In the following sections, two approaches to position control of the Stewart Platform are described. In the sequel, a controller based on inverse kinematics is proposed. In section
4.2.2. a controller utilizing forward kinematics is described.
Contrary to serial-link manipulators, the Stewart Platform inverse kinematics mapping is the fundamental transform and is straightforward to compute. It seems natural, therefore, to attempt to utilize the inverse mapping for the position control problem. As described previously (section 4.1.2.1), the inverse kinematics transforms a desired platform state X to a set of link lengths L. Achieving these commanded lengths is accomplished by controlling the extension of each prismatic joint. If it is assumed that this joint control can be accomplished by actuator position servos, then the high-level control problem reduces to the task of specifying smooth trajectories. As we shall see, however, it is important to understand exactly what constitutes "smoothness".
88

Given the task of moving the Stewart Platform from the current position and orientation to another position and orientation, it is necessary to change the current link lengths to a different set. If the change in state is small, then it is reasonable to assume that the lengths of the links will not change radically. However, if at least one state component
(either translational position or angular orientation) changes significantly or if the platform is near a singularity, then one may expect large jumps in link lengths. Consequently, the platform may move wildly through space, abruptly rotating and translating, as it transitions from the current to desired state. This type of behavior is, of course, extremely undesirable for a manipulator or end-effector involved in proximity operations! To prevent this from occuring, it is necessary to generate a trajectory of joint states such that the platform transitions smoothly between end-points.
Two methods of trajectory generation have been considered for the SPAM Stewart
Platform. In both approaches, current and desired platform states are described in Cartesian space. A number of intermediate way points between the two end points are then calculated by interpolation. In the first method, the interpolation is performed in Cartesian space, resulting in a Cartesian trajectory which is converted to joint states via inverse kinematics.
The advantage of this approach is that the platform state varies smoothly. For the second method, the end points at-e immediately converted to joint states and interpolation performed in joint space. This approach is characterized by constant actuator steps, but the resulting Cartesian trajectory may not be smooth. Since both methods result in continuous joint-space trajectories, it is left to operational testing to determine which approach is more desirable.
The inverse kinematic, or joint-based, controller for the Stewart Platform has the following characteristics:
* Desired platform state, specified in Cartesian space, is transformed into a trajectory in joint space.
* The joint space trajectory is used to command a sequence of joint states.
* The control of joint state is performed by independent joint position servos.
Figure 4.2.1 illustrates the joint-based controller in block-diagram form:
89

i Cartesian Inverse
Way Points F- Kinematics
OR
I
Inverse ~ Joint Space
I Kinematics Way Points
- - - - - - - I
Figure 4.2.1: Stewart Platform Joint Based Control
The joint based controller is attractive because it requires relatively few computations. In fact, if trajectory generation is performed before platform movement is started, then the only calculations that need to be done in real-time are in the six joint position servo loops.
4.2.2 Cartesian-Based Control
Although the joint based controller has many desirable characteristics, it has one glaring deficiency. Specifically, there is no actual feedback of platform state in the control loop. Minimization of error, therefore, depends on trajectory efficacy and performance of the joint position servos. The obvious solution to this problem is to include platform state in the loop. This task, however, is complicated for two reasons. First, it is extremely difficult to instrument the platform with a six degree-of-freedom sensor, especially underwater. It is much easier to sense prismatic joint extension with a linear position sensor. Secondly, if only the link lengths are available (via joint extension sensors), then the platform state must be inferred using forward kinematics. As explained in section
4.1.2.2, however, the forward mapping is difficult to solve and numerical methods require significant amounts of computation.
In spite of these difficulties, a control scheme may be developed that accounts for platform state. The proposed Cartesian based controller utilizes inverse kinematics in the forward loop and Newton-Raphson forward kinematics in the feedback loop. Errors between commanded and current (estimated) position, expressed in Cartesian space, are transformed by the inverse kinematics to joint position errors. These errors, in turn, command the joint position servocontrollers. The resulting platform state is obtained by
90

converting measured joint positions via forward kinematics. A block diagram summarizes this control scheme in Figure 4.2.2.
Figure 4.2.2: Stewart Platform Cartesian Based Controller
It is important to realize that the feedback platform state is only an estimate of the actual platform position and orientation because it is obtained with N-R forward kinematics. Since convergence of this numerical method is dependent on state gradients, precise state estimation may only be achievable with a large number of N-R iteration cycles.
Testing of the N-R forward kinematics over a wide range of platform states is required to determine the minimum number of iterations for acceptable state precision. Alternatively, it may be possible to replace the numerical forward kinematics with some form of state observer such as a Kalman Filter. Implementation, however, would require modelling of the Stewart Platform and actuator dynamics.
In the following sections, design of joint hardware for the SPAM Stewart Platform is discussed. To assemble a symmetrical Stewart Platform, it is necessary to design and construct three types of joints. The final designs for prismatic, Universal, and spherical joints are given in the following three sections. To provide feedback of prismatic joint extension, a linear position sensor was developed for underwater operation. This sensor is described in section 4.3.4. Finally, servo control methods for the prismatic joint are presented in section 4.3.5.
4.3.1 PHAD Revisited
As discussed in Chapter 3, designing high-performance or high-precision actuators for neutral buoyancy operation is non-trivial. The task is not impossible, however, as demonstrated by the joints used in the SPAM manipulator arm. These joints utilize the
PHAD actuator augmented with motion converting (linear-to-rotary) linkages. Since the basic PHAD is linear, it seems natural to utilize this actuator design for linear motion.
Consequently, the Linear-PHAD (L-PHAD) prismatic joint was developed for use in the
91

Stewart Platform. Though the name "L-PHAD" is perhaps redundant, it was chosen to maintain consistency with the revolute joint (R-PHAD) name.
In sections 3.3.2 and 3.3.3, sizing of the R-PHAD cylinders and solenoid valves was performed by considering joint torque requirements. Since the joints were required to produce large torque levels to satisfy tip force specifications, large pneumatic and hydraulic cylinders were required. For the Stewart Platform, however, prismatic joint forces are directly applied to the platform plate at full strength. As a result, smaller cylinders and solenoids are sufficient to meet prismatic joint force production goals.
The final design of the prismatic L-PHAD joint utilizes two Clippard UDR-12-12
(3/4" bore) and one Clippard UDR-17-12 (1-1/16" bore) cylinders. Each of these cylinders has a 12 inch stroke, which is the longest length available for small class cylinders. The two pneumatic UDR-12-12 cylinders produce 110 lbs of force when driven by 125 p.s.i.
compressed air. The UDR-17-12 cylinder was chosen for hydraulic use since it approximates the combined bore area of the two pneumatic cylinders. Similiar to the R-
PHAD implementations, Koganei 110-4El-Fl 1 solenoid valves provide air flow control for the L-PHAD. Control of water flow, however, is performed with Kip 141010 Series 1 solenoid valves instead of Laketown valves. The Kips were selected because lower flow rate and pressure requirements permitted the usage of smaller valves. A schematic of the L-
PHAD is given in Figure 4.3.1; detailed drawings are included in Appendix B. The assembled L-PHAD is pictured in Figure 4.3.2.
Clippard UDR-17-12 k~
Clippard UDR-12-12
N
s
Kip solenoid valve
Stabilizing
Figure 4.3.1: L-PHAD Design Schematic
92

Figure 4.3.2: Assembled L-PHAD
93

To provide the two degrees-of-freedom required by the Stewart Platform link base plate mounts, a simple universal joint was developed. This joint, shown schematically in
Figure 4.3.3, incorporates a gimbal pivot and off-the-shelf hardware from PIC, Inc.
L-PHAD Cyinder or Pon
Monting Block f
Shoulder Scrw
(PiC 4454)
I a
I
Bronze Bushing
-f
1-
-
- Gimba Pivow
Gimoal Stand
(PIC 57-4) f
I
Figure 4.3.3: Universal Joint Design schematic
The assembled Universal joint is pictured in Figure 4.3.4. Testing of this joint reveals that it has a uniform angular workspace, shown in Figure 4.3.5, with a maximum rolling angle of 55±2 degrees and maximum pitching of 40±2 degrees.
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Fi lue 4.3.4: Assembled Universal Joint Design
0 (degrees) p (degrees)
Figure 4.3.5: Universal Joint Workspace
The platform plate link mounting requires a three degree-of-freedom joint. True spherical joints, however, cannot realistically be implemented so that approximations are used in practice. Among the common spherical approximations, the ball-and-socket joint most closely mimics spherical joint workspace. Greater range-of-motion and better load capabilities may be achieved, however, with a properly designed gimbal arrangement. As a result, it was decided to approximate the spherical joint with a modified universal joint.
95

The final joint design, shown in Figure 4.3.6, augments the universal joint described previously with the addition of a swivel bearing. The assembled "spherical" joint is pictured in Figure 4.3.7.
-E
L-PHAD Cyintder or Piston
Mounting B----
Mounting Block
]Shoulder Screw
(PC 4454)
-f
I
I
Bronze Bushing
3 (PIC BI -23)
E
-L. \
~
Gimbal Pivo
Gimbal Stand
(PIC S7-4)
- Pivot Plare
Shoulder Screw
Teflon Washer (PIC 4454) rZ:.1
Bronze Bushing
(PIC BII-18)
Figure 4.3.6: "Spherical" (U-Joint-plus-Swivel) Design scheman'c
96

Figure 4.3.7: Assembled U-Joint-plus-Swivel Joint Design
97

Since this joint is a simple modification of the Universal joint, it has the same rolling and pitching angular workspace. The addition of the swivel, however, provides a full revolution of yawing. The combined workspace is shown below in Figure 4.3.8
V
14
9 e..
34 iO
I
I
I
[-.=110±40
-
Figure 4.3.8: U-Joint-plus-Swivel Workspace
4.3.4 JELLO Sensor
To provide a measurement of L-PHAD prismatic joint extension, a position sensor was needed. Unfortunately, most off-the-shelf linear position sensors are unsuitable for underwater operation due to the difficulty of waterproofing linear electronic assemblies.
Since rotary optical encoders can be modified for underwater operation, a number of designs attempted to use these sensors by converting linear to rotary motion.
Unfortunately, these designs proved to be unsuccessful since the resulting sensors were too bulky, did not provide high precision or accuracy, or were too mechanically complex.
98

In the end, it was necessary to abandon rotary enconders and to focus efforts on developing a custom linear sensor. The Joint Encoder with Localized Linear Optics
(JELLO) is the result of these efforts and is shown schematically in Figure 4.3.9 The assembled JELLO is shown in Figure 4.3.10.
I
I I-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I-
Si
L-PHAD
120 line/inch codestrip
Linear Optical Encoder
(H.P. HEDS-9200-LO0)
Figure 4.3.9: Joint Encoder with Localized Linear Optics (JELLO) schematic
Figure 4.3.10: Joint Encoder with Localized Linear Optics (JELLO)
The fundamental component of the JELLO is the Hewlett-Packard HEDS-9200-LOO incremental linear optical encoder. The HEDS-9200-L00, when used in conjunction with a
99

codestrip, generates linear position information in the form of quadrature signals. Since the mylar codestrip used contains 120 photo-etched lines per inch, quadrature decoding gives
1 the JELLO sensor has an inherent resolution of 480 or approximately 2 thousandths of an inch. Over the 12-inch stroke length of the L-PHAD this gives 5,760 counts of linear position:
(120lines4 counts12 inches)= 5760 counts inchA line
21
= 213 bits
(4.19)
4.3.5 L-PHAD Servo Control
Since only Stewart Platform position control was considered in section 4.2, only a
L-PHAD servo position servo was designed and tested. Specifically, a proportional-plusderivative (P-D) control structure was implemented in software on an IBM microcomputer.
Joint position was determined using the JELLO sensor and velocity was inferred from three step backwards differencing.
All testing of the L-PHAD P-D position servo was performed using the electronic circuitry and software designed for R-PHAD joint testing (see section 3.3.5). As such, the
L-PHAD PWM control signal was restricted to a coarse 4-bits. Additionally, the servo control loops were run at 9 Hz, due to solenoid hardware limits. Since this results in very low controller bandwidth, aliasing and sampling noise were significant concerns.
The L-PHAD P-D position servo has the same form as the R-PHAD position servo presented in section 3.3.5.1 except that linear instead of angular position is the controlled quantity. As a result, the control law is: uk = K(Xd-X)k - K2(xd-x)k- 1 (4.20) where x indicates L-PHAD position. In block diagram form, the P-D position servo is:
Figure 4.3.11: P-D Position Servo
Testing of the position servo was performed in neutral buoyancy using an unloaded
L-PHAD joint. The results of step command testing are shown in Figures 4.3.12 (a)-(c):
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o position
PWM Duty Cycle
1.2
1.0
0.8
0.6
0
0 0. 0 0 0 0 0 0 0
,0
'U *0 *
0.4
-
0
--------------------0.2
0.0
( 0.0
1.0
1.5
time (seconds)
2.0
Figure 4.3.12 (a): P-D Position Servo (Kp = 0.05, Kd = 0.01)
1" step response (normalized)
2.5
PWM Duty Cycle
1.2
1.0
0.8
0.6
0o
~ v o0
0.4
0
0
·
0.2
0.0
I
0
0
Figure 4.3.12 (b):
· . .· .
1
2 time (seconds)
3
P-D Position Servo (Kp = 0.05, Kd = 0.01)
3" step response (normalized)
4
0
I
101

o position
· PWM Duty Cycle
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 1 2 3 4 time (seconds)
5 6
Figure 4.3.12 (c): P-D Position Servo (Kp = 0.05, Kd = 0.01)
6" step response (normalized)
7
As the figures show, the P-D servo exhibits a smooth, overdamped response to step command inputs. For large inputs, the L-PHAD actuator is saturated for much of the step, resulting in constant L-PHAD velocity during the saturated period. For example, a six inch step, see Figure 4.3.12 (c), exhibits this behavior during the first 4.5 seconds. As the
L-PHAD nears the target position, the P-D servo commands smaller and smaller actuation, resulting in the overdamped response characteristic.
To determine if aliasing was occuring due to the low (9 Hz) sampling rate, fast quadrature sampling circuitry was constructed and operated on another IBM microcomputer. This Quadrature Observer ciruitry utilizes an Intel 8253 to generate hardware interrupts on fixed time intervals and is shown in Appendix A. Installed in an
IBM PC/XT microcomputer, the circuitry is capable of sampling and decoding quadrature signals over a 16-3,000 Hz. frequency range.
Quadrature signals were taken from the JELLO sensor position output lines and connected to the fast sampling circuit. A step test was then performed with the sampling circuitry operating in parallel. The normalized step response for a 6" step command is shown below in Figure 4.3.13 (a) and (b).
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position
PWM Duty Cycle
A
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 1 2 3 4 time (seconds)
5 6
Figure 4.3.13 (a): P-D Position Servo (K = 0.05, Kd = 0.01)
6" step response (normalized) with 9 z. sampling
7 position
1.2
1.0 -
0.8
0.6
0.4
0.2
.
0.0
0
1
2 3 time (seconds)
4 5
Figure 4.3.13 (b):
6" step response
P-D Position Servo (K = 0.05, Kd = 0.01)
(normalized), 100 Hz. sampled position
6
The two figures show the L-PHAD extension at two radically different sampling rates. The top figure (a) shows the position signal used by the 9 Hz. servo control loop. This step
103

response shows a smooth, overdamped system response. The bottom figure (b) shows the
L-PHAD extension, but at a 100 Hz. sampling rate. Comparing the two figures reveals little difference between the position plots, indicating an absence of aliased high-frequency behavior. As a result, it may be concluded that the low (9 Hz) controller bandwidth is adequate for controlling the L-PHAD system.
The design of the SPAM Stewart Platform presented interesting challenges. Due to the complexity of the parallel linkage, layout of the mechanism cou!d not easily be obtained given workspace specifications. As a result, a computer model of the Stewart Platform was used for analysis of varied linkage and plate geometries. There are a great number of methods for approaching CAD of a Stewart Platform. In (Stelman, 1988), for example, a complete kinematic model was implemented on a Silicon Graphics IRIS. Although this computer model is very useful for examining kinematic constraints and for mechanism design, the overall CAD system is quite complex; requiring a vast amount of FORTRAN code and IRIS graphic primitives. It is possible, however, to create a useful system for interactive layout without resorting to this amount of programming. In particular, Stewart
Platform geometry and inverse kinematics can be studied by using spreadsheet software.
To this end, a computer model of a symmetrical Stewart Platform was constructed using Microsoft Excel v2.2 on an Apple Macintosh II. Geometrical paramters (see section
4.1.1) are transformed into base and platform link mount points using (4.7) and (4.8).
Platform state, specified in 6-DOF Cartesian space, is mapped to link length and link/mount point angles. CAD of a Stewart Platform using this Excel model, therefore, involves simply specifying geometrical parameters along with desired platform states and observing the resulting joint lengths and angles. Since the platform translational and rotational specifications are given, and because physical actuator and joint limits are known, evaluation of theoretical Stewart Platforms is a straightforward task. Typical numerical and graphical displays provided by Excel are shown in Figure 4.4.1.
104

I ' o
01 a
Platform Inu. Kinematics r
I e r
30 r'
0 e
0
" fO
Rctuator Lengths
2
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7
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Platform Inu. Kinematics
Sb'rf Pljf" Cu _
(a)
,i
Actuator Lengths
1 X base
1 as a Z I rl I
rdw I base 1 Iut. rad I *lat. Se I j e
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0.71
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00
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2.0 25.0 30.00 35.00 4.00
Base Mount Angles
45.00
30.00
15,00 t r rA
'
-
I 2 3 4 5
Base Ptt
Plt P
Pts o
____
(b)
Figure 4.4.1: Excel CAD model of Stewart Platform
(a) z-axis translation only (b) z-axis plus 450 yaw
105

Initially, Stewart Platform designs were studied on a trial-and-error basis. After several attempts, a mechanism was specified that marginally fulfilled the design specifications. Iteration of this design was performed by varying the geometrical parameters. The resulting "optimal" Stewart Platform has the following parameters:
Table 4.2: SPAM Stewart Platform Parameters
Base Plate Radius (rb)
Base Mounting Angle (b)
Platform Plate Radius (rp)
Platform Mounting Angle (ap)
7.5 inches
35 degrees
5 inches
60 degrees which results in the base and platform mount points shown in Figure 4.4.2.
\
A_0--
/
I
I
I
/
/
I/
-460.0
°
5,
-
1
120.00- q/
I
I
\0
;
Plafonn
Figure 4.4.2: SPAM Stewart Platform Mounting Points
4.5
In this section, the physical hardware of the SPAM Stewart Platform has been fully described. At the time of this writing, all of the L-PHAD, Universal, and spherical joints have been constructed. The complete mechanical Stewart Platform has been assembled with
106

these joints mounted to two circular plates. Operational testing of the mechanism, however, has not performed due to delays in JELLO sensor, pneumatic power system, and electronic control system development.
The assembled SPAM Stewart Platform is shown schematically in Figure 4.5.1 and pictured in Figure 4.5.2 below. As the figures show, the Stewart Platform has six SPSlinks attached in the design configuration previously described. Both the base and platform plates are 18" diameter aluminum discs. Mounted on the platform plate is a circular box surrounded by a flotation ring. The box is pressurized and contains the twelve Koganei solenoids required by the six L-PHAD joints. The ring is constructed with Rohacell highdensity foam covered with fiberglass cloth and is used to help make the Stewart Platform neutrally buoyant.
Box
I. ..
.. ·· ·
Ring
r plaform spherical
(universal
+swivel) joint
L-PHAD prismatic
universal
base
Figure 4.5.1: SPAM Stewart Platform schematic
107

Figure 4.5.2: Assembled SPAM Stewart Platform
arm system described in section 3.4.3. Compressed air from 72 cu. ft. scuba tanks is regulated to 125-140 p.s.i. using a first-stage scuba regulator and fed to the Stewart
Platform solenoid box through 1/8" (I.D.) pressure tubing. A secondary line, tapped off the supply line, is used to pressurize the solenoid box after regulation via a Go, Inc.
regulator. Inside the solenoid box, this high-pressure supply is attached to a manifold connected to the twelve Koganei solenoids. High pressure Koganei output, commanded by the L-PHAD servocontroller, is routed to the L-PHAD pneumatic cylinders using CPC quick disconnect fittings.
A schematic of the complete Stewart Platform pneumatic system is provided in
Figure 4.5.3.
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I to Koganei solenoids
(L-PHAD)
I
I
Figure 4.5.3: SPAM Stewart Platform pneumatic system
(schematic)
4.5.3 Electronic Control System
Although testing of a single L-PHAD joint successfully used the single R-PHAD joint electronic control system (ECS), described in section 3.4.4, this arrangement was deemed unsuitable for Stewart Platform operation for three reasons. First, the complete
Stewart Platform implementation includes six L-PHAD joints, meaning that the R-PHAD
ECS would have to be duplicated six times. Secondly, since the R-PHAD ECS solenoid signals are generated on the surface, control of six L-PHAD's would necessitate a bulky set of long electrical lines. Finally, the inherent coarseness of the R-PHAD PWM signal (4bits) limits L-PHAD performance and precision.
To remedy these shortcomings, the Stewart Platform Electronic Control System
(SPECS) was designed using microprocessors. The resulting distributed system is extremely small in size and is capable of generating high-fidelity (i.e. 16-bit) PWM signals.
Moreover, because of the distributed systems approach, it was possible to reduce Stewart
109

Platform computation demands by locating the L-PHAD position and velocity servocontrollers in the microprocessors.
The microprocessors selected for SPECS are New Micros, Inc. "2x4" series
(NMIS-0021) microcomputers. The NMIS-0021 units, based on the Motorola F68HC11
MCU, are physically compact, incorporate a full implementation of the FORTH language, and are ideally suited for direct hardware control. Moreover, direct MCU address and data bus access is easily obtained by the addition of a New Micros' NMIS-0001 expansion/prototyping board. The New Micros' microcomputer hardware is shown in
Figure 4.5.4.
Figure 4.5.4: NMIS-0001 and NMIS-0021
In order to implement servocontrollers on the NMIS-0021, SPECS was required to use JELLO sensor feedback. Similar to the R-PHAD ECS design, Hewlett Packard HCTL-
2000 chips were selected to decode the JELLO quadrature signal to a 12-bit position word.
Due to physical limitations, however, only three of these chips could be placed on a single
NMIS-0001 board. As a result, it was necessary to split the control task between two
NMIS-0021 's with each computer controlling three L-PHAD joints. The final quadrature decoding circuitry design implemented on each NMIS-0001 is given in Appendix A.
During operation of the Stewart Platform, a surface computer sends position commands to the L-PHAD servos. Command transmission is accomplished using RS-422 serial communications between the surface computer and the two NMIS-0021's (see section 5.1). L-PHAD control signals, generated by servos written-in FORTH, are output through NMIS-0021 I/O ports and are transformed to solenoid signals with a transistor based power switching box. A block diagram of the SPECS is shown below:
110

Quadrature
.,..
L-PHAD commands to L-PHAD solenoids
Figure 4.5.5: Stewart Platform Electronics Control System
It should be noted, however, that this configuration of SPECS does not completely eliminate the need for surface to Stewart Platform signal lines. Since commands are sent from a controlling computer to the two NMIS-002 l's, a serial communications line must be included. Moreover, the two NMIS-0021's and the L-PHAD sensors require a +5 VDC supply. Although it is possible to collocate a battery and the Stewart Platform, it is simpler to utilize a power supply line. Finally, the Power Switching Box requires a +12 VDC supply to transform the NMIS-0021 control signals from CMOS level to the +12 VDC needed to operate L-PHAD solenoids. Since these solenoids draw considerable power, an additional power supply line allows sustained Stewart Platform operation.
111

Chapter 5
The task of implementing the complete SPAM system is not an easy one. Although anthropomorphic manipulator operation is straightforward, the addition of a Stewart
Platform micromanipulator greatly alters the situation. The integration of manipulator and
Stewart Platform hardware systems (i.e. electrical, mechanical, computational, etc.), for example, requires careful management of resources such as computational facilities.
Additionally, the control problem is increased in complexity from three to nine degrees-offreedom. Finally, logistical concerns such as user interfacing, trajectory generation, and task planning are significantly complicated. To address these problems an object-oriented philosophy has been adopted for operation of SPAM. This approach, originally intended to facilitate representation of complex data in computer systems, is a useful abstraction mechanism and lends itself extremely well to operation of distributed systems.
In the following sections, the integration of the anthropomorphic manipulator
(described in Chapter 3) with the symmetric Stewart Platform (described in Chapter 4) is discussed. Section 5.1 discusses physical issues concerning the integration of electrical and mechanical systems. Section 5.2 develops the object-oriented methodology, describes the
SPAM software architecture and details the nine degree-of-freedom control scheme.
Finally, Section 5.3 addresses user interfacing and explores operational concerns. It should be noted that at the time of this writing, the total integration of manipulator and Stewart
Platform has not been completed. Hence, some of the following subjects are theoretical in nature, and should be viewed merely as proposals for future system development.
The integration of the SPAM manipulator arm and Stewart Platform, hardware was separated into three phases. First, the Stewart Platform was attached tc the tip of the manipulator arm. Secondly, a pneumatic supply system was developed. Finally, computer systems were linked using network communications protocols.
112

The connection of the manipulator arm and Stewart Platform was accomplished by installing an mechanical coupling. This coupling, shown in Figures 5.1.1, is an adjustable, locking hinge with a ninety degree range. Adjustment/locking of the hinge angle is performed by the removal/insertion of a "pip-pin". The coupling's manipulator arm interface is identical to the joint/arm boom connection described in section 3.4.2. During typical SPAM operations, the Stewart Platform base plate is fixed normal to the manipulator arm axis. The adjustable coupling, however, provides additional flexibility for tasks which require an offset Stewart Platform.
Figure 5.1.1: Adjustable Hinge Coupling
To provide compressed air to the three manipulator arm joints (R-PHAD) and six
Stewart Platform joints (L-PHAD), a pneumatic supply system was designed. Since both types of joints were designed to operate with 125-140 p.s.i. air, it is theoretically possible to power all the joints from a single supply line. To provide the required flow rate and volume, however, would necessitate the use of large diameter pressure tubing.
Unfortunately, flexible tubing of the required size is not available. Additionally, an individual, single-state scuba regulator would be unable o provide the desired output of compressed air.
A more desirable approach to pneumatics is to implement a dual supply system. In this arrangement, the outputs from two first-stage scuba regulators are used to supply the
SPAM joints. Although it is possible to use one supply line for the manipulator arm and one supply for the Stewart Platform, this arrangement fails to consider operational requirements. Since normal SPAM operation involves coarse positioning with the manipulator arm followed by fine position tuning with the Stewart Platform, a
113

configuration utilizing two supply lines in parallel would be a more efficient allocation of resources. As a result, the SPAM pneumatic supply system uses one line for the manipulator shoulder joints and the other for the manipulator elbow and Stewart Platform joints. Though both lines are not continually used (i.e. the shoulder line is not active during
Stewart Platform operation), the higher pneumatic flow capability allows for better R-
PHAD performance.
In order to achieve good system response, given limited computational power, it was necessary to implement a distributed processing system for real-time operation. This system utilizes several microcomputers, described in the following section, which need to communicate with each other. To provide the necessary communications capability, two network protocols were implemented. First, the Pilot-Vehicle-Communications-System
(PiVeCS) is used for serial communications between IBM microcomputers. The PiVeCS protocol, developed for SSL use by R. Sanner, is a robust communications system intended to provide reliable hardware interfacing and efficient information exchange
(Sanner, 1990). Secondly, the Microprocessor-Microcomputer-Communications-System
(MiMiCS) was designed to provide communications between the New Micro's 68HC11 microprocessor systems and an IBM microcomputer. The MiMiCS protocol was designed to be similar to PiVeCS, utilizing the object-oriented paradigm of "message-passing" to handle information exchange.
In terms of physical hardware, the computer network is comprised of serial communication lines connecting microcomputer nodes. PiVeCS operates between two IBM microcomputers over a short RS-232 line running at 19,200 baud. MiMiCS connects two
New Micro's "2x4"'s with one of the IBM microcomputers via RS-422 lines operating at
9,600 baud.
As discussed previously, to obtain the highest performance system possible given limited computational resources, a distributed processing system was implemented. This system was designed using an object-oriented philosophy to abstract the SPAM system into various components. By this approach, various objects with internal, local states operate in specific environments with other objects. Each object is able to perform certain tasks and may interact with other objects (i.e. ask for information, request an action). No object, however, can ever directly modify the internal state of another. This localization of state is often referred to as "information-hiding" or "data-encapsulation" and this method of interaction is known as "message passing". Taken together, these techniques offer a
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powerful framework for organizing computational models and developing complex systems (Abelson, 1985).
To begin, the SPAM system is divided into eight objects based on subsystem function. These objects and their respective functions are described in Table 5.1:
Table 5.1: SPAM Object Definitions
User Inteface
(see section 5.3)
SPAM Controller
(see section 5.3)
Stewart Platform Controller
(see section 4.2)
Manipulator Arm Controller
(see section 3.2)
L-PHAD Controller
(see section 4.3.5)
R-PHAD Controller
(see section 3.3.5)
L-PHAD Joints
R-PHAD Joints
Receives user commands and produces displays showing current: manipulator 3-DOF tip state in base) and platform 6-DOF state in (tip)
OR platform 6-DOF state in base)
If necessary, transforms commands from the User Interface to manipulator tip commands in {base) and Stewart Platform commands in (tip)
Produces current manipulator tip state in
{base), platform state in tip) and base)
Generates L-PHAD position commands via platform controller and calculates platform state in tip) via FWDKIN.
Generates R-PHAD commands via arm controller and calculates arm state in base) via FWDKIN.
Generates L-PHAD control signals via position servo.
Generates R-PHAD control signals via position and rate servos.
Controls Stewart Platform 6-DOF platform location. L-PHAD state (lengths) output from JELLO sensor.
Controls Manipulator Arm 3-DOF tip position. R-PHAD state (angles) output from optical encoder.
Each object maintains a set of internal (local) data which it shares with other objects upon request. This structure is advantageous because it offers a clean, efficient structure for information exchange and eliminates the need for maintaining redundant sets of data. The
Manipulator Arm Controller, for example, calculates the current tip position with manipulator forward kinematics and provides the state information to the SPAM Controller.
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Similarly, the SPAM Controller provides this acquired state information to the User
Interface for output to the user. From a hardware perspective, moreover, this structure is quite natural; the L-PHAD Joints and the R-PHAD Joints maintain real data (e.g. joint state) and provide the information to other objects via sensor readings.
Implementation of these objects is straightforward. Obviously the R-PHAD Joints and the L-PHAD Joints are components of the manipulator arm (Chapter 3) and the
Stewart Platform (Chapter 4). The User Interface may be implemented in any number of ways, but keyboard entry and computer display (section 5.3) does not requires additional hardware. The allocation of controllers was determined by considering computational resources. Four microcomputers were available for SPAM operation. A summary of these systems is provided in Table 5.2:
Table 5.2: SPAM Microcomputer Systems
Pryor
R2-D2
Bill
Ted
IBM PC/AT compatible
80286 CPU running at 12 MHz
80287 floating point coprocessor
IBM PC/XT
8088 CPU running at 4.77 MHz
8087 floating point coprocessor
New Micro's "2x4"
F68HCl 1 CPU running at 2 MHz
On board FORTH interpreter
New Micro's "2x4"
F68HC11 CPU running at 2 MHz
On board FORTH interpreter
First, it was determined that the SPAM Controller, the Manipulator Arm Controller, and the
R-PHAD Controller have the highest computational demands. Consequently, these objects were placed on Pryor along with the keyboard-driven User Interface. Secondly, the
Stewart Platform Controller was assigned to R2-D2. Finally, the L-PHAD Controller was divided between the two New Micro's "2x4"s, Bill and Ted.
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A summary of SPAM object locations is given below in Table 5.3:
Table 5.3: SPAM Object Distribution
User Interface
Manipulator Arm Controller
R-PHAD Controller
Stewart Platform Controller
R2-D2
Objects communicate with each other using a message-passing scheme. Messages are sent from one object to another to request data or to ask that an action be performed.
For objects coexisting on a common microcomputer, messages are passed directly between software modules. If objects are located on different machines, however, messages are sent over a physical link using the appropriate serial communications protocol, PiVeCS or
MiMiCS. To facilitate streamlined message-passing, the eight objects have been configured in a tree structured network. The distributed processing system architecture, with communication channels, is given in Figure 5.2.1.
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iart Platform ontroler
MiMiCS
*-*
4-
Figure 5.2.1: SPAM Distributed Processing Network
The benefits of using a distributed processing system are readily apparent. Since computations have been split between several microprocessors, parallel processing of data may be performed. Once the user has specified desired system state (i.e. end-effector position), the SPAM Controller divides the task of controlling nine degrees-of-freedom into manipulator arm and Stewart Platform operations. High-level controllers, working in parallel, generate commands for the joint servos. These servos, in turn, produce signals to control the actual SPAM hardware. From a performance perspective, this system structure is extremely efficient because computational resources are utilized to the greatest extent possible.
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5.3
5.3.1
To ease the operation of a complex mechanism, careful consideration must be given to the user interface. In particular, the input of desired actions should not place excessive workload or burdens on the operator. For the SPAM system, this implies that specification of manipulator and Stewart Platform movement be easy for the user to express. Since commands are most intuitively expressed as Cartesian position and orientation, the design of the SPAM user interface should reflect Cartesian thought.
There are many method of implementing a Cartesian-based interface. Rotational and translational hand-controllers, for example, may be used to "fly" the desired hardware frame (e.g. manipulator tip, platform plate) in six degrees-of-freedom. The simplest implementation, however, is for the user to specify desired actions directly to a microcomputer through keyboard entry. This method is advantageous since it does not require the integration of additional hardware to SPAM and because it allows great flexibility through software design.
Assuming that all input is obtained with keyboard entry, the task of executing user commands is performed by the SPAM Controller object. This controller differs from the high-level controllers and joint servos discussed in previous chapters in that it does not actually perform control actions. Rather, the SPAM Controller acts as a supervisor by translating user commands into desired states for the manipulator arm and Stewart
Platform. For example, consider that an arbitrary trajectory has been specified. This trajectory contains a set of Cartesian frames that the user desires SPAM to achieve. The
SPAM Controller processes these frames and produces a set of commands, which may in fact be another Cartesian trajectory, for the manipulator and Stewart Platform controllers to
5.3.2 Operational Issues
Besides user interfacing, there are a number of other important operational issues.
First, there is the problem of trajectory specification. Given that SPAM has nine degreesof-freedom, one question is whether it is necessary to completely specify all nine degrees at each desired location. Since the manipulator arm was intended to provide 3-DOF coarse user to give 3-DOF specifications for trajectory way-points and 6-DOF at the end points. A
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processor then processes these incomplete specifications to produce smooth 9-DOF trajectories.
Secondly, there is the issue of obstacle avoidance to consider. For any robotic device, there is always a potential for collision with objects. If the operating system has a
priori knowledge of obstacles entering (or already existing in) the robot's reachable workspace, then trajectory modifications can be planned. However, if obstacles are not known to the system, contingency planning is problematic.
Finally, the SPAM system utilizes and produces large forces. If not controlled properly, these forces are potentially hazardous to humans working with SPAM or in the reachable workspace. As a result, the issue of human safety requires consideration. In terms of logistics, this means that SPAM must be operated in a manner conducive to safety at all levels. Fault handling and recovery must be implemented to deal with events such as control systems failure, mechanical breakage, and loss of power.
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Chapter 6
At this time, the entire SPAM system is not operational. The manipulator arm has only been tested in a planar 2-link planar configuration. To complete the manipulator, it is necessary to add a revolute shoulder yaw joint. Although such a joint has been designed, the R-PHAD-B of chapter 3, fabrication and operational testing need to be completed.
In terms of the Stewart Platform, all the joints (prismatic, universal, and spherical) have been completed. Installation of the electronic control and pneumatics systems, however, needs to be finished. Testing of the JELLO sensor has revealed that photoetched, mylar codestrips cannot be submerged for extended time periods, indicating that further research and development is necessary. Finally, microprocessor servo control and MiMiCS network interfacing have only been investigated to a limited extent.
A portion of the mechanically integrated SPAM system is shown in the following figures. The first, Figure 6.1.1, shows the elbow-to-Stewart Platform section with a 25 foot arm boom. The two smaller arm booms, 6 and 12 feet, can be seen alongside. In figure 6.1.2 SPAM is seen from a tip perspective, with a close-up of the Stewart Platform.
Figure 6.1.1: SPAM Elbow-to-Stewart Platform (elbow view)
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Figure 6.1.2: SPAM Elbow-to-Stewart Platform (tip view)
The development of SPAM, from concept inception to the present time, has spanned a period of two years. The first three months, July-September 1988, were spent investigating neutral buoyancy actuators and studying the viability of pneumatics for highprecision systems. The next year, October 1988-September 1989, saw the development of manipulator joint designs and the fabrication of Stewart Platform mechanisms. Finally, during the last eight months, October 1989-May 1990, actuator testing, sensor development, and implementation of joint servocontrol techniques have been performed
The original SPAM development plan proposed that all hardware systems
(electrical, mechanical and pneumatic) be constructed within the first six months. The actual construction of SPAM, however, has taken much longer. -In fact, after two years of work only a 2-link manipulator is operational and considerable Stewart Platform implementation work remains to be done. Looking back, it is clear that the substantial construction delay may be attributed to a single factor, design of the Pneumatic-Hydraulic Actuating Device for neutral buoyancy operation.
Several problems impeded smooth development of PHAD. First, obtaining pneumatic and hydraulic cylinders for neutral buoyancy operation was difficult. Besides satisfying force production specifications, these cylinders were required to be corrosionresistant, reliable at depth underwater, and cost-effective. After several months, PHAD was finally implemented with aluminum Clippard pneumatic cylinders and stainless-steel Aurora hydraulic cylinders. Unfortunately, the Clippard cylinders originally used contained a
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defective piston seal design, causing a delay in PHAD testing until improved cylinders could be obtained.
Secondly, guaranteeing smooth water flow through PHAD was a problem due to difficulties in acquiring robust solenoid valves. Initially, Kip solenoids were used in all
PHAD designs for water service. These valves were chosen due to compactness, low cost, and availability. Testing of the R-PHAD joint, however, revealed that the Kip solenoids were unable to handle the water pressure and water flow produced by 2" bore cylinders.
After contacting several distributors, it was decided that replacement of the Kip valves with another solenoid line would be required. The ensuing search resulted in custom manufactured high-performance (pressure rating vs. size) solenoid valves from the
Laketown Co. of Waconia, Minnesota.
Finally, and perhaps most significantly, the mechanical R-PHAD design proved to have inherent difficulties. Since all the cylinders are mounted by threading directly into aluminum blocks, joint friction is strongly dependent on thread alignment. In other words, very small tolerances must be maintained during fabrication or the joint will not move smoothly. Additionally, the threaded mounting made alignment of cylinder ports difficult, especially if snugly mounted cylinders was desired. Finally, the asymmetrical cylinder arrangement (required for symmetrical joint forces) resulted in potential for uneven piston loading.
6.3 Recommendations for Future Studies
At this stage of SPAM concept development, there are several implementation issues which remain unresolved and require investigation. Additionally, a great number of interesting manipulator arm and Stewart Platform topics warrant study and experimentation. Finally, there are very exciting neutral buoyancy space research areas for which SPAM is an excellent candidate.
6.3.1 Implementation Specific Issues
In terms of unfinished work, two obvious concerns are how well the design of the
R-PHAD-B manipulator shoulder yaw joint and the Stewart Platform will perform in neutral buoyancy operation. As discussed previously, the R-PHAD-B has been fully blueprinted, though not completely fabricated. Immediate attention should be given to completion of this joint and to submerged testing. For the Stewart Platform, final subsystem assembly and integration remain to be performed. Efforts should additionally, therefore, be given to this task.
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Although the current SPAM hardware systems perform adequately, it may be possible to achieve better performance by refinement of the PHAD design. To this end, it will be necessary to conduct a detailed study of actuator operational characteristics.
Especially important would be a characterization of water dynamics (flow properties, cavitation, etc.) through the PHAD cylinders and solenoids since this would allow better hydraulic design. Additionally, refinement of the PHAD mechanical linkage and connections could reduce mechanical slop and produce higher force and torque outputs.
Other issues of concern are computational structure implementation and user interfacing. The use of a parallel processing system opens a wide range of topics for study:
Optimality of the current distributed architecture for SPAM computations is one issue.
Investigation of alternative computational structures is another. As far as user interfacing, there are many unanswered questions since limited research has been performed thus far.
Research in this area may delve into areas such as input devices, information display, and human factors.
6.3.2 Manipulator Arm
Control engineering of serial-link manipulators is fascinating because the field is relatively young and extremely dynamic. Although the manipulator control systems discussed in this thesis would have been considered sophisticated a few years ago, by current standards they are quite unremarkable. Moreover, the design approach utilized for the SPAM manipulator arm, individual joint control, places inherent limitations on performance and robustness.
Consequently, it is appropriate to research and implement more advanced and sophisticated controllers. Some current manipulator schemes include adaptive control, nonlinear control, and optimal control. Of these, non-linear sliding-surface control seems especially promising since this technique can provide extreme robustness to non-linear systems. Additionally, there is some interest in novel strategies such as neural network and intelligent (e.g. fuzzy-logic) controllers.
Finally, there is an abundance of manipulator operational and logistical issues suitable for investigation. Present day path planning, for example, is largely heuristic in nature and almost exclusively utilizes trajectory curve splining. This approach is hardly optimal and any research, especially involving mathematical rigor, could lead to vast improvements. Another interesting topic is obstacle detection and avoidance. Previous research in this area has been focused on sensor fusion and vision processing. Applying such concepts to SPAM would be beneficial for tasks in crowed workspaces. Lastly, there is a need to determine efficient methods for handing of kinematic singularities. In
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particular, techniques that maintain smooth movement near singularities would greatly aid manipulator operation.
6.3.3
The approach to Stewart Platform control presented in this thesis is extremely limited since system dynamics have not been considered. The rationale for ignoring these dynamics was that neutral-buoyancy linear actuators could not provide high performance.
Development of the L-PHAD, however, has shown in fact this assumption was incorrect; that it is possible to create a robust actuator. Consequently, the door is now open for study of more sophisticated Stewart Platform control strategies. In particular, it is possible to direct efforts towards control of Stewart Platform forces, both internal and applied. To this end, it may be desirable to study impedance and admittance control techniques to create controllers for a dynamic Stewart Platform.
Additionally, it has been stated that the forward kinematics mapping of a Stewart
Platform is extremely difficult to solve in closed-form, and that a Newton-Raphson numerical method is typically used instead. This is not to imply that a closed-for n solution of the forward kinematics is not possible, or that other numerical solutions are less efficient, simply that N-R is used because it can produce a solution. However, since the
NR method has variable convergence properties and may be unstable in the presence of singularities, it would be prudent to investigate alternative means of performing forward kinematics. Since the SPAM Stewart Platform is a symmetrical implementation, it may in fact be possible to determine a closed-form solution.
Another area of interest is workspace analysis of a Stewart Platform. In general, formal analysis is difficult due to the inherent geometrical complexity and the multiloop linkage structure. Since the SPAM Stewart Platform is a symmetrical arrangement, however, it is possible to obtain approximate spatial limits by considering the workspace to be conical in shape (Yang, D.C.H and Lee, T.W., 1984). Although actual workspace analysis was not performed for the SPAM Stewart Platform, the basic method is to investigate translational limits along cross-sectional planes. For example, the platform center could be moved in the XZ and X'Z planes, of base) shown in Figure 4.4.3. The locus of reachable (i.e. achievable within joint limits) points would then be recorded.
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ZB
XB
Figure 6.3.1: SPAM Stewart Platform Base Frames
Finally, the current SPAM Stewart Platform implementation does not attempt to address several important issues. Link interference avoidance, joint workspace constraints, stability near singularities and fault detection/handling are certainly valid concerns when operating a Stewart Platform. Handling of these concerns, however, may be difficult since current, known methods require substantial amount of computational power. If, however, alternative (i.e. less computationally demanding) routines can be found then it certainly is viable to attempt implementation.
6.3.4 Space Research Topics
Although the study recommendations given in the preceding sections are certainly valid topics, the underlying motivational factor for developing SPAM is neutral buoyancy space research. Since neutral buoyancy offers many advantages (e.g. fidelity, scale) over other ground-based space simulators, investigation in this environment is especially worthwhile. In fact, the neutral buoyancy tank for space research has been compared in importance to the wind-tunnel for aircraft development (Akin, 1988).
A great many issues await investigation in neutral buoyancy. Of prime importance for efficient human expansion into space is research focusing on enhancing man/machine productivity. Study on determining optimal methods of integrating humans and robots
(autonomous, semi-autonomous, and teleoperated) will certainly have an impact on near term space activities, such as the construction of the Space Station. Additionally, research

qualifying and quantifying the use of a manipulator arm for positioning tasks will influence design of future man/machine systems, such as maintenance and structural assembly vehicles. Finally, the successful use of SPAM may spur further research into novel mechanism designs and space system concepts which transcend the imagination.
The research described in this thesis has created a firm foundation for SPAM in terms of conceptual development, mechanical design, and implementation methodology.
First, the SPAM concept was developed as a solution to neutral buoyancy SRMS simulation problems. By decoupling the system design into a three degree-of-freedom, revolute joint, manipulator arm augmented by a six degree-of-freedom, parallel-link, micromanipulator, the SPAM system is able to provide fine tip positioning as well as producing large forces during neutral buoyancy operation.
Second, extensive mechanical engineering has resulted in useful, efficient mechanisms. The development of PHAD has resulted in a new neutral buoyancy actuator with desirable performance characteristics at low cost. The manipulator arm revolute joints, in spite of some inherent design problems, have proven to be extremely robust and reliable during extensive testing. Using relatively simple servo controllers, the R-PHAD-A joints are able to produce high torque output and to achieve precise positioning. Additionally, the
Stewart Platform prismatic joint (L-PHAD) is a very compact linear actuator capable of high precision and performance. Furthermore, the JELLO sensor offers a true linear sensor for underwater use with extremely fine position resolution.
Third, the design of advanced, high-level controllers and of an object-oriented, distributed processing system offers SPAM the potential for sophisticated and robust operations. Cartesian and joint-based manipulator controllers provide SPAM with SRMS simulation capabilities superior to other simulators and provide the capability for highfidelity neutral-buoyancy research. Distributed processing through a parallel computer architecture allow SPAM, with nine physical degrees-of-freedom and substantial mathematical complexity, to achieve high system performance given limited computational resources.
The SPAM concept offers much potential for future SSL neutral buoyancy space research. By providing a robust and reliable manipulator, SPAM will be extremely useful in studies focusing on enhancing man/machine system productivity. In particular, tasks requiring fine positioning of humans and robots could benefit greatly from the use of
SPAM. These include such exciting topics as investigation of human/telerobot task coordination, satellite servicing, and structural assembly. At this point, though, work
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remains to complete and successfully implement the Stewart Platform Augmented
Manipulator. It is hoped, however, that the foundation created by this thesis will provide a solid base on which to build.
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Abelson, H., and Sussman, G. J., Structure and Interpretation of Computer Programs,
The MIT Press, Cambridge, Massachusetts, 1985.
Akin, D. L., "A Design Methodology for Neutral Buoyancy Simulation of Space
Operations", AIAA paper 88-4628, 1988.
Asada, H., and Slotine, J.-J., Robot Analysis and Control, Wiley and Sons, New York,
1986.
Astrom, K. J., and Wittenmark, B., Computer Controlled Systems, Prentice-Hall Inc.,
Englewood Cliffs, New Jersey, 1984.
Craig, John J., Introduction to Robotics, Addison-Wesley Publishing Co., Reading,
Massachusetts, 1986.
Dieudonne, J. E., Parrish, R.V., and Bardusch, R.E., An Actuator Extension
Raphson's Method, NASA TN D-7067, Nov. 1972.
Fichter, E. F., "A Stewart Platform-Based Manipulator: General Theory and Practical
Construction", International Journal of Robotics Research, Vol. 5, No. 2, Summer 1986.
Ismail, A. N., "The Design and Construction of a 6 Degree-of-Freedom Parallel-Link
Platform Type Manipulator", SM Thesis, MIT Dept. of Mechanical Engineering, 1988.
Miller, R. H., Minsky, M. L., and Smith, D., Space Applications of Automation,
Robotics, and Machine Intelligence Systems (ARAMIS), NASA CR- 162079, Aug. 1982.
Moore, J. H., Building Scientific Apparatus, Addison-Wesley Publishing Co., Redwood
City, California, 1989.
Ogata, K., Discrete-Time Control Systems, Prentice-Hall Inc., Englewood Cliffs, New
Jersey, 1987.
Sanner, R. M., "The MIT SSL Pilot-Vehicle-Control Station Communications Protocol",
(draft), Feb. 1990.
Stelman, N. M., "Design and Control of a 6 Degree-of-Freedom Platform with Variable
Admittance", SM Thesis, MIT Dept. of Mechanical Engineering, 1988.
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Stewart, D., "A Platform with Six Degrees of Freedom", Proceedings of the Institution of
Mechanical Engineers, Vol. 180, 1965-66.
Ussher, T. H., and Doetsch, K. H., An Overview of the Shuttle Remote Manipulator
System, NASA N85-16964, 1985.
Yang, D. C. H., and Lee, T. W., "Feasibility Study of a Platform Type of Robotic
Manipulator from a Kinematic Viewpoint", Journal of Mechanisms, Transmissions and
Automation in Design, Vol. 106, June 1984.
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This appendix contains schematics for the electronics used by the Stewart Plaform
Augmented Manipulator. All of the circuitry shown on these schematics has been breadboarded by wirewrapping at this time. Descriptions of each circuit follow:
Observer Board
The Observer Board was designed to asynchronously sample quadrature position signals and to generate IBM hardware interrupt requests. The design of the circuit centers on the Hewlett-Packard HCTL-2000 chip. The HCTL-2000 is a compact device (16-pin
I.C.) which provides a low-cost, efficient means of decoding quadrature signals to a 12-bit counter value. Since this chip continually samples the two input channels, resolving quadrature phase shifts to counters changes, it is extremely useful for monitoring a position encoder.
IBM interrupt signals are generated with an Intel 8253 Programmable Interval
Timer. The 8253, operating in mode #2 (Rate Generator), generates rising edges on the
IBM PC-BUS IRQ2 line at regular intervals. It should be noted that the 8253 Rate
Generator mode produces low pulses only one clock period wide, meaning the IRQ2 line is high for most of the time. This is not a problem since the 8259 interrupt controller used by the PC is only triggered by rising edges. Additionally, since the interrupt signals are wired to IRQ2, this board probably will NOT run on an PC/AT-bus since the AT uses IRQ2 to cascade 8259's.
To utilize the Observer Board, do the following:
1) Install the board in an IBM PC-BUS slot.
2) Connect the two quadrature input and ground lines to a quadrature generating device (e.g. optical encoder).
3) Run the QUADOBS software described in Appendix C.
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Since the 8253 is driven by a 1 MHz oscillator and has a 16-bit internal countdown register, the slowest sampling rate that may be requested is 15.23 Hz. The upper limit on sampling rate for a PC/XT running at 4.77 MHz is approximately 2 KHz. If quadrature position is displayed on the screen, sampling rates should be limited to 1 KHz, otherwise the system will operate VERY SLOWLY (due to tremendous overloading of the DOS interrupt handler).
This circuit is intended to control 1 or 2 SPAM R-PHAD or L-PHAD type joints and to read quadrature signals from 1 or 2 optical encoders. To operate a SPAM joint, control signals for 4 solenoid valves, two air (Koganei 110-4E1-12VDC) and two water
(Laketown or Kip), must be generated. The air solenoids require a binary signal, commanding ON/OFF state, whereas the water solenoids need PWM signals. To produce the necessary signals, two Intel 8255's and a 4-bit PWM generator (based on an '85 and
'163) are used. Decoded of quadrature input signals is performed with two HCTL-2000 chips.
To utilize the 2-Joint Controller, do the following:
1) Install the board in an IBM PC or PC/AT bus slot.
2) Connect a 26 line ribbon cable from the board's ribbon cable header to the
Manipulator Hookup Board (MHB).
3) Hookup power to the MHB.
4) Run the SPAM, PHAD or SPAM2 software described in Appendix C.
There are three important things to note. First, the addressing logic is setup such that the board appears at IBM I/O port addresses 0x3EO to 0x3E7. Secondly, the PWM generator is driven by the output of a '555 timer circuit (555-2 on schematic). Because of this, the PWM duty cycle frequency can be varied from 0 to approximately 100 Hz. simply by changing resistors (or utilizing a poteniometer). Finally, the software listed in (4) above
(as currently written) look for a PWM synch signal on 8255-2 PC4 line (pin 13) to determine control loop frequency. As a result, this line cannot be disconnected without rewriting part of the software (specifically, the routine "SYNCHT').
Manipulator Hookup Board (MHB)
This circuit's primary function is to provide transformation of solenoid control signals from TTL to 12 VDC levels. The actual signal transformation is performed with
132

transistor (TIP 31 and MJ11028) switching. LED's are used to indicate active (12 VDC) solenoid lines. The secondary function of the board is to provide a regulated 5 VDC supply to three optical encoder lines. This is accomplished with a 7805 voltage regulator connected to the 12 VDC supplied by battery #1.
To utilize the MHB, do the following:
1) Connect a 26 line ribbon cable between the MHB and controller board (e.g. 2-
Link Controller).
2) Connect one to three 12 VDC batteries to the board via the banana plugs. (Note:
Battery #1 MUST be connected to generate optical encoder power).
Solenoid End Plug
The two Koganei solenoids used by each manipulator arm joint (R-PHAD-A) are mounted on a PVC plug. This plug is then used to seal the flotation tube of an arm boom.
The schematic shows the wiring of between the end plug 5-pin Amphenol (AMP) connector, the two Koganei 110-4E1-12VDC solenoids, and the 4-pin SureSeal.
NMIS-0021 RS-422 XCVR
Although this circuitry appears in the New Micro's "100 Squared" system documentation, and is intended for use with the "100 Squared" microcomputer, it works perfectly with the "2x4" microcomputer as well. The function of the circuit, as might be inferred from the name, is to provide transmission/reception of RS-422 serial communications signals. To utilize the RS-422 XCVR, connect the SO line to the "2x4" SI line and the SI line to the "2x4" SO line. RS-422 receive and transmit lines should then be connected to the appropriate lines. For more details, consult the "100 Squared" system documentation or the TI databook for the 75176 chip.
NMIS-0021 Quadrature Decoder
This circuit is designed to be constructed on a New Micro's NMIS-0001 prototype expansion board and to provide a rNMIS-0021 (New Micro's "2x4" microcomputer) with the capability to decode three quadrature input signals. The design utilizes two '139 decoders and three HCTL-2000 chips. Though the circuitry is straightforward, verification of successful function has not been accomplished at this time.

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I-- I I- I ·r -e- --
This appendix contains design drawings for the Stewart Platform Augmented
Manipulator. All dimensions are given in English Standard decimal and fractional units.
The drawings are categorized into the following six groups:
R-PHAD-A
R-PHAD-B
Schematics and detailed drawings for the R-PHAD-A used for the SPAM Manipulator Arm shoulder and elbow joints.
Schematics and detailed drawings for the R-PHAD-B intended for the SPAM Manipulator Arm waist joint.
Arm Booms
Schematics and detailed drawings for the arm boom tubes used in the SPAM Manipulator Arm.
Detailed drawings for the adjustable hinge used as the SPAM Stewart Platform/Manipulator Arm coupling
Schematics and detailed drawings for the Universal
Joint used in the SPAM Stewart Platform.
Schematics for the layout of the SPAM Stewart
Platform.
All drawings were current as of 6 May 1990.
140

R-PHAD-A Drawings
141

R-PHAD-A Drawings
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I~~~~~~~~~~~~~~~~~~

Appendix C
- I I --II -- d I I I JI -
This appendix contains a complete listing of the software used to operate and test
the Stewart Platform Augmented Manipulator. All software code vas written for the
Microsoft C v5.1 Optimizing Compiler and is intended to be run on an IBM PC/XT,
PC/AT or compatible. All of the software generates color video display and assumes that an
IBM CGA or CGA-emulating video card is present. Additionally, the manipulator arm control software (noted below) requires that the Manipulator Controller board (see
Appendix A) be installed due to hardware signals used for control loop timing.
The following software is described in this appendix:
SPAM
PHAD
SPAM2
SPLAT
QUADOBS
Open-loop and closed-loop control of a single R-PHAD-A joint. Requires the Manipulator Controller.
Open-loop and closed-loop control of a single L-PHAD joint Code is identical to SPAM software except for small modifications. Details of differences are given in the listing. Requires the Manipulator Controller.
Open-loop and closed-loop control of a 2-link planar manipulator with R-PHAD-A joints. Requires the
Manipulator Controller.
Stewart Platform kinematic testing. Intended to control the
Stewart Platform, but hardware interfacing and coding was not completed.
Quadrature position sampling. Requires the Quadrature
Observer (see Appendix A).
All code listings were generated on 4 May 1990.
185

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