Design of a Humanoid Biped for Walking Research
by
Daniel Joseph Paluska
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
Master of Science
at the
OCT 0 2 2003
LIBRARIES
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2000
@ Massachusetts
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
Institute of Technology 2000
LIBRARIES
Signature of Author
Department of Mechanical Engineering
August 31, 2000
Gill A. Pratt
Assistant Professor of Electrical Engineering and Computer Science, MIT
Thesis Supervisor
C ertified by ................................
.
Certified by........
Ernesto Blan6'0-Adjunct Professor of Mechanical Engineering, MIT
Thesis Supervisor
A ccepted by ......................................
Ain onin
Chairman, Departmental Committee on Graduate Students
Design of a Humanoid Biped for Walking Research
by
Daniel Joseph Paluska
Submitted to the Department of Mechanical Engineering
on August 31, 2000, in partial fulfillment of the
requirements for the degree of
Master of Science
Abstract
This thesis presents the design of the robot M2. The primary motivation behind the work is to
create a platform for research into bipedal walking. Bipedal robots have been built in the past, but
most of them relied heavily on lessons from robotic arm research. There is evidence that suggests
actuation and design for legged locomotion should deviate from the past standard of robotic arm
design. Specifically, there should be an emphasis on low impedance actuation, shock tolerance,
passive control mechanisms, and weight reduction. Human data which supports these points is
presented.
The robot M2 was designed with these things in mind. M2 is a humanoid bipedal robot with
twelve active degrees of freedom. It is essentially a torso and two legs and with linear dimensions of
a 50th percentile US male. It weighs approximately 60 lbs(25kg). All the active degrees of freedom
are powered using Series Elastic Actuators, which provide force control and shock tolerance. For
simplicity, degrees of freedom above the hip are absent.
Thesis Supervisor: Gill A. Pratt
Title: Assistant Professor of Electrical Engineering and Computer Science, MIT
Thesis Supervisor: Ernesto Blanco
Title:Adjunct Professor of Mechanical Engineering, MIT
3
Acknowledgments
The development of the robot has been a three person project from the beginning. Jerry Pratt
and David Robinson worked on the robot with me. Jerry performed preliminary simulations to
determine feasibility of mass distributions and power requirements. David Robinson is responsible
for the actuator design. I also had lots of help from Ben Krupp and Chris Morse who each had there
own robot to build in the process. Pete Dilworth contributed plenty of tips from his own bipedal
robot building experience. Allen Parseghian has been working hard with me trying to get the robot
to actually walk. John Hurst has helped with debugging some actuator problems and designing a
battery rig. Thanks to Mike Wessler and Andreas Hofmann for creation of and help with software
tools. Thanks to Chris Barnhart for developing the DSP platform and handling my ignorance of all
things DSP.
During the construction, I had help from many people. We had several soldering parties in the
lab which involved people sitting around the main lab table soldering. Jerry, Ben, Chris, Mike,
Gaddy, Pete, and others participated in these. In addition, Jess helped me with cable making and
was an immense help with my supposed native language.
Professor Pratt has been a wonderful advisor. I am constantly amazed at how he has always
placed his students first. I have loved working in the lab and getting to play around!
Special thanks goes to my friends and family who have made the time outside the lab great!
You've kept me sane during the worst of thesis despair.
This research was supportd by DARPA under contract number N39998-00-C-0656.
Contents
1 Introduction
1.1
1.2
2
Human Characteristics
2.1 The Human Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
11
2.2
4
5
9
10
2.1.1
3
9
Goals of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Weight Distribution
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Link Lengths . . . . . . . . . . . . .
Human Motion . . . . . . . . . . . . . . . .
2.2.1 Energetics of Human Walking . . . .
2.2.2 Human Kinetic and Kinematic Data
Robots and Actuators
3.1 Robotic Arms vs. Robotic
3.2 Passive Dynamic Walkers
3.3 Powered Bipedal Walkers
3.4 Series Elastic Actuators .
11
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19
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24
25
Electronics and Control Systems
5.1 Electronics Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
27
W alkers
. . . . .
. . . . .
. . . . .
Robot Mechanical Design
4.1 General Robot Architecture
4.2 The Design . . . . . . . . .
4.2.1 Overall Structure . .
4.2.2 Actuators . . . . . .
4.2.3 Ankle . . . . . . . .
4.2.4 Foot . . . . . . . . .
4.2.5 Hip . . . . . . . . .
4.2.6 Knee . . . . . . . . .
5.1.1
5.2
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48 Volt bus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Robot Sensors . . . . . . . . . . .
Custom Circuit Boards . . . . . . . . . . .
5.2.1
The Signal Conditioning Boards .
5.2.2
The Analog Force Control Boards
5.2.3
The Analog Breakout Board . . .
5.2.4 The Power Distribution Boards . .
5.2.5
5.3
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27
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31
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The DSP and Analog I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
Control Software
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4
31
5
CONTENTS
A Joint Math
A .1 K nee Joint . . . . . . . . . . . . . . . . . . . . . . .
.........................................
A.2 Ankle Joint .........
A .3 H ip Joint . . . . . . . . . . . . . . . . . . . . . . . .
A .3.1 H ip P itch . . . . . . . . . . . . . . . . . . . .
A .3.2 Hip Roll and Yaw . . . . . . . . . . . . . . .
34
. . . . . . . . . . . . . . . . . . 34
36
. . . . . . . . . . . . . . . . . . 37
. . . . . . . . . . . . . . . . . . 37
. . . . . . . . . . . . . . . . . . 37
B Electrical Schematics
39
C Suppliers and Costs
C .1 C osts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
53
List of Figures
2-1
The X velocities of the various parts of the body during a normal walking cycle.
Adapted from data in Winter(20). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2 The frontal plane dimensions of a 50th percentile U.S. male. Adapted from data in
Dreyfus(2). All dimensions are in inches. . . . . . . . . . . . . . . . . . . . . . . . . .
2-3 Several strides of the compass gait shown with corresponding potential and kinetic
energy curves. From Krupp(8).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-1
3-2
Some previous powered bipedal walking robots. . . . . . . . . . . . . . . . . . . . . .
An annotated rendering of the Series Elastic Actuator which is used in the robot M2.
Modeled and rendered by David Robinson. . . . . . . . . . . . . . . . . . . . . . . .
12
13
14
17
18
4-1
A photo of the completed robot and a joint schematic view of the robot. The schematic
shows active degrees of freedom only. The optional passive toe joint is not shown. .
4-2 The dimensions of the biped in the frontal plane. The body and links are approximately axially symmetric about their longitudinal axis. Dimensions are in inches.
4-3 A schematic of the ankle joint actuation scheme. The axes shown are fixed to the
center of the universal joint. The points A,E, and 0 are referenced in Appendix A.
4-4 The dimensions of the biped foot with passive toe joint. The X's represent the location
of the load cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-5 A schematic of the biped hip. The pitch actuator is not shown. It lies along the axis
of the thigh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-6 A photo of the biped thigh illustrating the hip pitch cable drive system. . . . . . . .
4-7 The ranges of motion on the robot ankle joint. The ankle roll is symmetric(+- 20 deg).
4-8 The range of motion of the robot knee. The knee has 80 degrees of motion. . . . . .
20
21
23
23
24
24
25
26
5-1
An overview of the biped electronics. Thick lines indicate power transfer and arrowheads indicate information flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2 A photo of M2 with annotations of electrical systems. . . . . . . . . . . . . . . . . .
5-3 A photo of the biped strain gauge signal conditioning board. This board handles two
strain gauges. There are a total of four of these boards on the robot. . . . . . . . .
5-4 A photo of the analog force control and joint pot buffer board. There are six identical
boards on the robot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-1 The robot knee joint with superimposed lines and points. Points 0, A and M all refer
to pin joints. 0 is the knee joint. M is where the actuator is mounted to the thigh
and A is where the actuator is attached to the shin. . . . . . . . . . . . . . . . . . .
A-2 A line drawing of the knee for the calculation of knee actuator desired force. The
actuator is the line segment MA. This drawing also pertains to the geometry of the
hip and ankle joints but the hip and ankle actuators have motions out of the plane
whereas the knee actuator is always in the plane perpendicular to the knee axis. . .
6
28
29
30
30
35
35
LIST OF FIGURES
A-3 A simple view of the actuation of the robot ankle. This is a tranverse plane slice of
the robot ankle. Point 0 is the intersection of the X and Y axes as well as the center
of the ankle universal joint. Points Al and A2 represent the attachment points of the
two actuators respectively. Forces in the actuators create torques about both the X
and Y axes. Joint rotations change the relative lengths of the X and Y projections(rz
and ry) of the moment arms, therefore affecting the torque to force transformation.
A-4 The robot hip joint schematic. Point 0 refers to the hip universal joint. The Z(hip
yaw) and Y(hip roll) axes intersect at point 0. Point Mr refers to the universal joint
on the body where the roll actuator is mounted. Point A, refers to the ball joint on
the thigh where the roll actuator is attached. Point MY refers to the pin joint where
the yaw actuator is attached to body. Point Ay is the pin joint attachment of the yaw
. . . . . . . . .
actuator to the yaw universal block. It is hidden in this schematic.
Page 1 of 6 of the biped force board. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page 2 of 6 the biped force board. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page 3 of 6 of the biped force board. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page 4 of 6 the biped force board. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page 5 of 6 of the biped force board. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page 6 of 6 the biped force board. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Page 1 of 2 of the strain gauge conditioning board. . . . . . . . . . . . . . . . . . . .
Page 2 of 2 of the strain gauge conditioning board. . . . . . . . . . . . . . . . . . . .
Page 1 of 1 of the analog I/O breakout board. This board is designed to interface
with the ANA070 and ANA064 from Digital Designs and Systems. . . . . . . . . . .
B-10 Page 1 of 1 of the M2 power distribution board. This board has two different population options. One to power the DSP and one to power the Intersense IS-300 tracker.
B-1
B-2
B-3
B-4
B-5
B-6
B-7
B-8
B-9
7
36
37
40
41
42
43
44
45
46
47
48
49
List of Tables
2.1
2.2
4.1
Human Mass Distribution. From Dempster(3). . . . . . . . . . . . . . . . . . . . . .
Human walking parameters from normalized data contained in Human Walking(18).
Forces and power calculated for a for 1.83 m(6'2"), 80 kg(1781b) person. Table displays
non-concurrent maximum values which occur during an average walking cycle. . . .
11
15
Robot Joint Specifications. Torque and rad/s numbers are given for maximum moment arm. Power, torque, and velocity are symmetric due to the actuator. *The
ankle roll and pitch are not independent. Their maximum values can not be applied
sim ultaneously. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Approximate distribution of mass in humans, the biped M2, and McGeer's kneed passive dynamic walker(PDW). Human data adapted from Dempster and Gaughran (3).
Robot weight distribution is driven primarily by actuator locations. Each actuator is
approxim ately 1.2kg(2.5 lbs). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
Circuit Boards on the Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sensors on the Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
28
C.1 Basic robot budget. See Robinson et al.((17)) for more detail on the actuator. This
budget does not include prototyping or development costs. Part quantities and individual costs are not necessarily meant to imply identical parts but rather to give an
average price for all units of a certain type. . . . . . . . . . . . . . . . . . . . . . . .
54
4.2
5.1
5.2
8
19
Chapter 1
Introduction
1.1
Goals of Thesis
The goal of this research project was to design a three dimensional, free standing bipedal robot. The
main goal of the biped, M2, is to be a testbed for control ideas and walking research. Originally
the robot was not specifically 'humanoid,' but after a bit of research we determined it would be the
best course of action for several reasons.
" There is a vast amount of data regarding human form and motion.
" The robot can be considered a human replacement for hazardous situations.
" The robot will be large enough to avoid problems of miniaturization.
" Ideas regarding human control of locomotion can be tested.
This thesis concentrates on documenting the mechanical portion of the project. The design of
the robot was guided by several specific goals which include walking 1 m/s, climbing normal stairs,
looking biological, turning dynamically, a three year life-span, and ten hours working time between
mechanical or electrical failures.
The following points dominated the design decisions of the robot.
1. Series Elastic Actuators Series Elastic Actuators(12) are used for all of the active degrees
of freedom. These actuators provide force control as well as shock tolerance. Evidence suggests both factors are necessary for the task of biologically similar walking. The low output
impedance of the actuators allows us to take advantage of the robot's natural dynamics. All
joints employ the same actuator design to minimize complexity and facilitate repairs.
2. Human Proportions The use of human proportions allows for easy comparison with biomechanics data. Human sizing also allows for use of large, standard components which are easy
to see and debug. Also, by using human proportions, the research stays focused on walking
and not on miniaturization.
3. Lightweight The robot frame is carbon fiber and most other components are plastic or aluminum. The necessary actuator forces are kept low. A less massive robot is more manageable
in a research environment. It is easier to handle and less likely to damage itself or harm
researchers.
4. Mechanical Control Mechanisms Each joint (most importantly the knee) has adjustable
stops with rubber pads. The foot of the robot is equipped with a passive toe joint. This
joint has an adjustable range as well as a return spring. The limit stops are essentially high
frequency non-linear PD loops which are difficult to implement in digital control even with the
use of sophisticated electronics and sensors. The low impedance actuators allow for uncertain
9
CHAPTER 1.
INTRODUCTION
10
contact, an inevitable occurence during walking on rough terrain. These mechanical features
eliminate the need to operate any digital high frequency control loops on the robot.
The robot is a three dimensional continuation of the work that began with the planar robot Spring
Turkey(13) and continued with the planar robot Spring Flamingo(15). The previously enumerated
points are the key areas where M2 differs from some other current three dimensional humanoid
walkers(6, 21) which rely more on high impedance actuation and trajectory following control schemes.
1.2
Summary of Thesis
This thesis presents the design of the humanoid robot M2.
" Chapter 2 describes the human mechanisms and the forces, torques, velocities, etc. which are
exhibited during a normal walking cycle. The human is a good starting point for the design
of the robot. Human locomotion is well documented and there is a wealth of information on
the human walking motion.
" Chapter 3 describes previous robots and actuators. It presents some of the differences between
robotic arm and walking robot technology. There is a brief introduction to Series Elastic
Actuators.
" Chapter 4 describes the mechanical specifics of the robot.
" Chapter 5 details the electronic, sensor, computer, and control systems on the robot.
* Chapter 6 gives some conclusions and some advice for future research.
" Appendix A describes the transformations from joint torques to actuator linear forces.
" Appendix B contains all the schematics for the custom circuit boards on the robot.
" Appendix C has a list of all of the suppliers that were used.
Chapter 2
Human Characteristics
There is a large database of knowledge regarding both the human form and human motion. We
believe that mechanical characteristics found in humans aid in the control of walking and we should
try to consider which of these characteristics can be embodied with current mechanical and robotic
technologies.
2.1
The Human Form
2.1.1
Weight Distribution
An approximation of the human weight distribution is shown in Table 2.1.
From this we can see that nearly 70% of the mass in humans is located at the waist and above.
Figure 2-1 shows the linear velocities(in the walking direction, X) of different body areas. It can
be seens that the body has the least fluctuation in forward velocity and the foot has the most
fluctuation.
Since kinetic energy is a direct function of velocity, the lower extremities have the greatest
fluctuations in kinetic energy. It is clear that more mass at the feet means more energy change.
If this energy is all lost it would be very costly. In efficient walking, the mass is able to resonate
with gravitational or elastic potential energy. An example of this can be seen in the compass gait
described in the next section.
2.1.2
Link Lengths
The dimensions of a 50th percentile male are shown in Figure 2-2. The center of gravity is just
above the hip at approximately 38".
Table 2.1: Human Mass Distribution. From Dempster(3).
Body Area
Head, neck, Shoulders, Thorax
Arm
Ab/Pelvic
Thigh
Shin and foot
Percentage per Part
31%
5%
27%
10%
6%
11
No. of Instances
1
2
1
2
2
Total Mass Percentage
31%
10%
27%
20%
12%
12
CHAPTER 2. HUMAN CHARACTERISTICS
-
ribcag(
/
4
/
/
3
~
,~.
..
-
shin t-p
knee
-
I
/
I
-
/,.
--
ankle
--
toe
-1
*Ij
1
'-I
4j
2
0
1
0
5
10J
15
20
25
30
3
0
4
50
55
60
65
1
-1
Frame Number
Figure 2-1: The X velocities of the various parts of the body during a normal walking cycle. Adapted
from data in Winter(20).
CHAPTER 2. HUMAN CHARACTERISTICS
13
-69.10
6.10
60.20
56.70
i
L
7.00
(Hip Spacing)
14.20
LI
-KHI
36.50
19.80
0
I
I
I
I
3.20
3.90
-
0
Figure 2-2: The frontal plane dimensions of a 50th percentile U.S. male. Adapted from data in
Dreyfus(2). All dimensions are in inches.
CHAPTER 2. HUMAN CHARACTERISTICS
14
KE
PE
I\
\
/
\
/
/
Figure 2-3: Several strides of the compass gait shown with corresponding potential and kinetic
energy curves. From Krupp(8).
2.2
2.2.1
Human Motion
Energetics of Human Walking
Data in Rose et al.(18) shows us that a 1801b person walking at a normal pace consumes about 320
Watts of power. It is estimated that roughly one quarter of that is mechanical power. This means
that at a comfortable pace, a 1801b human can walk with only 80 Watts of mechanical power. This
can be a somewhat depressing fact considering one of the electric motors used on the robot M2 can
output 90 Watts continuously - and there are 12 motors on the robot! Hopefully research on M2
will allow future robots to walk as mechanically efficient as a human.
A simplified human gait known as a compass gait can give us insight into the energetics of
walking. The compass gait model consists of two rigid, massless legs attached at the hip with a pin
joint. A point mass is modeled at the hip joint. With the only degree of freedom located at the hip,
the body is forced to follow an arc defined by the length of the leg. The compass gait can be seen
in Figure 2-3.
The compass biped has instantaneous, discretely changing dynamics. It simply changes from
one inverted pendulum to another when the swing leg touches the ground. Calculating the external
work on the model, namely the potential and kinetic energy of the system
PE =
MgLcosO
(2.1)
KE
MgL(1-cosO)
(2.2)
=
By graphing the equations 2.1 and 2.2 in Figure 2-3, the cyclical nature of potential energy and
kinetic energy can be seen. Note that the kinetic energy is maximum when the potential energy is
minimum and vice versa. Similar cyclical transition of potential and kinetic energy was recorded
CHAPTER 2. HUMAN CHARACTERISTICS
hip(pitch)
hip(roll)
hip(yaw)
knee(pitch)
ankle(pitch)
ankle(roll)
15
deg
rad/s
Nm
W
30,-18
8,-7
5,-15
68,8
10,-15
na
3.6,-2.0
1.6,-1.0
4.0,-3.0
5.8,-7.8
3.0,-4.2
NA
-111.0
-63.5
8.0
-71.4
-63.5
40.0
56
+-28
-16
-79.5
280
-16
Table 2.2: Human walking parameters from normalized data contained in Human Walking(18).
Forces and power calculated for a for 1.83 m(6'2"), 80 kg(1781b) person. Table displays nonconcurrent maximum values which occur during an average walking cycle.
in human subjects by McMahon (11) using force plate data to calculate the changes in mechanical
energy of the body's center of mass.
The compass gait is similar to the behavior found in the passive dynamic walkers described in the
next section. There is also evidence that humans use some passive dynamics during the gait cycle. At
the beginning of swing phase, the leg receives a tiny impulse of energy and then the natural pendulum
motion carries it forward to extension. The leg receives another tiny impulse of energy to bring it
to a sudden halt before touchdown. Electromyographic data record by McMahon (11) shows little
electrical activity in the leg muscles of humans during the swing phase at normal walking speeds.
This suggests that the leg is swinging freely during this period. In addition, electromyographic
records show significant electrical activity in leg muscles during stance.
2.2.2
Human Kinetic and Kinematic Data
There is a wealth of data from recordings of human motion. These recordings have been transferred
into data regarding joint motions and joint torques during the walking cycle. In addition, the
author relied on a rather low-tech method for extracting velocity data from the graphical position
data. Power, torque, position, and velocity data for an average human walking cycle are shown in
Table 2.2.
Chapter 3
Robots and Actuators
3.1
Robotic Arms vs. Robotic Walkers
Many high performance robotic arms and hands have been developed for use in factories, space, and
research(19). It might seem to an outside observer that these technologies could be exploited for
use in a legged robot. Most of the time this is not the case. There are several reasons why.
" Fixed vs. Floating Reference Robotic arms are generally fixed to an inertial reference
frame(factory) or a body whose mass is large enough that it can be considered fixed(spacecraft).
A walking robot is not fixed to any reference frame and has a limited set of torques which it
can apply due to its limited contact with the world.
" Onboard vs. Offboard Robot arms can often place their heavy motors at their fixed end.
Then the motors are only responsible for moving the frame of the arm and not themselves.
Because a walking robot must carry all its components, the motors support themselves as well
as the structure of the robot. Carrying power is also an issue for walking robots although most
are tethered due to battery limitations.
* Environmental Awareness Robot arms are not usually expected to perform in unknown
situations. They generally are designed for specific working conditions and their ability to
handle unexpected disturbances is limited. Ideally, walking robots are supposed to handle
rough and unknown terrain.
" Success Metrics Robotic arms are often judged on their ability to position their end effectors
precisely. Robotic walkers are usually not judged on their ability to position precisely but
rather on their ability to get from Point A to Point B without falling down.
" Impacts Most robot arms are not designed to handle impacts. Walking, however, has an
impact at every touchdown.
3.2
Passive Dynamic Walkers
Much research has been done on completely passive walking machines (5, 1, 4). Passive dynamic
walkers use Earth's gravity as a power supply. They rely on special geometry and mechanical mechanisms as control systems to achieve gaits very similar to the compass gait depicted in Figure 2-3.
Though they are not robots in the traditional sense, they can give insight into walking machines.
These 'robots' exploit passive dynamic elements and mechanical mechanisms to achieve highly efficient gaits. In the limit, a passive dynamic walker relies entirely on passive dynamic motions and
thus requires no external power source other than a small incline. Several passive legged 'robots'
such as these have been constructed and succesfully demonstrated (5, 1, 4, 9).
16
CHAPTER 3. ROBOTS AND ACTUATORS
17
Figure 3-1: Some previous powered bipedal walking robots. From top left to bottom right are
WL-10RV1 from Waseda, P2 from Honda, Toddler from UNH, the Moscow State University Biped,
SD-2 from Clemson and Ohio State, Biper from University of Tokyo, Meltran II from Mechanical
Engineering Lab in Tsukuba, and Timmy from Harvard. Figures compiled by J. Pratt.
3.3
Powered Bipedal Walkers
Many bipedal walking robots have been built over the years. Several of these robots are shown in
Figure 3-1. These biped walking robots fall into two broad categories: those which predominantly
use pre-recorded trajectory playback and those which predominantly use an algorithmic controller.
All the robots employ a high impedance actuation scheme and none take advantage of natural
dynamics.
Passive dynamics were successfully implemented in actuated robots as well. J. Pratt (16) developed algorithms that used the natural dynamics of the swing leg to efficiently control a planar
bipedal robot. More recently, J. Pratt has developed three-dimensional simulations of M2 using
passive elements such as a knee cap, a compliant ankle, and a passive swing leg to achieve natural
looking and efficient walking.
3.4
Series Elastic Actuators
Series Elastic Actuators(SEA's)(14) are actuators which have an elastic element in series with the
motor and gear train. A sensor measures the displacement of the elastic element and force is implied
by Hooke's Law, F = kx. In short, SEA's provide force control, shock tolerance, and low impedance
actuation. A more detailed account of their benefits and limits can be found in Robinson et al.(17)
A rendering of the SEA used on M2 can be seen in Figure 3-2. The brushless DC motor is
modified to have a ballscrew as its rotor. The output of the ballscrew is attached to an aluminum
CHAPTER 3. ROBOTS AND ACTUATORS
18
Figure 3-2: An annotated rendering of the Series Elastic Actuator which is used in the robot M2.
Modeled and rendered by David Robinson.
piece which is sandwiched between a set of linear compression springs. The other ends of the
springs are attached to the output of the actuator. A linear potentiometer measures the ballscrew
displacement with respect to the output shaft, thereby measuring the spring compression and giving
an indication of the force output.
On the specific SEA designed for M2(17), a simple analog PD controller is implemented to control
the spring deflection. When the output of the actuator is clamped, a force control bandwidth of
30hz is observed. The actuator is capable of outputting 300 lbs and capable of resolving forces on
the order of 1.5 lbs.
Chapter 4
Robot Mechanical Design
This chapter presents the design specifics of the bipedal robot M2.
4.1
General Robot Architecture
The robot stands approximately 5 feet high and weighs 60 pounds. The robot has 12 active degrees
of freedom. Table 4.1 lists the specifications for the joints of the robot. Power at each joint is the
same due to the single actuator design employed for all the joints. The power to the individual
degrees of freedom of the ankle joint is limited by the power of the other.
The robot joint ranges of motion were chosen based on data from humans as well as the robot
Spring Flamingo and preliminary dynamic computer simulations.
4.2
4.2.1
The Design
Overall Structure
A photo of the robot and a joint schematic view are shown in Figure 4-1. The leg of the robot has
six active degrees of freedom plus an optional passive degree of freedom in the foot. The vertical
axis, Z, is the yaw axis. The X axis is the roll axis and the Y axis is the pitch axis. The hip has
three degrees of freedom. These three degrees of freedom are made up of a universal joint (yaw and
roll) followed by a pin joint (pitch). The pitch pin joint is offset slightly(about 2cm) from the yaw
and roll axes.
The frontal plane dimensions of the robot are shown in Figure 4-2. The dimensions are very close
to the dimensions for a 50th percentile US male as given by Whitney(2). The ranges of motion are
adapted from robot simulations and data found in Rose, et al.(18), Winter(20), and Kapandji(7).
hip(pitch)
hip(roll)
hip(yaw)
knee(pitch)
ankle(pitch)
ankle(roll)
deg
80,-30
30,-20
30,-15
80,0
45,-20
20,-20
rad/s
7.3333
6.8
5.5
8.8
8.8
7.3
Nm
50
59
67
42
88*
100*
Drive Type
Pulley
Push-rod
Push-rod
Push-rod
Push-rod
Push-rod
Table 4.1: Robot Joint Specifications. Torque and rad/s numbers are given for maximum moment
arm. Power, torque, and velocity are symmetric due to the actuator. *The ankle roll and pitch are
not independent. Their maximum values can not be applied simultaneously.
19
20
CHAPTER 4. ROBOT MECHANICAL DESIGN
Sagittal
Frontal
44
Transverse
Z - yaw
Y - pittch
X - roll
Figure 4-1: A photo of the completed robot and a joint schematic view of the robot. The schematic
shows active degrees of freedom only. The optional passive toe joint is not shown.
CHAPTER 4. ROBOT MECHANICAL DESIGN
21
-60.00
16.00
7.25
(Hip Spacing)
Hip Universal
(Yaw, Roll)
40.00
37.75
37.00
Hip
Knee
Pitch Axis
Pitch Axis
/
-1
20.00
4.50
Shin and Thigh
Width
Ankle Universal
(Pitch, Roll)
I
4.00
3~
00
0
Figure 4-2: The dimensions of the biped in the frontal plane. The body and links are approximately
axially symmetric about their longitudinal axis. Dimensions are in inches.
CHAPTER 4. ROBOT MECHANICAL DESIGN
Body Part/Area
Shin & Foot (x2)
Thigh (x2)
Ab/Pelvic
Arm (x2)
Thorax to Head
Human
6%
10%
27%
5%
31%
22
Biped Robot
13.5%
11%
51 %
NA
NA
PDW
10%
15%
50%
NA
NA
Table 4.2: Approximate distribution of mass in humans, the biped M2, and McGeer's kneed passive
dynamic walker(PDW). Human data adapted from Dempster and Gaughran (3). Robot weight
distribution is driven primarily by actuator locations. Each actuator is approximately 1.2kg(2.5
lbs).
The mass distribution of the robot is dominated by the location of the actuators within the
links. As a result, the robot's mass distribution is centered lower than an average human's. Table
4.2 shows the percentage mass distributions for an average male, M2, and a planar passive dynamic
walker(10). The robot mass distribution is closer to that of a planar passive dynamic walker than to
that of a human. Due to successful computer simulations(16), it was not necessary to add additional
weight to the torso in order to put the proportions more in line with a human.
4.2.2
Actuators
The actuators used in the robot are 90W, 1.2KG Series Elastic Actuators(17). They are capable of
a maximum force of roughly 1320N (3001bs) and a maximum speed of roughly 0.28 m/s (11 in/s).
The actuators have a force control bandwidth of 30Hz. Linear actuators where chosen over rotary
actuators due to the available space in the robot. Linear actuators allowed for placement along the
longitudinal axis of the leg links. The actuators are symmetric in their power, speed, and force
capabilities.
4.2.3
Ankle
The ankle of the biped is a universal joint. The pitch axis is followed by the roll axis. This is a slight
deviation from the structure of the human ankle. The human ankle is often likened to a universal
joint where the second axis is at 45 degrees to the first rather than at 90 degrees(7). For engineering
simplicity we use a universal joint with orthogonal axes. The instantaneous power requirement for
ankle pitch is the greatest. The actuators were placed in a configuration so they can act together in
the pitch direction.
Photos of the ankle are shown in Figure 4-7 and a schematic of the ankle and its actuators are
shown in Figure 4-3. The ankle has two series elastic actuators placed along the longitudinal axis
of the shin. The actuators are mounted by a universal joint near the top of the shin and attached
to the foot by a ball and socket joint (rod-end). This is a linkage variation of a standard geared
differential. When the actuators push in unison, a moment is generated about the pitch axis. When
they push in opposite directions, a roll moment is generated.
4.2.4
Foot
Two different feet were designed for the robot. One foot is a simple rectangular design with four
single axis load cells residing at each of the corners. This foot closely resembles the foot that was
used in computer simulations in the lab. Another more involved foot was designed in order to explore
the roll of the toes in walking.
CHAPTER 4. ROBOT MECHANICAL DESIGN
23
A
Actuato
Y axi
E
0
X axi
Ball Joint
0
Figure 4-3: A schematic of the ankle joint actuation scheme. The axes shown are fixed to the center
of the universal joint. The points A,E, and 0 are referenced in Appendix A.
Heel
Ankle
Joint
.19
Toe
2.882
.
8
8Joint
ont
A_
Figure 4-4: The dimensions of the biped foot with passive toe joint. The X's represent the location
of the load cells.
The more intricate second foot of the biped robot contains a passive joint which is modeled after
the toe of a human. The joint is believed to smooth the center of mass trajectory of the body during
a walking cycle(18). The toe joint is simply a pin joint with two limit stops and a soft return spring.
Ground contact and sensing on the foot consists of four single axis load cells. One cell is placed
at the heel and three cells are placed in a triangle at the toe/ball of the foot. The three cells in the
toe are all constrained to the same plane. The three toe contact points can rotate about the foot
Y-axis with respect to the heel contact point. The layout of the sensors can be seen in Figure 4-4.
Standard through-hole button load cells are used. There is a rubber bumper which contacts the
ground roughly 0.875" in diameter attached to each load cell. On the simple four point foot there
is a rectangular pastic piece with a 0.25" piece of neoprene for grip and shock absorbtion. This can
be seen in Figure 4-7. Single axis load cells were chosen over a six axis sensor because of their size
and weight, and chosen over strain gauges because of their ease of use and quick replaceablility.
On the more complicated biped foot, force control and a passive toe joint are the reasons the
four contact points of the foot are not over-constrained. Since ankle roll is force controlled rather
than position controlled, it can adjust itself so the three points of the toe lie flat. The passive toe
24
CHAPTER 4. ROBOT MECHANICAL DESIGN
Mr
Yaw
R0
0
L
YL
Body irame
Roll
Pitch
My
Ar
Thigh
Figure 4-5: A schematic of the biped hip. The pitch actuator is not shown. It lies along the axis of
the thigh.
Figure 4-6: A photo of the biped thigh illustrating the hip pitch cable drive system.
joint(a pitch joint) then allows the fourth point on the heel to lie flat as well.
4.2.5
Hip
The biped hip has three degrees of freedom. The joint consists of a universal joint followed by a
slightly offset pin joint. A schematic of the hip is shown in Figure 4-5. The yaw axis is first and the
the yaw actuator is mounted to the body frame with a pin joint. The roll actuator is next. Since its
attachment point passes through the roll angle, it is mounted to the body by a universal joint. Its
endpoint is attached by a ball and socket joint. The pitch actuator, which is not shown, lies along
the longitudinal axis of the thigh. It is the only actuator which is attached using a cable and pulley
rather than a rod-end. The range of motion of the hip pitch joint is the largest. The moment arm
changes associated with a drive arm would be too great at the extents of the pitch motion. At sixty
degrees from the perpendicular drive position, the moment arm would be half its original length.
CHAPTER 4. ROBOT MECHANICAL DESIGN
25
Figure 4-7: The ranges of motion on the robot ankle joint. The ankle roll is symmetric(+- 20 deg).
4.2.6
Knee
The robot knee is a simple pin joint. The joint is actuated by a SEA located in the thigh. Two
photos demonstrating the range of motion of the knee can be seen in Figure 4-8.
CHAPTER 4. ROBOT MECHANICAL DESIGN
Figure 4-8: The range of motion of the robot knee. The knee has 80 degrees of motion.
26
Chapter 5
Electronics and Control Systems
5.1
Electronics Overview
The basic electronic subsystems of the robot are shown in Figure 5-1. The robot is powered by a
48 Volt power supply. There is also an Ethernet connection not shown in the figure which can be
used to load control code and retrieve data from the on-board computer. The circuit boards are
summarized in Table 5.1. The sensors are summarized in Table 5.2.
All signals are sent and received differentially between the computer and the analog boards.
5.1.1
48 Volt bus
All the electronics on the robot receive power from a 48 Volt bus. The current setup has the robot
connected to several offboard 48V power supplies. All the electronics were designed with this power
bus in mind. The voltage choice was dictated by the brushless motor amplifiers. It was also chosen
because it is a standard voltage and the robot will eventually be augmented with batteries for future
autonomous demos.
5.1.2
Robot Sensors
The robot is equipped with a total of 33 sensors. There are 12 rotary potentiometers that are used
to measure joint position and this is differentiated to give the joint velocity. The joint position
measurements are relative displacements between joints. There are 12 linear potentiometers which
measure the spring compression in the Series Elastic Actuators. These signals are local to the analog
force control loop only. They are not used by the DSP in the control. There are 8 single axis load
cells on the feet of the robot. These sensors are connected to the strain gauge conditioning board
which amplifies and buffers the signal on its way to the DSP. There is a single Intersense Inertia
Table 5.1: Circuit Boards on the Robot
Motor Amplifiers
DSP
ANA074
ANA063
Analog Force Control Board
Power Distribution Board
Signal Conditioning Board
IS-300 Signal Conditioner
QTY
12
1
1
1
6
2
4
1
27
Voltage Input
+48
+5
5,12
5,12
+48
+48
12
+12
Vendor
Copley Controls
Dideas
Dideas
Dideas
Leg Lab
Leg Lab
Leg Lab
Intersense
CHAPTER 5. ELECTRONICS AND CONTROL SYSTEMS
28
Table 5.2: Sensors on the Robot
Sensor
Rotary Potentiometers
Linear Potentiometers
Single-Axis Load Cells
3-axis inclinometer
QTY I Voltage Input
12
+-5
12
+-5
8
+-9
1
NA
Vendor
Bourns
Novotechnik
Transducer Techniques
Intersense
48Volt bus
Vesibla Snsrs
Brushless
Motor Amp
Actuator
Computer
A/D and D/A
C
Analog PID
Regulated 5V
Buffers
S
-Power
-+-5
+- 12
Instrumentation
L
,
Joint
Pots
Load Cells
Figure 5-1: An overview of the biped electronics. Thick lines indicate power transfer and arrowheads
indicate information flow.
CHAPTER 5. ELECTRONICS AND CONTROL SYSTEMS
29
CubeTM which measure the roll, pitch, and yaw(magnetic) of the robot body. The Inertia Cube is
connected to a IS-300 motion tracker unit which communicates with the DSP through a RS-232
serial line. Table 5.2 provides a summary of the robot sensors. Figure 5-2 contains an annotated
photo of M2 with the sensor locations.
Figure 5-2: A photo of M2 with annotations of electrical systems.
5.2
5.2.1
Custom Circuit Boards
The Signal Conditioning Boards
The signal conditioning boards are four layer printed circuit boards. They have a ground plane, a
power plane, and two routing layers. The signal conditioning boards handle two 350 ohm wheatstone
bridge sensors each. They have adjustable gain and offsets.
5.2.2
The Analog Force Control Boards
The analog force control board provides two channels of PID force control for the Series Elastic
Actuators and two channels of joint potentiometer buffering and differentiation. The analog force
control boards have a 48 Volt power input and communicate with the DSP through differential
amplifiers and receivers.
The analog force control boards are four layer printed circuit boards. They have a ground plane,
a power plane, and two routing layers.
CHAPTER 5. ELECTRONICS AND CONTROL SYSTEMS
30
Figure 5-3: A photo of the biped strain gauge signal conditioning board. This board handles two
strain gauges. There are a total of four of these boards on the robot.
Figure 5-4: A photo of the analog force control and joint pot buffer board. There are six identical
boards on the robot.
CHAPTER 5. ELECTRONICS AND CONTROL SYSTEMS
5.2.3
31
The Analog Breakout Board
The analog breakout board connects to the ANA070 and ANA064 analog input and output boards.
It has no power and simply allows for the use of smaller connectors to easily distribute the 64
channels of analog input and output from the ANA070 and ANA064 boards. There are two 64 pin
connectors which connect to the ANA064 and ANA070 boards respectively. Then there are multiple
3,5, and 10 pin connectors which connect to the signal conditioning boards and analog force control
boards. The analog breakout board is a two layer printed circuit board.
5.2.4
The Power Distribution Boards
The power distribution board has a 48 Volt input and outputs a variety of lower voltages. It appears
in two places on the robot. There is one printed circuit for the two power distribution boards but
there are two different DC-to-DC converters which are used when assembling the board.
* Board Configuration 1 This board supplies power to the DSP (+5V) and two analog boards
(+-12V, +-5V). The analog and digital grounds are isolated.
e Board Configuration 2 This board provides power to the Intersense IS-300(+12V) and the
four signal conditioning boards (+-12V).
The power distribution boards are four layer printed circuit boards. They have a ground plane,
a power plane, and two routing layers.
5.2.5
The DSP and Analog I/O
M2 has a custom DSP system that was designed by Chris Barnhart at Digital Designs and Systems.
The DSP is a Texas Instruments C-31. There are three circuits boards that make up the system.
1. DSP. Mulitple Serial Lines and Digital I/O.
2. 16 Analog Ins, 16 Analog Outs, and Ethernet.
3. 32 Analog Inputs.
5.3
Control Software
Control code for the robot is written in C. It is compiled offline on a Unix machine and downloaded
to the robot via Ethernet. The main robot control code runs at 500Hz on the DSP and sends desired
forces to the analog boards. Currently, the control system treats the actuator and analog boards as
a 'black box' force source. This means it is assumed that the desired force sent out to the actuator
is the actual force applied to the joint. This is true within the realm of frequencies needed for
walking(less than 15Hz). The analog boards have PD control loops for the Series Elastic Actuators.
The analog boards also buffer and differentiate the joint potentiometers and send the information
to the DSP.
This is similar to the electronics used for Spring Flamingo. The main differences are the addition
of Ethernet for faster communication with the outside world and differential send and receive for
signals within the robot.
Bibliography
[1] Jesper Adolfsson, Harry Dankowicz, and Arne Nordmark. 3-d stable gait in passive bipedal
mechanisms. Proceedings of 357 Euromech, 1998.
[2] Henry Dreyfus Associates. The Measure of Man and Woman. Whitney Library of Design, New
York, 1993.
[3] W.T. Dempster and G. Gaughran. Properties of body segments based on size and weight.
American Journal of Anatomy, 1965.
[4] J. Fowble and A. Kuo. Stability and control of passive locomotion in 3d. Proceedings of the
Conference on Biomechanics and Neural Control of Movement, pages 28-29, 1996.
[5] Mariano Garcia, Anindya Chatterjee, and Andy Ruina. Speed, efficiency, and stability of
small-slope 2d passive dynamic bipedal walking. IEEE International Conference on Robotics
and Automation, pages 2351-2356, 1998.
[6] K. Hirai, M. Hirose, Y. Haikawa, and T. Takenaka. The development of honda humanoid robot.
IEEE International Conference on Robotics and Automation, 1998.
[7] Ibrahim Adalbert Kapandji. The Physiology of the Joints. Churchill Livingstone, 1982.
[8] Benjamin Krupp. Design and control of a planar robot to study quadrupedal locomotion.
Master's thesis, Massachusetts Institute of Technology, August 2000.
[9] Tad McGeer. Passive dynamic walking. International Journal of Robotics Research, 9(2):62-82,
1990.
Passive dynamic biped catalogue.
[10] Tad McGeer.
Symposium of Experimental Robotics, 1991.
Proceedings of the 2nd International
[11] Thomas A. McMahon. Mechanics of locomotion.
Reasearch, 3(2):4-28, 1984.
The International Journal of Robotics
[12] Gill A. Pratt and Matthew M. Williamson. Series elastic actuators.
Conference on Intelligent Robots and Systems, 1:399-406, 1995.
IEEE International
[13] J. Pratt, P. Dilworth, and G. Pratt. Virtual model control of a bipedal walking robot. IEEE
International Conference on Robotics and Automation, pages 193-198, 1997.
[14] Jerry E. Pratt. Virtual model control of a biped walking robot. Master's thesis, Massachusetts
Institute of Technology, August 1995.
[15] Jerry E. Pratt and Gill A. Pratt. Exploiting natural dynamics in the control of a planar bipedal
walking robot. Proceedings of the Thirty-Sixth Annual Allerton Conference on Communication,
Control, and Computing, pages 739-748, 1998.
[16] Jerry E. Pratt and Gill A. Pratt. Exploiting natural dynamics in the control of a 3d bipedal
walking simulation. Proceedings of the International Conference on Climbing and Walking
Robots (CLAWAR99), 1999.
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BIBLIOGRAPHY
33
[17] David W. Robinson, Jerry E. Pratt, Daniel J. Paluska, and Gill A. Pratt. Series elastic actuator development for a biomimetic robot. IEEE/ASME International Conference on Advanced
Intelligent Mechatronics, 1999.
[18] Jessica Rose and James G. Gamble. Human Walking. Williams and Wilkins, 1994.
[19] Mark Roshiem. Robot Wrist Actuators. John Wiley and Sons, Inc., 1989.
[20] D. A. Winter. Biomechanics and Motor Control of Human Movement. John Wiley and Sons,
Inc., New York, 1990.
[21] Jinichi Yamaguchi, Eiji Soga, Sadatoshi Inoue, and Atsuo Takanishi. Development of a bipedal
humanoid robot - control method of whole body cooperative dynamic biped walking. IEEE
International Conference on Robotics and Automation, pages 368-374, 1999.
Appendix A
Joint Math
Since all of M2's rotary joints are actuated by linear actuators, transformations are needed to get
from joint torques to actuator forces. These are dependent upon the joint layout and actuation
scheme. If the force is known, the torque is somewhat easily computed using the formula, T = ix F.
operation can be rewritten as a matrix multiplication T = AF
xF
The cross product T =
where A is a singular matrix.
7 = r XF
j
i
rI
r2
F1
F2
k
r3
F3
=
0
-r 3
r2
r3
0
-ri
-r2
r1
0
f
=
AF
(A.1)
However, if the cross-product is written as 7 =R Fl sin(O) then we can easily invert. In the
case of most of the robot joints, this requires use of the arctan function or the law of cosines to
find the angle 0. In general, the direction of F is fixed by the geometry of the joint and F1 is the
quantity of real interest.
A.1
Knee Joint
The knee joint is a single degree of freedom rotary joint allowing relative motion between the shin
and the thigh. When all the joints of the robot are zero(it is standing with locked knees), the knee
axis is parallel to the global Y axis. Rotation about the knee joint is referred to as pitch.
The knee actuator is connected to the knee joint via a push rod of length 1OA1 = rk at the shin
and a fixed pin joint at the thigh.
The knee joint has three points of interest which we will use for the derivation of the transformation. The knee pivot 0, the actuator pushrod attachment A, and the actuator mounting pivot
M. The robot knee joint and points can be seen in Figure A-1 and a simple line drawing is seen in
Figure A-2.
r= r x F
(A.2)
rk sin(ZOAM)Fknee
The actuator force required given Tk is
Fke7
nee
where Fknee is a scalar and
ZOAM
=Of
ixed +
(A. 3)
rk sin(ZOAM)
ZOAM can be defined as follows
Ok -
ZAM
Of ixed + Ok -
34
arctan r sin(Ofixed + 9 k)
L 1 + r sin(Ofixed
-
+ Ok)
(A.4)
35
APPENDIX A. JOINT MATH
Figure A-1: The robot knee joint with superimposed lines and points. Points 0, A and M all refer
to pin joints. 0 is the knee joint. M is where the actuator is mounted to the thigh and A is where
the actuator is attached to the shin.
L
Oknee
A
M
/ Ofixed
LMA
Figure A-2: A line drawing of the knee for the calculation of knee actuator desired force. The
actuator is the line segment MA. This drawing also pertains to the geometry of the hip and ankle
joints but the hip and ankle actuators have motions out of the plane whereas the knee actuator is
always in the plane perpendicular to the knee axis.
APPENDIX A. JOINT MATH
36
X
x
r
r
A2 $
Al
ry
Figure A-3: A simple view of the actuation of the robot ankle. This is a tranverse plane slice of
the robot ankle. Point 0 is the intersection of the X and Y axes as well as the center of the ankle
universal joint. Points Al and A2 represent the attachment points of the two actuators respectively.
Forces in the actuators create torques about both the X and Y axes. Joint rotations change the
relative lengths of the X and Y projections(r, and ry) of the moment arms, therefore affecting the
torque to force transformation.
The angle between the shin and the thigh is Ok and the constant, Of ixed, is the angle between the
shin and the segment OA. It is also possible to derive the equations avoiding the inverse tangent by
using the law of cosines.
It would be possible to simplify the equations a bit by assuming the actuator is always parallel
to the thigh, i.e. ZAM = 0. This simplifies the equations and shouldn't reduce accuracy much
considering that L, > L 2 . Equation A.3 then becomes
(A.5)
Fknee =
rk sin(Of ied
+ Ok)
where Fknee is once again a scalar quantity.
A.2
Ankle Joint
The ankle joint is a universal joint(2 d.o.f.) allowing relative motion between the foot and the shin.
When all of the joints of the robot are zero, the axes of the ankle joint line up with the global X
and Y axes. The Y axis is proximal to the shin. Rotation about the Y axis is referred to as pitch
and rotation about the X axis is referred to as roll. The math for the ankle is an extension of the
math for the knee.
We can consider the ankle as two decoupled cases of the knee joint. Then one can simply add
the forces from Tr7oll and Tapitch. There is a slightly more complicated analogy to the knee in two
planes of the ankle. The ankle roll considers what is happening in the XZ plane and the ankle pitch
considers what is happening in the YZ plane. Both planes are coming out of the page in Figure
A-3. Each plane looks similar to the knee diagram shown in Figure A-2. The main difference is that
OA = r is a function of the other ankle angle.
37
APPENDIX A. JOINT MATH
R
Mr
Yaw
L
Roll
L
Body trame
Yaw
Pich
MY
Ar
Thigh
Figure A-4: The robot hip joint schematic. Point 0 refers to the hip universal joint. The Z(hip
yaw) and Y(hip roll) axes intersect at point 0. Point M, refers to the universal joint on the body
where the roll actuator is mounted. Point A, refers to the ball joint on the thigh where the roll
actuator is attached. Point MY refers to the pin joint where the yaw actuator is attached to body.
Point Ay is the pin joint attachment of the yaw actuator to the yaw universal block. It is hidden in
this schematic.
A.3
Hip Joint
A.3.1
Hip Pitch
The math for the hip pitch is the simplest of all the joints since the hip pitch actuator is attached
by a pulley. The desired torque at the joint(Thp), leads to the force(fhp) command to the hip pitch
linear actuator.
fA
-
(A.6)
Thp
Thippitch
The transformation from actuator velocity to joint velocity is quite simple as well.
Whp
A.3.2
(A.7)
Velhp
Hip Roll and Yaw
The yaw actuator transformation is identical to that of the knee actuator except for the addition of
a small term which can be ignored with little affect.
The actuator force required given Thya, is
F
-ya'
Thyaw
sin(/OyAyMy)
6
hroll
(A.8)
where E is a small factor due to the torque applied to hip roll which is a function of the hip roll
and yaw angles. Oy, Ay, and My are defined as they were in the case of the knee.
APPENDIX A. JOINT MATH
38
The actuator force required given Throll can be simplified to
Fhroll =hr
hr (1 + Ehyaw)
(A.9)
sin(/ZOhrAhrMh,)
The exact equation for the hip roll incorporates the yaw angle. Since the hip roll actuator
attachment point Ahr is attached to the leg below the yaw degree of freedom, the points Ohr, Ahr,
and Mhr do not always lie within the plane perpendicular to the roll axis as in the case of the knee
joint where they are fixed in the plane perpendicular to the knee axis.
When the roll actuation plane(plane formed by the three points Ohr, Ahr, Mhr) is skewed with
respect to the roll axis, a small torque will be contributed to the yaw axis. This is where the term
term in it.
Ehroll comes from in Equation A.8 and this is why the hip roll equation has the Chya,
Appendix B
Electrical Schematics
This Appendix contains the electrical schematics for all the custom circuit boards used on the robot.
The basic functionality of the boards and their role in the overall robot is decribed in more detail
in Chapter 5. There are six pages for the analog force board, 2 pages for the signal conditioning
board, 1 page for the analog breakout board, and 1 page for the power distribution board.
39
5
4
1
3
1
I
2
5
TP1
PB1
Test
Pcit
plus12
J1
+12
o:FST
GC
OUT
BC1
DC/DC
lu f
H
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+-12V
48INCONN
BC2
luf
SGND
DFC10U48D12
REG1
7N
SGNDO
GND2
TP3
I
Test
+ciOUT
GND1
GND20
GND2
GND3
GND4
2 Actuator
CD
PC2
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2
2 Joint Pot
DSP
CD
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out
to
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Appendix C
Suppliers and Costs
This section contains a list of all the suppliers that were used in development of the robot.
Digital Designs and Systems
3266 North Meridian Street
Indianapolis, IN 46208
317-931-8190
http://www.dideas.com/
microcontrollers, a/d and d/a conversion, vision systems, ready built and custom designs
Stock Drive Products
2101 Jericho Turnpike,
Box 5416
New Hyde Park, NY 11042-5416
(516)328-3300
Mechanical Parts
Berg
499 Ocean Avenue
Box 130
East Rockaway, NY 11518
(516)596-1700
Mechanical Parts
NOVOTECHNIK
237 CEDAR HILL STREET
MARLBORO, MA 01752
(508) 485-2244
Potentiometers
SMALL PARTS INC
13980 NW 58TH COURT
PO BOX 4650
MIAMI LAKES, FL 33014-3115
(800) 220-4242
Mechanical Parts
CENTURY SPRING COMPANY INC
BOX 15287
222 EAST 16TH STREET
50
APPENDIX C. SUPPLIERS AND COSTS
LOS ANGELES, CA 90015-0287
(800)237-5225
Springs
Newark Electronics
41 Pleasant Street
Methuen, MA 01844
(800) 463-9275
Electronic Parts
REC ENGINEERING COMPANY(Bob)
20 HOPKINS STREET
WILMINGTON, MA 01887-2210
(508)657-6517
Machining
Eastern Tool(Joe)
Somerville, MA
(617)497-6703
Machining
Transducer Techniques
43178 Business Pk. Dr.
Temecula CA 92590
1-800-344-3965
Load cells.
Intersense, Inc.
73 Second Avenue
Burlington MA 01803
(781)-270-0090
Multi-axis inclinometer.
Digi-Key Corporation
701 Brooks Ave. South
Thief River Falls, MN 56701-0677
(800)344-4539
Electronic Parts
Copley Controls Corporation
410 University Avenue
Westwood, MA 02090
(617)329-8200
FAX: (617)329-4055
Amplifiers
Cooner Wire Company
9265 Owensmouth
Chatsworth, CA 91311
(818)882-8311
Flexible Wire
51
APPENDIX C. SUPPLIERS AND COSTS
CFC, Inc.
179 Bear Hill Road
Waltham, MA 02154-1001
(617)890-1878
FAX: (617)890-7098
MODEM: (617)890-7193
Circuit Board Fabrication
Advanced Circuits
Colorado, http://www.4pcb.com
Circuit Board Fabrication, online ordering
NSK -linear motion division
Elmhurst, IL 60126-1016
ATTN: Sandy x2638 or Jackie x2677
tel:1-800-255-4773
fax:630-924-8197
Ballscrews
Litton Poly-Scientific
1213 North Main Street
Blacksburg, VA 24060
(828)837-5115
Attn: Barbara Smith x231
fax (828)837-0846
Brushless DC motors
McMaster Carr
BOX 440
NEW BRUNSWICK, NJ 08903-0440
(908)329-3200
Mechanical Parts
QUALITY COMPOSITES INC
8385 S ALLEN STREET No.140
SANDY, UT 84070
(801)565-8003
FAX: (801)565-8225
Carbon Fiber Tubes
Sava Industries, Inc.
4 N. Corporate Drive, P.O. Box 30
Riverdale, NJ 07457-0030
(201) 835-0882
Steel Cable, crimps and crimp tools.
Tristar Plastics
Shrewsbury, MA
800.874.7827x3203(mike rudel)
fax 508.845.1200
52
APPENDIX C. SUPPLIERS AND COSTS
53
Rulon bushings
W.S. Deans
10875 Portal Drive
Los Alamitos CA 90720
714-828-6494 Robin
Wet noodle wire
US Sensor Corp
1832 West Collins Ave.
Orange, CA 92867
714-639-1000
Terry ext 104
Thermal sensors for mo unting amps to heat sinks
Tra-Con
45 Wiggins Ave.
Bedford, MA 01730
1.800.872.2261
781.275.6363
Glue for glueing thermal sensors to amp heat sink.
Tower Hobbies
PO Box 9078
Champaign, IL 61824-9078
1-800-637-6050
Batteries and charger
C.1
Costs
This section contains the costs associated with the robot M2. Costs and quantities given do not
include spares. The general lab policy is to order 50 percent spares on everything. I think that
anyone else developing a similar robot should do the same. See Table C.1 for details.
APPENDIX C. SUPPLIERS AND COSTS
Component
Actuator, Amp
Custom Computer
CFRP frame
Machining
Vestibular
Misc Parts
PCB's
Load Cells
TOTALS
54
QTY
12
1
8
1
1
200
10
8
Each US $
1500
10,000
300
30,000
10,000
20
1,000
450
Total US $
18,000
10,000
2500
30,000
10,000
4000
10,000
3600
88,100
Table C.1: Basic robot budget. See Robinson et al.((17)) for more detail on the actuator. This
budget does not include prototyping or development costs. Part quantities and individual costs are
not necessarily meant to imply identical parts but rather to give an average price for all units of a
certain type.