Design, Development, and Dynamic
Characterization of Multi-Axis Force Sensing
Composite Footpad
AMC M
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
by
JUL 3 0 2014
Guangtao Zhang
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Submitted to the Department of Mechanical Engineering
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February 2014
@ Guangtao Zhang, 2014. All rights reserved.
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jpuary 17, 2014
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redac.ed
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Design, Development, and Dynamic Characterization of
Multi-Axis Force Sensing Composite Footpad
by
Guangtao Zhang
Submitted to the Department of Mechanical Engineering
on January 17, 2014, in partial fulfillment of the
requirements for the degree of
Bachelor of Science in Mechanical Engineering
Abstract
Accurate ground reaction force measurements are important for the development,
implementation, and control of high speed legged locomotion robots. From previous
research studies, a composite force sensing footpad has been developed, tested, and
characterized statically at the MIT Biomimetics Lab. The developed footpad sensor
must also be characterized dynamically prior to its implementation with the MIT
Cheetah robot. This study includes the design, development, and dynamic characterization of the footpad sensor.
In order to characterize the developed footpad sensor dynamically, a custom impact tester has been designed, fabricated, characterized, and verified. The developed
impact tester was shown to satisfy all the specified functional requirements and is
capable of producing a range of impact conditions to cover the possible operational
modes of the MIT Cheetah robot such as running, walking, galloping, or hopping.
The previously developed static ANN model was shown to be highly imprecise
and a dynamic ANN model was developed to better predicate the force profile during
impact. The dynamic ANN model was shown to perform 400% better at predicting
peak impact force.It was also verified with additional dynamic testings of the footpad
sensor, and RMSE = 3.17% for a maximum reference force reading of 3000N was
achieved for the developed dynamic ANN model.
The footpad sensor was redesigned and fabricated to integrate with the MIT
Cheetah robot. Numerous Cheetah robot hopping experiments were carried out, and
the footpad sensor was able to detect ground contact accurately and precisely. 'No
damage nor performance degrading of the developed footpad sensor was observed
at the end of the experimentation. Though further testing and optimization of the
composite footpad sensor is required, the developed prototype has shown promising
results under both static and dynamic conditions, which suggests that a composite
footpad force sensor is not only a viable approach for force sensing but also likely
to take place of the rigid force sensing devices in the high speed locomotion robots'
arena.
3
Thesis Supervisor: Sangbae Kim
Title: Assistant Professor
4
Acknowledgments
I would like to thank Meng Yee (Michael) Chuah (PhD candidate at MIT Biomimetic
Robotics Lab) for his guidance and collaboration on this project as well as his support
throughout the design, fabrication, and testing stages.
I would also like to thank Professor Sangbae Kim for the opportunity to work
at the MIT Biomimetic Robotics Lab, both as a UROP and a thesis student. I am
very grateful for Professor Kim's mentoring and support over the years. Through my
research projects, I have learned so much about design and conducting research that
could not be attained otherwise.
Special thanks to Dr. Hae Won Park (Postdoctoral researcher at MIT Biomimetic
Robotics Lab) for his collaboration on running the Cheetah robot experiments; Dr.
Sang Ok Seok (graduated from MIT Biomimetic Robotics Lab) for helping with high
speed camera and LabView data acquisition; Xiaowei Zhang (graduate student at
Professor Tomasz Wierzbicki's lab) for his assistance on Instron testing; and Jacques
Luk-Cyr (graduate student at Professor Lallit Anand's lab) for lending his expertise
on Finite Element Analysis (FEA) simulations.
5
6
..........53
Contents
1
Introduction
17
2
Previous Work
21
3
4
5
2.1
. . . . 21
Compliant Footpad Sensor . . . . . . . . . . . . . . .......
2.2
Static Characterization ..............
.......
. .. . . . 23
25
Impact Testing
. . .
...
3.1
Impact Tester Design.. . . . . . . . . . . . . . . . . . .
3.2
Impact Tester Fabrication . . . . . . . . . . . . . . . . . . . . ...
3.3
Characterization
27
. . .
. . . . . . . . . . . . . . . . . . . . . . .... .
3.3.1
Reference Force Reading Validity . . . . . . . .. . . . . . .
3.3.2
Repeatability . . . . . . . . . . . . . . . . . . ........
3.3.3
Operational Range..... . . . . . . . . . . . . . . . . . . . 41
..
25
29
.. 30
.
37
43
Dynamic Characterization
4.1
Experimental Setup . . . . . . . . . . . . . . . . . . ... .... 43
4.2
Results and Discussion... . . . . . . . . . . . . . . . . .
. . ..
. .
44
4.2.1
Static Model Verification . . . . . . . . . . . . . . . . . . . . . 46
4.2.2
Dynamic Model Development . . . . . . . . . . . . . . . . . .
48
4.2.3
Dynamic Model Verification . . . . . . . . . . . . . . . ...
50
53
Footpad Sensor for Cheetah Robot
5.1
Design . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2
Mold Design and Fabrication...
. . . . . . . . .. . . . . .. .
7
. . .
57
6
.... . ..71
.90
Fiberglass Enforced Polyurethane Rubber Shell . . . . . . . .
58
5.2.2
Polyurethane Plastic Backplate . . . . . . . . . . . . . . . . .
61
5.2.3
Elastomer Filling . . . . . . . . . . . . . . . . . . . . . . . . .
64
5.3
Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
5.4
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . .
Material Characterization
.1
7
5.2.1
71
M aterial Testing . . . . . . . . . . . . . . . . . . . . . . . .
onclusion
7.1
67
75
Future Work....... . . . . . . . . . . . . . . . . . . . . . . . . . 76
Appendices
81
A Dynamic ANN Model Verification
83
B Backplate Fabrication
85
C Instron Testing
87
D Material Testing Results
89
D .1 EcoFlex 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .
D.2 VytaFlex 60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
89
List of Figures
2-1
Pressure sensor array.
Top two rows are shown with the top port
removed, the bottom row shows the off-shelf sensor package. The blue
elements mounted onto the PCB board are capacitors. The green board
is the PCB and the clear block underneath PCB is the acrylic back
plate. This image is reproduced from [13].
2-2
. . . . . . . . . . . . . . .
22
Footpad sensor prototype shown next to a penny. The PCB assembly
was completely submerged within the rubber. In this image, the acrylic
back plate is at the bottom and forces are applied to the rubber surface
of the footpad sensor. This image is reproduced from [13]. ......
2-3
22
The footpad sensor was attached to a CNC mill quill while a F/T
sensor was attached to the mill table. This image is reproduced from
[13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .
3-1
. . . .
23
Schematic of the designed impact tester. The footpad sensor will be
attached to the dropping carriage. Impact velocity can be controlled by
changing the height of drop, while adding or removing weights adjusts
the magnitude of impact. The footpad sensor will be dropped onto the
force platform sensor which provides the referencing force measurements. 26
3-2
The constructed impact tester. The linear rails are vertical, with one
on each side. The dropping carriage is horizontal while two weights
were added to its top as shown. The force platform was placed right
underneath the footpad sensor, which was mounted to the bottom side
of the dropping carriage.
. . . . . . . . . . . . . . . . . . . . . . . .28
9
-3
Close up view of the footpad sensor being attached to the impact tester.
The force platform was placed right underneath the footpad sensor.
3-4
29
A screen shot of obtaining the dropping carriage's position from the
high speed video using the Tracker software. . . . . . . . . . . . . . . 30
8-5
Dropping carriage position is plotted against time. Position information was obtained from analyzing the high speed video files in the
Tracker software. Two dropping carriage weights dropped from the
same height are plotted, 1.14kg and 3.49kg.
. . . . . . . . . . . . . .
31
3-6
Both position data and quadratically fitted results are plotted. . . . .
32
3-7
Velocity of the dropping carriage (1.14kg in mass) plotted against time.
33
3-8
Referencing force plate readings when mdroingcarriage= 1.14kg.
33
3-9
Referencing force plate readings when
mdroingcarriage =
. . .
1.14kg. Zoomed
view for the first force peak. . . . . . . . . . . . . . . . . . . . . . . .
34
3-10 Comparison between triangular approximation for the first force peak
and referencing force plate readings when mdroingcarriage = 1.14kg.
35
3-11 Impact speeds of the dropping carriage determined from recorded high
speed videos plotted against the initial dropping height for two various
carriage masses. . . . . . . . . . . ... . . . . . . . . . . . . . . . . . .
38
3-12 Comparison between experimental data on impact speeds plotted against
VInitial DroppingHeight and their linearly fitted functions. . . . .
39
3-13 Peak impact force measured using the reference force platform plotted against the initial dropping height of the carriage for two various
carriage m asses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3-14 Comparison between measured peak impact force and their linearly
fitted functions.
4-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
Footpad sensor's voltage outputs plotted against time when dropped
from 10cm and mdrWing carriage
=
force is also plotted against time.
10
1.14kg.
The measured reference
. . . . . . . . . . . . . . . . . . . .
45
4-2
Comparison between reference force measurements and predicted re46
sults from the previously developed static ANN model [13]... ...
4-3
A zoomed in view for the comparison between reference force measurements and predicted results from the previously developed static ANN
model [13]. . .
.47
4-4
......
. ..
. .. . . ..
..
. . ..
. . ..
. .
..
Comparison between reference force measurements, predicted results
from the previously developed static ANN model [13], and dynamically
developed ANN model. . . . . . . . . . . . . . . . . . . . . . . . . . .48
.49
4-5
Zoomed in view of Figure 4-4. . . . . . . . . . . . . . . . . . . . .
4-6
Comparison between reference force measurements and predicted results from dynamically developed ANN model. The carriage was dropped
from 10cm with
5-1
mdrping carriage =
1.14kg.
. . . . . . . . . . . . . . .
CAD rendering of the assembly between the newly designed footpad
sensor onto the Cheetah robot's leg. . . . . . . . . . . . . .
5-2
50
. . . .
54
PCB for the newly designed footpad sensor after being populated with
components. The four mounting holes (one at each corner) will be used
to screw the PCB onto the polyurethane plastic backplate. . . . . .
5-3
Assembly rendering for the newly designed footpad sensor.
55
Shown
from left to right: fiberglass enforced polyurethane rubber shell (yellow body), PCB assembly (green body), elastomer filling (transparent
body), and a polyurethane plastic backplate (violet body).
5-4
....
56
Cross sectional view of the backplate-PCB subassembly submerged
within the elastomer material. In this image, backplate is represented
by violet, PCB is represented with green, and grey represents the elastom er filling. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .
.57
5-5
CAD rendering for the molding of the fiberglass enforced polyurethane
rubber shell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.58
5-6
Fiber glass enforced polyurethane rubber shell while curing of the liquid
resin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .
11
59
7 The finished fiberglass enforced polyurethane rubber shell. ......
60
-8
Failure mode for the original design of the positive mold. . . . . . . .
60
-9
Backplate molds filled with Task 4 resin while curing. . . . . . . . . .
61
5-10 3D printed backplate mold failure mold and its molded component.
As shown, most of the through hole ports were plugged with material
broke off from the mold. . . . . . . . . . . . . . . . . . . . . . . . . .62
>-11 3D printed parent molds filled with compliant polyurethane rubber
.. .63
resin while curing. . . . . . . . . . . . . . . . . . .. . . . . . . .
-12 Compliant molds filled with Task 4 resin while curing for molding the
backplate component. . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
$-13 From left to right of this image: the the 3D printed parent mold, the
compliant mold, and the molded back plate component..
. . . .
64
0-14 PCB-backplate assembly. The PCB was screwed onto the backplate
with spacers in between.
ports removed .
The pressure sensors are shown with top
. . . . . . . . . . . . . . . . . . . . . . . . . . .
.64
5-15 The finished footpad sensor with cured inner elastomer filling. ....
65
5-16 Image shown the newly designed footpad sensor been installed onto
the front left leg of the MIT Cheetah robot. . . . . . . . . . . ... . . .
66
5-17 Reference force measurements and footpad sensor outputs are plotted
from the Cheetah hopping experiment . . . . . . . . . . ... . . . . . .
67
5-18 Pressure sensor layout for the newly designed footpad sensor. . . . . .
68
5-19 Zoomed in view of the footpad sensor outputs.
...
69
. . . . . .
70
. . . . . . .
5-20 Image shows the saturation of the footpad sensor outputs.
6-1
Material specimen for characterizing the material property of molded
polyurethane rubber. The image shows a material specimen molded
out of VytaFlex 10 liquid resin (made by Smooth-On).
6-2
. . . . . . . .
Plot of collected Instron data on VytaFlex 10: extension of the specimen versus the resulted force . . . . . . . . . . . . . . . . . . .
6-3
72
Calculated true stress strain values plotted for VytaFlex 10.
12
..
72
. . . . .
74
A-1 Comparison between reference force measurements and predicted results from dynamically developed ANN model. The carriage was dropped
83
from 20cm with mdropping carriage = 1.14kg. RMSE = 2.47%. .....
A-2 Comparison between reference force measurements and predicted results from dynamically developed ANN model. The carriage was dropped
from 20cm with mdroppingcarriage = 1.14kg. RMSE
=
84
3.50%. .....
A-3 Comparison between reference force measurements and predicted results from dynamically developed ANN model. The carriage was dropped
from 30cm with mdroppingcarriage = 1.14kg. RMSE = 3.57%
84
....
B-1 Degassing the wetted 3D printed mold and remaining resin in vacuum
chamber. The image shows the air escaping from the mixed Task 4
. .
85
B-2 A close up view for the 3D printed mold failure after demolding. . . .
86
C-1 Instron testing of a VytaFlex 60 specimen. . . . . . . . . . . .
87
resin and causing the resin to foam. . . . . . . . . . . . . .... . .
. .
D-1 Plot of collected Instron data on EcoFlex 10: extension of the specimen
versus the resulted force. . . . . . . . . . . . . . . . . . . . . . . . . .
D-2 Calculated true stress strain values plotted for EcoFlex 10.
. . . .
89
90
D-3 Plot of collected Instron data on VytaFlex 60: extension of the specimen versus the resulted force. . . . . . . . . . . . . . . . ... . ... . .
D-4 Calculated true stress strain values plotted for VytaFlex 60.
13
. . . .
90
91
14
List of Tables
Number of experimental trials for dynamic testing of the footpad sensor
prototype. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
Mapping between pressure sensor groups and sensor layout. ......
69
.
4.1
5.1
15
16
Chapter 1
Introduction
Ground reaction force measurements are critical for designing a well-performed controller for a quadruped robot, especially when running at high speeds [1]. To monitor
the reaction forces generated when the robot pushes against its environmental boundaries, the foot of the robot offers a unique force sensing location as it is the only point
of interaction with the surroundings. Alternative ways to measure forces at different
locations might not provide enough information to secure locomotion stability. In
order to achieve accurate force measurements, such force sensors must be able to operate across a large dynamic range, from light touch to the peak of impact. Moreover,
both normal and shear forces need to be sensed in order to obtain sufficient information to balance the body of the robot. From a mechanical perspective, these sensors
need to be able to withstand the impact force repetitively while running. Because
the force sensor will be integrated with the robot's foot, it should also bear the three
key features for designing a robotic foot: (a) ability to adapt to contours of ground;
(b) capability to absorb impact; and (c) store and release energy [2]. Additionally,
conventional rigid sensors pick up inertial forces caused by the mass of the sensing
element when used in locomotion applications [3]. Therefore, a rigid force sensor
could not fulfill such requirements. Though there are numerous studies on tactile
force sensing [4, 5], a force sensing solution that satisfies all functional requirements
aforementioned is not readily available.
Continuous sensing of the variable contact force is defined as tactile sensin
17
in
the field of robotics [6]. Many industrial robots and humanoid robots achieve tactile
sensing using force/torque (F/T) sensors [7, 8, 9]. However, off the shelf F/T sensors
are often bulky in size and add undesired weight to the robotic system, which might
be costly energetically.
Though F/T sensors are great in their repeatability and
linearity, their rigid nature deviates from the key design features of a robotic foot.
Several studies have been investigating compliant force sensing approaches, such as
the silicon-based integrated circuit strain gauges bonded onto a flexible printed circuit
board [10], the silicon-based piezoresistive sensor embedded in elastomer [11], and the
conductive fabric based sensor using Electrical Impedance Tomography (EIT) [12].
However, none of above was developed with the intent of being integrated into the
foot of a running robot. Many of the existing compliant force sensors are limited in
their range, resolution, and repeatability.
Designing the force sensor with the specific application in mind can result in
many advantages such as minimized profile, optimized range and resolution, as well
as customized sensing area. A multi-axis force sensing composite footpad was recently
devploped by Michael Chuah at the MIT Biomimetic Robotics Lab [13], and a proofof-concept prototype was fabricated and tested. The proposed footpad design is able
to offer both sufficient ground traction and durability against repeated impact by
utilizing hyperelastic polymers. The multi-axis force sensing composite footpad is
consist of an array of barometric pressure sensors embedded within polyurethane
rubber. Both normal and shear forces can be detected indirectly by recording the
readings from each barometric sensor resulted from volumetric displacement due to
the applied force. To map the relationship between normal/shear forces and the the
barometric sensor outputs, a model can be constructed upon a one-time training
procedure using Artificial Neural Network (ANN). A static model of the footpad
sensor was developed in the past and showed promising results in terms of accuracy
and consistency of its measurements. The tested prototype is able to detect normal
forces up to 300N with a RMSE of 0.66% and up to 80N in the x and y-axes with an
RMSE of 3.69% and 5.91% respectively.
To integrate this new sensing technology with MIT Cheetah robot to detect ground
18
contact as well as impact forces, characterization of the sensors impact response was
performed. The multi-axis force sensing composite footpad was dynamically characterized by recording the sensor's outputs when impacting a referencing force measuring device with a prescribed force and velocity. To achieve the desired impact
force and velocity, a customized impact-testing fixture was designed, fabricated, and
characterized. The footpad sensor was then tested using the newly developed impact
tester. The impact force profile was first predicted using the existing static model,
then compared against the referencing force reading for consistency. A brand new
dynamic model associating force measurements with pressure sensor readings was developed using ANN utilizing the collected experimental results. Additional dynamic
testings were used to validated the developed dynamic ANN model. The footpad
sensor was redesigned to be integrated into the MIT Cheetah Robot and placed at
the bottom of the robot's feet for hopping tests. The newly revised footpad sensor
design was fabricated and testing results were collected and quantified. Further improvement of the footpad sensor was also a key focus. Material property testings
for polyurethane rubber with various durometer were carried out for optimizing the
range and sensitivity of the footpad sensor along with experimental findings.
19
20
Chapter 2
Previous Work
The developed proof-of-concept prototype of the composite footpad sensor has only
been characterized under static conditions as mentioned previously. To provide understanding of the current footpad sensor's design, fabrication, and its characterization,
this chapter will summarize the prior work on the sensor development carried out by
Michael Chuah [13]. In addition, the shortcomings of the current sensor prototype
will be discussed as well.
2.1
Compliant Footpad Sensor
The current footpad sensor prototype is consist of barometric pressure sensors, printed
circuit board (PCB), acrylic back plate, and polyurethane rubber. Nine pressure
sensors (Freescale Semiconductor MPXH6400A) axe mounted onto a 40mm by 50mm
PCB board in a 3 by 3 grid. The top port of each of the pressure sensor was cut open
to improve its sensitivity by exposing more of the contained silicon based piezoresistive
transducer. The assembled PCB is them screwed onto a acrylic back. plate to protect
the PCB board under stress. The finished assembly is shown in Figure 2-1. The
sensors were spread out to map the stress distribution when forces are applied.
The entire assembly (shown in Figure 2-1) was then embedded within polyurethane
rubber which was molded using VytaFlex 10 (Smooth-On). The finished sensor prototype is shown in Figure 2-2. After submerging each of the pressure sensor within
21
Figure 2-1: Pressure sensor array. Top two rows are shown with the top port removed,
the bottom row shows the off-shelf sensor package. The blue elements mounted onto
the PCB board are capacitors. The green board is the PCB and the clear block
underneath PCB is the acrylic back plate. This image is reproduced from [13].
the polyurethane rubber, any forces applied onto the footpad will influence the output reading of each of the pressure sensor differently. The applied normal and shear
forces could be calculated using each of the pressure sensor reading and the calculated results are unique. A model was developed that maps pressure sensor outputs
to forces applied using ANN.
Figure 2-2: Footpad sensor prototype shown next to a penny. The PCB assembly
was completely submerged within the rubber. In this image, the acrylic back plate
is at the bottom and forces are applied to the rubber surface of the footpad sensor.
This image is reproduced from [13].
22
2.2
Static Characterization
The developed footpad sensor prototype, shown in Figure 2-2, was characterized under
static conditions [13]. An industrial 3 axis CNC milling machine (HAAS Super Mini
Mill 2) was used to achieve accurate positioning of the footpad sensor. The footpad
sensor was attached to the quill using a custom designed mount while a 6-axis F/T
sensor (ATI Industrial Automation SI-660-60) was attached to the mill table using a
second mount as shown in Figure 2-3. The pressure sensor outputs for each of the
nine sensors and the F/T sensor readings are recorded using a National Instruments
(NI) CompactDAQ 9205 interfaced with LabVIEW. MATLAB was used for further
data processing as well as the model development utilizing MATLAB's neural network
toolbox.
Figure 2-3: The footpad sensor was attached to a CNC mill quill while a F/T sensor
was attached to the mill table. This image is reproduced from [13].
First, the CNC mill machine was programmed to run through a known path with
the footpad in contact of the F/T sensor. Then, the footpad was traversed in both
x-axis and y-axis independently by
3mm from its origin position while a known
normal load is applied to the rubber face of the footpad sensor. 1mm displacement
in z-axis was able to generate a significant change in normal force for the prototyped
footpad sensor. A swept sine signal generated by the mill (900mm/min) was also
used for performing system identification of the tested footpad sensor.
The testing results suggest that the developed footpad sensor can measure both
23
normal and shear forces with promising accuracy. The tested footpad sensor is able
to detect normal force up to 300N with a RMSE 'of 0.66% and shear forces up to 80N
in the x and x-axis with an RMSE of 3.69% and 5.91% respectively [13]. However,
there are a number of shortcomings of the current prototype that are in need of
improvement.
" Alternative sensor placement pattern to optimize shear force detection
* Increased dynamic force range by exploring other kinds of compliant material
and pressure sensors
* On board microcontroller for data processing
24
Chapter 3
Impact Testing
Testing under static conditions alone cannot offer sufficient understanding and verification of the sensor's capability of detecting impact forces. As aforementioned, the
intent for the developed footpad sensor is to be integrated to the MIT Cheetah Robot
for detecting contact with the ground as well as the impact forces. Therefore, the
developed footpad sensor must also be characterized dynamically prior to integration
with the MIT Cheetah Robot. This chapter will outline the dynamic testing and
characterization of the previously developed footpad sensor prototype.
3.1
Impact Tester Design
To test the footpad sensor under dynamic conditions, the velocity and magnitude
of impact must be controlled in order to investigate into the repeatability of the
measurements as well as the dynamic behavior of the sensor itself.
Therefor, a
custom designed impact tester is needed to control both the velocity and magnitude
of impact of the footpad sensor. The proposed design for the impact tester will drop
the mounted footpad sensor along with a dropping carriage in a controlled linear
manner. The drop will be constrained using the linear roller blocks and their mating
rails (Speed Guide OSGR 25) to only one degree of freedom. The velocity of impact
can be controlled and varied by dropping at different heights. The magnitude of
impact can also be controlled and varied by adding on different weights to the footpad
25
sensor dropping carriage. As mentioned in Chapter 2, a referencing force measurement
device is needed for both the validation the sensor as well as the development a model
to map pressure sensor outputs to forces. Thus, the footpad sensor will be dropped
onto a 2-axis force platform (PasPort PS-2142) made by Pasco sampling at 1000Hz.
The schematic of the designed impact tester is shown in Figure 3-1.
--.---- Additional Weights
g
Dropping Carriage ........... ..
F op d S n o
g ~b
Sensor
Lp~--JFootpad
--.Pasco Force Platform
Figure 3-1: Schematic of the designed impact tester. The footpad sensor will be
attached to the dropping carriage. Impact velocity can be controlled by changing the
height of drop, while adding or removing weights adjusts the magnitude of impact.
The footpad sensor will be dropped onto the force platform sensor which provides the
referencing force measurements.
The other key feature the impact tester must fulfill is the ability to produce identical impact conditions repetitively. Furthermore, the impact tester need to be able
to simulate impact conditions of the actual Cheetah Robot's foot impact with the
ground while running to minimize the gap between controlled dynamic characterization and actual filed testing. From previous studies carried out in the lab, the MIT
Cheetah Robot typically strikes the ground with a impact velocity around 0.5m/s
and impact forces in the magnitude of thousands of Newtons. Hence, the impact
tester will be designed to achieve impact velocities from 0.1 - 2m/s to investigate the
sensor's behavior to a variety of impact velocities. In addition, the dropping carriage
must be able to handle a number of weights to achieve desired impact magnitude.
26
3.2
Impact Tester Fabrication
Aluminum structural framing parts (made by 80/20) were used for the ease of fabrication. The linear roller rails were mounted onto the 80/20 frame and the dropping
carriage was attached to the linear roller blocks (one on each side) which ride on the
rails. The footpad sensor was screwed onto to the bottom of the dropping carriage
via a custom made mount. The frame was constructed to maximize stiffness and
minimize undesired compliance. The force platform was placed right underneath the
footpad sensor on the ground. The force platform is not attached to the impact tester
frame and rather separate on its own to eliminate any unwanted dynamic shocks that
might get transmitted through the rigid frame. The constructed impact tester is
shown in Figure 3-2.
27
Figure 3-2: The constructed impact tester. The linear rails are vertical, with one on
each side. The dropping carriage is horizontal while two weights were added to its
top as shown. The force platform was placed right underneath the footpad sensor,
which was mounted to the bottom side of the dropping carriage.
Figure 3-3 shows a close up view of the footpad sensor being mounted to the
bottom side of the dropping carriage. Additional weights could be placed right above
the footpad sensor to reduce possible dynamic behaviors in other directions. When
dropped, the footpad sensor will impact the force platform at its center to achieve
optimum reference force readings. Both footpad sensor outputs and force platform
readings were collected. All wirings were made sure to be loose and offer no resistance
to the motion of the dropping carriage.
28
Figure 3-3: Close up view of the footpad sensor being attached to the impact tester.
The force platform was placed right underneath the footpad sensor.
3.3
Characterization
A few test runs were carried out to confirm the functionality of the designed impact
tester as well as validating its satisfaction of all requirements mentioned previously in
Section 3.1. The characterization tests were designed to confirm the reference force
readings, the repeatability of the impact tester, and the range of impact conditions
the impact tester is capable of producing. It is important to characterize the impact
tester prior to any experiments to eliminate any errors or uncertainties that could be
introduced by the test setup itself.
29
3.3.1
Reference Force Reading Validity
Confirming the reasonableness of the reference force readings produced by the force
platform is critical since these reference force measurements will be used to establish
the dynamic model of the developed footpad sensor. Therefore, the reference force
readings will be collected and compared against theoretical predications for verification. The entire drop of each test was captured using a high speed camera (Mikrotron
Eo Sens MC1363, 500fps). The video files were later analyzed using a graphic tracking software (Tracker 4.82) to obtain the position of the dropping carriage over time.
Figure 3-4 shows a screen shot of using Tracker 4.82 to obtain position over time. A
coordinate system was setup inside the software (indicated by the pink axises) as well
as a referencing length (indicated by the blue segment). The dropping carriage was
tagged with a green sticker and tracked by the software (indicated by the red dot).
Figure 3-4: A screen shot of obtaining the dropping carriage's position from the high
speed video using the Tracker software.
Both with and without additional weights dropped from identical heights were
tested to confirm that the magnitude of impact is indeed controllable by adjusting
the mass of the whole dropping carriage assembly. The obtained positions of the
dropping carriage as a function of time are plotted in Figure 3-5. As shown, both
with and without additional masses added to the dropping carriage are plotted. The
mass of the dropping carriage assembly is 1.14kg with no additional mass and 3.49kg
with 10lb of weights added. The weight of the whole dropping carriage assembly was
30
determined by placing a digital scale underneath the dropping carriage when it is
at rest. Furthermore, the acceleration of the drop is higher with a heavier dropping
carriage.
This observation is consistent with the physical intuition that damping
effects are less affective to a heavier dropping carriage. The secondary bounce is also
higher for dropping carriage with additional weights added since the potential energy
stored initially is linearly proportional to the mass of the dropping carriage.
25
-1.14kg
-3.49kg
20-
-
15
10
50
0
0.5
1.5
1
Time(s)
2
Figure 3-5: Dropping carriage position is plotted against time. Position information
was obtained from analyzing the high speed video files in the Tracker software. Two
dropping carriage weights dropped from the same height are plotted, 1.14kg and
3.49kg.
By fitting the obtained position information to a quadratic function, the acceleration of the dropping carriage can be quantified. Figure 3-6 plots both the position
profile of the dropping carriage (no additional weights case, mass is 1.14kg) as well
as the quadratic fit of the position. The position profile is rather smooth and the fit
is able to achieve a summed square of residuals (SSE) of 2.01 x 10-05. The fit also
predicts a dropping acceleration of -3.37m/s
2
which is smaller than gravitational
acceleration due to frictional losses that are inherent to the impact tester itself.
31
25 r
Position data for 1.14kg
Quadratic fit
15
W2
0
-
20
10
p4
5
0
0
0.5
1
Time (s)
1.5
2
Figure 3-6: Both position data and quadratically fitted results are plotted.
The velocity of the dropping carriage can be obtained by finding the numerical
derivatives of the positions. Figure 3-7 shows the velocity of the dropping carriage
when its mass is 1.14kg. The velocity profile can be broken down to several stages:
" from Os < t < 0.2s the dropping carriage is at rest, thus the velocity is zero
" the negative velocity initially (0.2s < t < 0.46) corresponds to the dropping
phase under gravitational force, the speed of the dropping carriage increases
linearly as a function of time
" the discontinuities of the velocity profile indicates the impact of the footpad
sensor against the referencing force platform
" the footpad bounces couple of times before coming to rest; Figure 3-7 indicates
that the dropping carriage has bounced three times before coming to rest.
* eventually the dropping carriage loses all of its potential energy and comes to
rest for t > 0.8s
From Figure 3-7, the impact velocity of the dropping carriage is -1.34m/s at t
=
468ms. After impact the velocity of the dropping carriage is 1.15m/s at t = 476ms.
32
1.5 r
1
0
*
0.5
U
1 0mgm
0
.0
>0
-0.5 F
0
0
-1
-
5
.
-1
0
0.2
0.4
0.6
0.8
1
1.2
Time (s)
Figure 3-7: Velocity of the dropping carriage (1.14kg in mass) plotted against time.
Therefore the duration of the impact timpact = 8ms and the impact itself is an inelastic
collision where the kinetic energy of the dropping carriage is not conserved.
10000
800-
0
0
600*
0
400-
0
0
0
200
*0
m
ni-i
-200'0
0.2
0.4
0.6
Time (s)
0.8
1
Figure 3-8: Referencing force plate readings when mdropping carriage-= 1.14kg.
The recorded reference forces are plotted in Figure 3-8 for the same trial of experiment shown in Figure 3-6. The forces were measured using a force platform discussed
in 3.1.
As shown the reference forces are plotted against time, and the maximum
33
force was determined to be 939N. Zooming into the first force peak shown in Figure
3-9, there are eight data points, and the force platform was set to sample at 1000Hz.
Therefore, the duration of impact was determined to be 8ms, same as what was
concluded from analyzing the high speed videos.
1000-
0
800
0
0
600-
0
0
400
0
200-
0o
-200
0.09
00000
0
00000
0.095
0.1
0.105
Time (s)
0.11
0.115
0.12
Figure 3-9: Referencing force plate readings when mdroppng carriage = 1.14kg. Zoomed
view for the first force peak.
Impulse Balance
J Fdt
(3.1)
The total impulse due to the impact as defined in Equation 3.1 can be found by
finding the area under the first force peak shown in Figure 3-9. Also, as Figure 3-9
indicates, the force profile can be roughly approximated as triangular.
Thus, the
impulse due to impact can be approximated by Equation 3.2 by calculating the area
of the triangle which base is timpact and height is
1
2
Fpak.
J = 1timpactFeak
(3.2)
The peak impact force Feak could be solved if the total impulse J and time of
impact timpact are given. As mentioned previously, J could be determined by finding
34
the area under the first force peak (Figure 3-9) via numerical integration. In addition,
the time of impact was concluded to be timpact = 8ms by examining Figure 3-9. Hence,
by solving Equation 3.2
Fpeak =
1027N, compare to the force platform maximum
reading 939N, the approximated value is 9% greater. However, it does suggest that
a triangular approximation for the force profile during impact is a viable approach.
As Figure 3-10 shows, the blue circles indicate the reference force measurements; the
cyan dotted line marks zero force reading; and the red line indicate the triangular
approximation with
Fpeak
1000
= 1027N.
0
Reference Force
800
600
400
00
2000
0 ---
00000
'
-200
0.09
---------------0.095
0.1
0.105
Time (s)
0.11
0.115
0.12
Figure 3-10: Comparison between triangular approximation for the first force peak
and referencing force plate readings when mdropping carriage = 1.14kg.
The approximated peak impact force is higher than the maximum force platform
reading. This could be caused by two error sources: (1) the errors that are inherent
to the triangular assumption itself; and (2) not capturing the actual peak impact
force due to the limitation of the force platform's sampling rate (1000Hz). Note that
in Figure 3-10, the force platform was reading ON initially prior to the impact and
negative force readings after the impact. This is caused by the internal dynarmics
of the force platform itself. After impact, the footpad sensor along with the dropping carriage leaves the force platform, however, the measuring surface itself is also
35
accelerating upward which causes the negative reading of the force measurement.
Momentum Conservation
From impulse balance alone cannot validate force platform's measurements, because
the data collected using force platform was also used in the approximation calculation
outlined previously.
A completely independent source of measurement is need to
conirm the validity of the reference forces measured by the force platform. Thus, the
peak impact force will also be estimated only using high speed video data and the
mas s of the dropping carriage, mdroppingcarriage= 1.14kg in this case. As Figure 3-7
has shown, the impact velocity of the dropping carriage is vimpa
=
-1.34m/s and
the velocity after impact is Vafter = 1.15m/s. The duration of the impact could also
be determined by examining the number of frames recorded during impact, timpact =
8mS. Therefor, the momentum change due to impact is the following:
AP
=mAy
=Mdroping
carriage(Vafter
-Vimpact)
(3.3)
he change of momentum also equals to impulse resulted from impact, therefore,
set
quation 3.2 and 3.3 equal, after rearranging Equation 3.4 can be determined.
Fpeak
=
2
(Vafter
mdropping carriage
-
Vimpact)
timpact
he peak impact force Feak can be determined after evaluating Equation Equation
3.4 with information obtained from analyzing high speed videos. The predicted value
for peak impact force is Feak = 710N, compare to the force platform maximum
reading 939N, the approximated value is 24% smaller.
A smaller predicted peak
impact force is mainly due to the limitation on high speed camera's sampling rate
(500fps in this case).
The peak impact force predication is linearly proportional
to the estimated momentum change of the dropping.
The momentum change was
esti ated by determining the velocity change before and after the impact. Continue
to t:ace the error, the velocity of the dropping carriage were obtained from the position
information. To calculate the velocity of the dropping carriage, the positions were
36
differentiated numerically which means dividing the position change between cach
frame over the time difference between each frame recorded. The high speed camera
was set to record at 500fps which means the time difference between each frame
is 2ms. Therefore, by obtaining the velocity, the calculation process itself is already
averaging out the velocities for each 2ms time interval and in turns provides a smaller
momentum change of the dropping carriage. Taking into account the total duration
of the impact is timpat = 8ms, averaging velocity over a 2ms time interval results in
large reduction of the predicted peak impact force.
Though the estimated peak impact force from high speed video recordings is not
error free, it does suggest that the reference force measured by the force platform is
reasonable and valid. Hence, the force platform will be used throughout the rest of
this study serving as a referencing force measurement tool.
3.3.2
Repeatability
The other key feature the impact tester must fulfill is the capability to produce
identical impact conditions repetitively.
Thus test runs were conducted to exam
the repeatability of the designed impact tester. Each drop were evaluated from two
perspectives: impact velocity and magnitude of impact.
Impact Velocity
The impact velocity of the dropping carriage for each experiment condition was determined from recorded high speed videos described previously in Section 3.3. E ach
experimental condition was repeated multiple times, and both initial dropping height
and weight of the dropping carriage were varied. As shown in Figure 3-11, the impact
velocity for each drop is plotted against the initial dropping height. Moreover, the
blue circles indicate test runs with no additional weights added (m
1.14kg) and
red asterisks indicate experimental trials when the mass of the dropping carriage is
3.49kg. The impact velocity is proportional to the initial dropping height.
37
-
2.5
0
1.14kg
* 3.49kg
0-
W
1.5
0
1
0.1
0.15
0.2
0.25
0.3
Initial Dropping Height (m)
0.35
Figure 3-11: Impact speeds of the dropping carriage determined from recorded high
speed videos plotted against the initial dropping height for two various carriage
masses.
As Figure 3-11 shows, the variation between identical trials is minimum considering possible error introduction in data collection processes. Thus, the designed impact
is capable of producing impact velocity repetitively. Currently the dropping carriage
is dropped by hand, it is possible that human operation might cause additional errors. A possible future improvement on the current impact tester design to include
mechanical release to drop the carriage.
According to Newton's Laws, the terminal velocity of an ideal free fall object
is linearly proportional to the square root of the initial dropped height. Therefore,
Figure 3-12 plots the impact speed collected empirically against the square root of
initial dropping height as well as the linearly fitted lines.
collected when
mdroppingcarriage =
The linear fit for data
1.14kg achieves SSE = 0.018, and SSE = 0.003
when fitting the data obtained when
mdroping carriage =
3.49kg. The SSE is lower for
data collected with a heavier carriage since undesired uncertainties are less significant
when the dropping carriage is accelerating to a higher velocity. Furthermore, the slope
of the fit is also greater for a heavier dropping carriage. This is in agreement with
previous conclusion discussed in Section 3.3.1 that a heavier dropping carriage is able
38
to overcome more frictional losses and accelerate at a slightly higher acceleration than
a lighter dropping carriage.
2.5o 1.14kg
* 3.49kg
2
1.5
0
0
0
0.35
0.4
0.45
0.5
0.55
Square Root of Initial Dropping Height (viii)
Figure 3-12: Comparison between experimental data on impact speeds plotted against
NInitial DroppingHeight and their linearly fitted functions.
Magnitude of Impact
The magnitude of impact was evaluated by examining the peak impact force read by
the referencing force platform for each drop. Similarly, both initial dropping height
and the mass of the dropping carriage were varied. Furthermore, each experimental
condition were conducted multiple times to validate the impact tester's ability to
produce magnitude of impact consistently for a given test condition. As Figure 313 shows, the captured peak impact forces were plotted against the initial dropping
height of the carriage. Again, blue circles are data collected when
mdroppingcarriage =
1.14kg and peak impact forces observed when mdroppingcarriage = 3.49kg are denoted as
red asterisks. The peak impact force increases as the initial dropping height increases.
Moreover, for identical initial dropping height, the impact force is much greater for a
heavier dropping carriage. From Figure 3-13, the variation of measured peak impact
force is minimum between trials with identical experimental conditions. Therefore,
the designed impact tester is capable of producing magnitude of impact repetitively.
39
3uuu
2500
0 1.14kg
3.49kg
2000
1500
A4
1000-
500
0.1
0.3
0.15
0.2
0.25
Initial Dropping Height (m)
0.35
Figure 3-13: Peak impact force measured using the reference force platform plotted
against the initial dropping height of the carriage for two various carriage masses.
For a heavier carriage, the variation on peak impact force between trials is larger
than a lighter dropping carriage as shown in Figure 3-13.
This is majorly due to
the fact that additional weights were added to the top of the dropping carriage and
are secured down using a screw. Sometime, during impact, the center of mass of the
added weights can shift out of plane and disrupt the linear motion which in turn
varied the captured peak impact force. A further improvement could be included to
the impact tester to better secure the weight and ensure the center of mass of the
whole dropping carriage assembly does not shift out of plane during impact. The other
possible source of error is the limitation of the sampling rate of the force platform.
Bec ause the sampling rate is limited to 1000Hz, the force platform is not capturing
the actual peak of impact force but rather a point that is near the absolute maximum.
When the dropping carriage is heavier, the peak impact force is also greater with a
narrower force profile.
The captured the measured peak impact force could vary
depends on which point near the actual peak impact force is captured by the force
platform. This error source could be further eliminated by using other alternative
force sensors with higher sampling rate as reference force measurement tool.
40
-
3000
0 1. 14kg
920-* 3.49kg
2500
-
1500
1000500
0.1
Figure 3-14:
0.3
0.2
0.25
0.15
Initial Dropping Height (m)
0.35
Comparison between measured peak impact force and their linearly
fitted functions.
The measured peak impact force seems to be linearly related to the initial dropping
height of the carriage, as shown in Figure 3-14. Hence, the collected data were fitted
to a linear function. The coefficient of determination (R2 ) is 0.97 for data collected
when mdropping carriage
=
1.14kg, and R 2 = 0.98 when madropping carriage
=
3.49kg. From
Figure 3-14 the fitted slope is greater for a heavier dropping carriage since there were
less frictional losses for a heavier dropping carriage.
3.3.3
Operational Range
The last key feature the impact tester must satisfy is the sufficient operational range
to produce a variety of impact conditions. As stated in Section 3.1, the impact tester
is required to be able to achieve impact velocities from 0.1- 2m/s as well as generating
a range of magnitude of impact. This is critical to simulate the running condition of
the MIT Cheetah Robot which typically strikes the ground with a impact velocity
around 0.5m/s and impact forces in the magnitude of thousands of Newtons.
Figure 3-11, shows impact speed from lm/s to 2m/s. Though data for impact
speed below lm/s were not shown in Figure 3-11, there is virtually no bound to
41
the minimum impact velocity the impact tester is capable of producing. A smaller
imp act velocity can always be produced when dropping the carriage as a lower initial
dropping height. Thus, this confirms that the designed impact tester is able to satisfy
the impact velocity specification.
Figure 3-13, shows the peak impact force varying from 720N to 3000N.
By
adjusting the total mass of the dropping carriage assembly, numerous magnitudes of
the impact can be produced. There is no specific range requirement for the magnitude
of impact due to the lack of understanding on the current Cheetah running conditions.
Therefore, the designed impact tester is satisfactory considering its ability to generate
a wide range of magnitude of impact.
42
Chapter 4
Dynamic Characterization
After the design, fabrication, and validation of the custom designed impact tester
the footpad sensor prototype as described in Section 2 was characterized dynamically using the developed impact tester. Previously developed static model [13] was
also applied to the dynamically obtained footpad sensor outputs to exam the static
model performance under dynamic conditions. This chapter will outline the ANN
modeled results when using static model for dynamic testings of the footpad sensor. Furthermore, a dynamic ANN model was developed and compared to the static
ANN modeled results. The developed dynamic ANN model was also verified with
additional dynamic testings and shown promising results.
4.1
Experimental Setup
The footpad sensor prototype was characterized and verified under static conditions
[13] prior to be tested dynamically using the custom developed impact tester. The
footpad sensor was screwed onto the the bottom side of the dropping carriage and
reference force was measured by placing the force platform directly underneath the
footpad sensor. The footpad sensor was tested under various impact conditions in
terms of impact velocity and the magnitude of impact. The footpad sensor prototype
was tested under a wide range of impact conditions to ensure the sensor's capability t
be integrated with the MIT Cheetah robot which undergoes a wide range of operation
43
Mlnodes including walking, running, galloping, and hopping etc. The impact velocities
ranges from lm/s to 2m/s based on analyzing the high speed videos, and the peak
imnpact force varies from 720N to 3000N according to the reference force platform's
measurements. To optimize the footpad sensor's performance when applied to legged
locomotion robots, the tested impact conditions were chosen to cover all the possible
operation modes of the MIT Cheetah robot.
Table 4.1: Number of experimental trials for dynamic testing of the footpad sensor
prototype.
Mdrappngcarriage
=1.
14kg
mndrppng carriage =3.49kg
DroppedHeight = 10cm
3
3
DroppedHeight = 20cm
4
3
DroppedHeight = 30cm
3
4
All the experimental trials are summarized in Table 4.1. As shown, both the
dropped height and the mass of the dropping carriage were varied to generate variety
inpact conditions. The footpad sensor was also tested under each impact condition
multiple times, and the number of trials under each condition is also listed in Table
4.1. Footpad sensor outputs were recorded at 1000Hz for each experimentation trial
using LabView, and the reference force measured by the force platform were also
recorded with a sampling rate of 1000Hz via the PASCO SPARKvue software.
4.2
Results and Discussion
The recorded footpad sensor's outputs and reference force measurements were analyzed and will be discussed in this section. First, the footpad sensor's voltage outputs
for each one of its nine embedded pressure sensors were plotted and examined to
ensure the sensor's capability of capturing dynamic signals. Furthermore, the voltage
outputs were compared against reference force measurements to assess time delay
in the footpad sensor's response. As Figure 4-1 shows, the footpad sensor's voltage
44
outputs (nine signals since the footpad sensor has nine embedded pressure sensors)
were plotted against time together with the reference force measured.
As shown in Figure 4-1, the footpad sensor was able to detect the impact signal as
well as the consecutive bounces after its initial impact with the force platform. When
comparing against measured reference force, the occurrence of each impact agrees
well. There is clear intervals between each impact and the voltage outputs for each
impact diminishes as time increases due to energy losses in damping. Even though
the footpad sensor was made out of compliant material, the sensor was able to recover
quickly after each impact and clearly indicate each impact event.
1000
6
-1
-2
-3
-4
4-
500
-5
6
7
9
IRef
Force
-
0
0
'
50
100
'
150
'
200
Time (ms)
'
250
''500
300
350
400
Figure 4-1: Footpad sensor's voltage outputs plotted against time when dropped from
10cm and mdropping carriage = 1.14kg.
The measured reference force is also plotted
against time.
However, the current footpad sensor was found to be mostly saturated during
the impact period. As shown in Figure 4-1, the voltage profiles during impact have
blunt peaks for the first two impact incidents. After the first two impact incidents,
smooth voltage profiles were observed during the impact. Thus, the current footpad
45
prototype is incapable of high impact force and saturate when impact force is large.
More footpad sensor saturation was observed for larger magnitudes of impact.
Comparing the footpad sensor's voltage outputs against the measured reference
force, the signals between each impact incident were a lot cleaner for the footpad
sensor's outputs. This could be resulted from measurement noise introduced by the
inertial behavior of the force platform itself. The recorded high speed videos have
shown that the top measuring staged of the force platform moves agitatedly even
after loosing contact with the footpad sensor. This observation further supports the
need to move away from rigid force sensors for high speed applications.
4.2.1
Static Model Verification
The previously developed static ANN model (see Section 2) [13] was applied to the
dynamically obtained footpad sensor outputs, and the obtained results are shown in
Figure 4-2. All 20 trials of dynamic experiments (listed in Table 4.1) were plotted in
Figure 4-2. Blue indicate the reference force measurements whereas green denotes for
the calculated static ANN model results from the collected footpad sensor's voltage
outputs.
3000
-Ref
-Static
Force
ANN
2000
1000
0
0
2000
4000
6000
8000
10000
Index
12000
14000
16000
18000
Figure 4-2: Comparison between reference force measurements and predicted results
from. the previously developed static ANN model [13].
46
As Figure 4-2 shows, The static ANN model barely captures any impact force
peaks. Though the maximum impact force for each trials varies according to the
reference force platform measurements, the static ANN model was not able to predict
any change in peak force magnitude across all 20 trials of experiments.
Figure 4-3 shows a zoomed in view of the results plotted in Figure 4-2. As shown,
the static ANN model developed previously was not capable of capturing highly
dynamic footpad sensor's outputs.
-Ref
-Static
800
Force
ANN
600
a400-
0
100
150
200
Index
250
Figure 4-3: A zoomed in view for the comparison between reference force measurements and predicted results from the previously developed static ANN model [13].
The goodness of the model was quantified by calculating the Root Mean Square
Error (RMSE) expressed in Equation 4.1, where
y
denotes the reference force mea-
surements and y represents the force calculated by applying the static ANN model to
the recorded footpad sensor's outputs. The RMSE for data presented in Figure 4-2
was calculated to be 4.73% with maximum reference force of 3000N. Compare to the
footpad sensor's performance under static condition (detect normal force up to 300N
with a RMSE of 0.66% [13]), the accuracy of the static ANN model degraded greatly
when applied to dynamic footpad sensor's outputs.
47
RMSE=
(4.1)
(giyi)2
2
When calculating the ratio of maximum static ANN modeled force and maximum
reference force measured, the static ANN model only result in a ratio of 0.21 which
means the static model is only capable of capturing
} of the
measured impact peak
force. Therefore, the static ANN model is insufficient when applied to the footpad
sensor's outputs recorded under dynamic conditions.
4.2.2
Dynamic Model Development
To account for the deficiency of the static ANN model outlined previously, a dynamic
ANN model was developed using both the footpad sensor's voltage outputs and the
reference force measurements as inputs. The dynamically developed ANN model was
then compared to the static ANN model discussed earlier and verified with additional
dynamic testings of the footpad sensor.
3000
-Ref
Force
-Dynamic
ANN
Static ANN
2000
1000
0
0
2000
4000
6000
8000
10000
Index
12000
14000
16000
18000
Figure 4-4: Comparison between reference force measurements, predicted results from
the previously developed static ANN model [13], and dynamically developed ANN
model.
A 10 nodes neural network model was used to obtained the dynamic ANN model.
48
As Figure 4-4 shows, the reference force measurements, the static ANN model predictions, and the dynamic ANN model outputs were plotted for all 20 trials of the
experiments (4.1). As shown, the dynamically developed ANN model is more capable
at predicting forces under dynamic conditions and agrees better with reference force
measurements.
RMSE for the dynamic ANN model was calculated to be 3.27% with the same
maximum reference force of 3000N.
Compare to RMSEstatic ANN
=
4.73%, the
dynamic ANN model has less error but the improvement is subtle. This observation
could be caused by the fact that must of the data points collected were quasi static,
and the number of data points during the impact duration is few compare to the
size of the entire data set. Thus, a better way of quantifying the performance of the
developed dynamic model is to calculate the ratio between the maximum dynamic
ANN prediction and the maximum reference force measurements.
The ratio was
calculated to be 0.88 for the dynamic ANN model instead of 0.21 for the previously
developed static ANN model. This result suggests that the dynamically trained ANN
model is much more capable of capturing the impact peak force than the static ANN.
-Ref Force
-Dynamic
ANN
-Static ANN
8006000400
200-
100
120
140
160
Index
Figure 4-5: Zoomed in view of Figure 4-4.
Figure 4-5 shows a zoomed in view of the Figure 4-4, which better demonstrates
49
that the dynamically trained ANN model generates better predictions than the previously developed static ANN model.
4.2.3
Dynamic Model Verification
Additional dynamic tests for the footpad sensor prototype was conducted to verify
the developed dynamic ANN model. Four tests with various impact conditions were
carried out and resulted in RMSE = 3.17% which is similar to the dynamic training
result listed previously. The results for one of the four experiments is shown in Figure
4-6 (see the results from the other three trials in Appendix A).
800-Ref
Dynamic ANN
600-
a
Force
400
4)
'.4
0
200
-
ILI
0
-200'
0
200
400
600
Time (ms)
800
1000
Figure 4-6: Comparison between reference force measurements and predicted results
from dynamically developed ANN model. The carriage was dropped from 10cm with
mdropping carriage = 1.14kg.
As shown, the developed dynamic ANN model was able to predict the impact
force well from the recorded footpad sensor's voltage outputs. The ratio of maximum
dynamic ANN force prediction and the maximum reference force measured is as high
as 0.9258 for the data shown in Figure 4-6.
50
The quality of the developed dynamic ANN model is limited by the accuracy of
the reference force measurements. Currently, the reference force measurements are
contaminated with inertial noise from the sensing stage of the force platform itself.
Moreover, the sampling rate of the reference force is also limited to 1000Hz. More
data points during the impact during could be acquired with a improved sampling
rate which will lead to better ANN model construction. The ANN model could also
be further improved by redesigning the footpad sensor to avoid any pressure sensor
saturation and obtain more distinguished signals.
51
52
Chapter 5
Footpad Sensor for Cheetah Robot
The footpad sensor was redesigned to be integrated with the Cheetah Robot. The
newly designed footpad sensor must be able to attach to the robot's foot easily and
firmly. Furthermore, the attachment cannot be permanent in case of a need to rep ace
the footpad sensor. The footpad sensor is also required to withstand the impact of the
foot and have sufficient durability while running. The outer geometry of the footpad
sensor should also be adjusted based on the leg geometry of the MIT Cheetah Robot.
5.1
Design
The newly designed footpad sensor consists of a fiberglass enforced polyurethane
rubber shell, PCB assembly, elastomer filling, and a polyurethane plastic backplate.
To fulfill the requirement of easy and firm attachment, the proposed design for the
new footpad will have four flaps (one on each edge) to wrap around and strapP ed
onto the Cheetah robot's leg shown as Figure 5-1.
In addition, the polyuretane
plastic backplate was designed to mate with the pocket located at the end of the
Cheetah robot's leg to constraint the footpad sensor from moving side ways due to
shear forces. This way, the attachment is not only firm but also can be attached or
replaced easily. In Figure 5-1, the leg of the Cheetah robot is shown as the gray body;
the foot pad sensor is assembled into the outer glass enforced polyurethane ru ber
shell. The polyurethane plastic backplate is also visible in this CAD rendering and
53
shown as the teal colored body. When the leg of the Cheetah robot strikes the ground,
it is typically striking at an angle rather than perfectly vertical. Therefore, as Figure
5-1 shows, the footpad sensor is strapped onto the leg at an angle rather than directly
underneath to better capture the normal and shear force reacted while impact.
Figure 5-1: CAD rendering of the assembly between the newly designed footpad
sensor onto the Cheetah robot's leg.
The outer shell of the footpad sensor will be made out of fiberglass enforced
polyurethane rubber to ensure the integrity of the footpad sensor under impact as
well as its durability over the course of the experiment. An other reason for choosing
a rubber based outer shell is to still allow the transmission of force through the
materials and eventually be captured by the pressure sensors.
Six pressure sensors (Freescale Semiconductor MPXH6400A) are mounted onto a
32mm by 39mm PCB board in a 3 by 2 grid. The number of pressure sensors were
reduced to six sensors instead of nine sensors as the earlier prototype is to better
fit the footpad sensor underneath the foot of the Cheetah robot. As described in
Section 2, the sensitivity of the pressure sensor was improved by removing the top
54
port of the pressure sensor to expose more of the contained silicon based piezoresistive
transducer. The finished PCB board assembly is shown in Figure 5-2; as shown, the
top port of the pressure sensor has not been removed yet. The sensors are packed
quite close to each other already as shown, thus the package size of the pressure sensor
will become a limiting factor on how small the footpad sensor can be.
Figure 5-2: PCB for the newly designed footpad sensor after being populated with
components. The four mounting holes (one at each corner) will be used to screw the
PCB onto the polyurethane plastic backplate.
The assembled PCB is then screwed onto the molded polyurethane plastic backplate to prevent the PCB from fracturing under impact. The PCB-backplate assembly
(also shown in Figure 5-14) is then dropped into the fiberglass enforced polyurethane
rubber shell and submerged within elastomer material.
Figure 5-3 shows the ex-
ploded assembly view of this newly designed footpad sensor. As shown, the yellow
body represents the fiberglass enforced polyurethane rubber shell; the transparent
body around the green object represents the elastomer material that surrounds the
PCB; The green body represents the PCB (components mounted on the PCB are not
shown here); and finally the violet body represents the polyurethane plastic backplate.
Moreover, the features located at the top face of the polyurethane plastic
backplate (the opposite side from where PCB was screwed on) was used to mate with
the Cheetah robot's leg pocket as mentioned previously.
55
Both the fiberglass enforced polyurethane rubber shell and the polyurethane plastic backplate were molded separately. Then the PCB will be populated with components and screwed onto the molded polyurethane plastic backplate. The assembled
PCB-backplate unit will be then placed into the fiberglass enforced polyurethane
rubber shell. Liquid elastomer resin was then poured into the fiberglass enforced
polyurethane rubber shell to fill in any voids as well as covering up all the pressure
sensors mounted on the PCB. As shown in Figure 5-3, there is a lip around the
fiberglass enforced polyurethane rubber shell pocket to catch the edges of the molded
backplate and locate the pressure sensors positions. It is important to be able to
control the location of each of the pressure sensors precisely since the pressure sensor outputs are dependent on their embedded location within the elastomer filling.
Therefore, well controlled pressure sensor locations could minimize the performance
variations across footpad sensors.
Figure 5-3: Assembly rendering for the newly designed footpad sensor. Shown from
left to right: fiberglass enforced polyurethane rubber shell (yellow body), PCB assembly (green body), elastomer filling (transparent body), and a polyurethane plastic
backplate (violet body).
56
The last step for fabricating this newly designed footpad is to pour in the liquid
elastomer resin filling to cover up all the pressure sensors mounted on the PCB. It is
important that the elastomer resin has a firm attachment to both the rubber shell and
the PCB-backplate subassembly since it is the only link holding together the rubber
shell and the PCB-backplate subassembly. To ensure sufficient mechanical locking
between the elastomer and the molded backplate, conical holes were introduced to
the backplate piece to trap the elastomer resin while molding. Figure 5-4 shows the
cross sectional view of the backplate with PCB screwed on and embedded within the
elastomer material. The conical holes located on the backplate component allows
the elastomer resin to enter and creates a locking feature to prevent the backplatePCB subassembly from detaching from the elastomer filling. In Figure 5-4, violet
represent the backplate cross section, green represent the PCB, and gray represent
the elastomer filling. This locking features were introduced into the polyurethane
plastic backplate from knowledge gained with the previous iteration of prototyping
to ensure the attachment integrity between the pressures sensors and elastomer filling.
Figure 5-4: Cross sectional view of the backplate-PCB subassembly submerged within
the elastomer material.
In this image, backplate is represented by violet, PCB is
represented with green, and grey represents the elastomer filling.
5.2
Mold Design and Fabrication
As mentioned previously, both fiberglass enforced polyurethane rubber shell and
polyurethane plastic backplate are molded. A detailed description for the mold design
57
for each of the two parts as well as their fabrication procedures will be outlined in
this section.
5.2.1
Fiberglass Enforced Polyurethane Rubber Shell
The fiberglass enforced polyurethane rubber shell was molded out of liquid polyurethane
rubber resin (VytaFlex 60 by Smooth-On). The fiberglass was embedded into the
polyurethane rubber while the molding process. The molds for molding the shell consist of two halves: a positive mold as well as a negative mold. As Figure 5-5 shows, the
green body represent the negative mold where there are cavities for the polyurethane
rubber resin to fill; the violet body represent the positive mold which was used to
displace the polyurethane rubber resin to desired geometry; and the yellow body represent the fiberglass enforced polyurethane rubber shell after the completion of the
molding process.
Figure 5-5: CAD rendering for the molding of the fiberglass enforced polyurethane
rubber shell.
Both the positive half and the negative half of the mold are 3D printed using a
uPrint 3D printer (made by Stratasys). The rubber shell enforced with fiberglass will
be molded under room condition. Thus, 3D printing is a adequate manufacturing
58
process in this case since the molds are not expected to take significant loads. The
surface finish of the rubber shell is not important, thus, the concerns for the surface
finishing of the 3D printed molds are not necessary. To align the positive half mold
to the negative half mold, there are four corner brackets designed onto to the top
surface of the negative mold shown in Figure 5-5. The relative position between the
positive and the negative piece of the mold in the vertical direction is also constraint
with mechanical stops such that the positive mold cannot not be pushed down further
once it reaches desired location. The molds were designed with minimum 3' of draft
on all its faces to ensure easy demolding.
At first, the polyurethane rubber resin was mixed and prepared. Then the fiberglass cloth was cut to shape and fully wetted with the mixed resin. Meanwhile,
both the positive mode and the negative mold are wetted completely after applying
the mold release spray multiple times. All the wetted components as well as the
remained resin are placed into a vacuum chamber for degassing (vacuum chamber
made by Abbess Instruments). Degassing is a critical step to avoid any trapped air
bubble within the mold that could result as voids in the finished part.
Figure 5-6: Fiber glass enforced polyurethane rubber shell while curing of the liquid
resin.
Figure 5-6 shows the fiberglass enforced polyurethane rubber shell while curing of
the liquid resin. As shown, The fiberglass was molded with the polyurethane rubber
together to a unibody. After curing for 24 hours, the part was taken out of the
59
molds and rough edges were trimmed away using a pair of fabric cutting scissors.
The finished component is shown in Figure 5-7, as shown, the finished part is pretty
homogeneous and no obvious voids. More importantly, the lip around the shell pocket
is well defined and offers sufficient locating feature when assemble with PCB and
polyurethane plastic backplate.
Figure 5-7: The finished fiberglass enforced polyurethane rubber shell.
Originally, the positive mold was shelled out to preserve material as well as reducing time needed for 3D printing. However, as shown in Figure 5-8, the positive
mold was broken while demolding.
Figure 5-8: Failure mode for the original design of the positive mold.
As Figure 5-8 shows, the back flange was detached from the dome which confines
60
to the inner pocket of the rubber shell. Thus, the positive mold was strengthened by
removing the shelling feature as well as thickening the back flange of the mold.
5.2.2
Polyurethane Plastic Backplate
As mentioned previously, the PCB is screwed onto the backplate to prevent PCB
from cracking under impact. Therefore, the backplate component need to be stiff
and strong. The requirement on the mechanical integrity of the backplate component
eliminates the possibility of 3D printing.
It is possible to machine the backplate
component out of a solid block of raw material, however, machining is a tedious and
expansive procedure. Thus, the backplate component will be molded out of liquid
polyurethane plastic (Task 4 made by Smooth-On).
Figure 5-9: Backplate molds filled with Task 4 resin while curing.
At first, a similar procedure as described in Section 5.2.1 was proceeded.
For
molding the backplate component, only the negative mold is needed (the cavity mold),
and the mold was designed to be 3D printed. A minimum 3 draft angle was introduce
to all faces of the backplate mold for easy demolding. After printing the mold, mold
release was applied multiple times. The Task 4 resin was mixed and used to wet
61
the mold thoroughly before degassing in the vacuum chamber. After degassing, the
cavity mold was filling up by the Task 4 resin and left to cure. Figure 5-9 shows the
molds filled with the Task 4 resin while curing.
However, it was later discovered that it was rather difficult to demold because
both the mold and the part are rigid. In additional there were quite a number of
small features on the mold which make the demolding process more difficult. Even
though a great amount of mold release spray was applied, the mold was still damaged
during the demolding process. As Figure 5-10 shows, most of the small features on the
mold broke off and stuck with the molded backplate (a close up view of the broken 3D
printed mold is shown in Figure B-2). As a result an alternative approach is needed
to mold the backplate piece.
Figure 5-10: 3D printed backplate mold failure mold and its molded component. As
shown, most of the through hole ports were plugged with material broke off from the
mold.
The mold for molding the backplate piece was then made out of compliant material by pouring liquid polyurethane rubber resin (VytaFlex 20 made by Smooth-On)
into an other set of parent molds. The parent molds for molding the molds for the
backplate component was 3D printed. Because the parent molds will be molding
compliant material, thus 3D printing is a viable solution. The parent molds were
spared with mold release first before wetted with the VytaFlex 20 resin. The parent
molds along with the remaining resin were then placed in the vacuum chamber to
degas. Finally, the molds were taken out of the vacuum chamber and filled up with
62
the remaining resin and left to cure. As shown in Figure 5-11, the parent molds were
filled with compliant polyurethane rubber resin while curing.
Figure 5-11: 3D printed parent molds filled with compliant polyurethane rubber resin
while curing.
After the VytaFlex 20 resin was fully cured, it was demolded from the parent molds
to be the compliant mold for molding the backplate component. After applying mold
release agent, wetting and degassing, the compliant molds were filled up with Task
4 resin and left to cure. Figure 5-12 shows the compliant molds (VytaFlex 20) filled
with Task 4 resin while curing.
Figure 5-12: Compliant molds filled with Task 4 resin while curing for molding the
backplate component.
As expected, It was very easy to demold the backplate component from the compliant mold. All the features were registered onto the molded backplate piece and
there was no visible damage to the compliant mold after demolding. The compliant mold was then used multiple times and its functionality remained. The 2-step
63
molding process was able to resolve the mold failure problem presented earlier in this
section. As Figure 5-13 shows, from left to right: the 3D printed parent mold, the
compliant mold, and the molded back plate component. The resulted backplate component was tight tolerated and mate well with the Cheetah robot's leg. The screw
mounting holes were then taped using a MO.3 x 0.5 tap for screwing on the PCB.
Figure 5-13: From left to right of this image: the the 3D printed parent mold, the
compliant mold, and the molded back plate component.
5.2.3
Elastomer Filling
The final step for fabricating this newly designed footpad sensor is to embed the PCBbackplate subassembly (shown in Figure 5-14) into elastomer filling and integrate with
the rubber shell (shown in Figure 5-7).
Figure 5-14: PCB-backplate assembly. The PCB was screwed onto the backplate
with spacers in between. The pressure sensors are shown with top ports removed.
64
As Figure 5-15 shows, the PCB-backplate subassembly is placed into the fiberglass
enforced rubber shell and located using the lip mentioned previously in Section 5.1.
A liquid polyurethane elastomer filling (VytaFlex 10 made by Smooth-On) was then
used to fill the inside pocket of the rubber shell as well as submerging the PCB along
with its mounted pressure sensors. All the components were well wetted with the
VytaFlex 10 liquid resin before placed in the vacuum chamber to degas. After degas,
the whole assemble was left to cure under room condition for 24 hours.
Figure 5-15: The finished footpad sensor with cured inner elastomer filling.
5.3
Testing
The newly designed footpad sensor was then attached to the front left leg of the MIT
Cheetah robot for testing (shown in Figure 5-16). mbed microcontroller was used for
data acquisition (100Hz) which logs all the pressure sensors' outputs as a function of
time. Currently, the footpad sensor outputs can only be logged for 10 seconds due to
the limitation of on board memory. The hosting electronics were implemented on a
breadboard and strapped to the Cheetah robot's leg while testing (Figure 5-16). The
footpad sensor was strapped onto the front left leg of the Cheetah robot using zip
ties for easy attachment and removal.
The Cheetah robot was then programmed to hop in place with the footpad sensor
attached to characterize the sensor's performance when integrated to the robot's leg.
Furthermore, a force platform (sampling at 1000Hz) was placed right beneath the
65
footpad sensor for referencing force measurements. Both footpad sensor outputs and
reference force platform readings were recorded and later analyzed to verify the performance of the newly developed footpad sensor. Additionally, the Cheetah robot was
programmed to hop with and without the footpad sensor attached to exam whether or
not the introduction of such footpad sensor disturbs the system stability. High speed
videos (240fps) were also recorded throughout the entire duration of the experiment.
Figure 5-16: Image shown the newly designed footpad sensor been installed onto the
front left leg of the MIT Cheetah robot.
66
5.4
Results and Discussion
1000
0
500
0
0
K
_
3
500
1000
5000
1500
2000
I
I
-0
4000
3000
I
3
4
~~I
-
&
00 2000
M41000
-2
-
g
0
500
1000
1500
2000
Time (ms)
Figure 5-17: Reference force measurements and footpad sensor outputs are plotted
from the Cheetah hopping experiment.
The recorded results for both the footpad sensor outputs and the reference force
measurements are plotted against time in Figure 5-17. As shown, the x-axis is time
measured in millisecond. The top subplot shows the reference force measured using
the force platform and the bottom subplot shows the footpad sensor outputs. The
reference force was measured in Newtons and the footpad sensor output is a plain
voltage reading where 0 correspond to OV and 212 = 4096 correspond to 5V. As
Figure 5-17 shows, the Cheetah robot was rested on the force platform initially which
causes an initial non-zero reading for both the footpad sensor and the reference force
platform. The Cheetah robot was then programmed to hop repetitively on the force
67
platform which can also be seen in both the reference force measurements and the
footpad sensor outputs.
In Figure 5-17, each one of the pressure sensor's output was plotted against time
in the bottom subplot. The pressure sensor layout is shown in Figure 5-18, sensor 0
and 3 are under the "toes" of the Cheetah robot, whereas sensor 2 and 5 are under
the "heel" part of the robot's foot.
Figure 5-18: Pressure sensor layout for the newly designed footpad sensor.
The Cheetah robot was controlled to generate a prescribed force profile to hop.
Note that prior to the "Gaussian" -like force profile, there is a large peak force to the
left of it. This is caused by the landing of the robot which has much faster dynamics
than the preparation to hop phase. Furthermore, the footpad sensor outputs follow
closely to the reference force measurements which validates the functionality of the
newly designed footpad sensor.
A zoomed in view of the footpad sensor outputs are shown in Figure 5-19. As
shown, each one of the six pressure sensors' outputs were plotted together against
time. Prior to impact, output from each one of the six pressure sensors were distinct
and no similarity can be drawn from the acquired data. However, during the impact,
the sensors' outputs can roughly be grouped into three groups of two. In Figure 5-19,
68
the teal colored and blue colored lines follow each other closely. Likewise, the magenta
line and the green line are closely related as well as the red line and the yellow line.
The similarity of the pressure sensor outputs within each one of the three groups is
extremely obvious.
5000
-0
4000 --
I
0g
-3
3000 -4
-- 5
2000
1000
0
550
600
650
Time (ms)
700
750
Figure 5-19: Zoomed in view of the footpad sensor outputs.
The mapping of this observation to the pressure sensor layout shown in Figure 518 is summarized in Table 5.1. As the Cheetah robot hops vertically, the observation
outlined in Table 5.1 agrees with physical intuition that pressure variation along
the length of the foot (heel-toe) is dominant. This observation further validate the
functionality of designed footpad sensor.
Table 5.1: Mapping between pressure sensor groups and sensor layout.
Group 1
Sensor 0 and 3
"toe"
Group 2
Sensor 1 and 4
"palm"
Group 3
Sensor 2 and 5
"heel"
Moreover, as shown in Figure 5-19, the "toe" sensors (sensor 0 and 3) captures
the largest signal. In contrast, the "heel" sensors (sensor 2 and 5) barely output any
69
signal. The observed difference in output between the "toe" and the "heel" sensors
are determined by the angle at which the foot has struck the floor.
Figure 5-20 is an other zoomed in view of the footpad sensor outputs plotted
against time. As shown sensor 0, 3, and 4 reached its maximum reading (4096) for a
period of time which indicate sensor saturation during the hopping experiment. The
correct input force could still be calculated from the footpad sensor's output given
that half of the pressure sensors are still within its operational range. However, this
might introduce an negative effect on the footpad sensor's accuracy and sensitivity.
Thus, a stiffer elastomer filling could be tested to avoid the pressure sensor saturation
when integrated to the Cheetah robot.
5000
-0
4000
-2
-3
3000 -- 4
-4
2000
1000
0
900
950
1000
Time (ms)
1050
1100
Figure 5-20: Image shows the saturation of the footpad sensor outputs.
The Cheetah robot's hopping experiment was repeated numerously over several
days span. The installed footpad had no visual damage and no obvious performance
change was observed after completing all the testings. The attachment of the developed footpad sensor to the Cheetah robot's leg also lasted through the entire
experimentation period.
70
Chapter 6
Material Characterization
Material characterization of the elastomer used is critical to understand the footpad
sensor's performance as well as gaining additional insights on further optimizatioa of
the footpad sensor in terms of its range and sensitivity. Currently, the polyurethane
rubber filling was molded into the footpad sensor from its liquid resin and the matqrial
property of the elastomer filling after curing is not well characterized. As mentioned
in Chapter 2, the stiffness of the elastomer filling if the governing factor in term of
the range and sensitivity of the developed footpad sensor. Thus, understanding the
material properties of the elastomer materials are important not only for future de ign
iterations of the footpad sensor but also constructing finite element analysis (FEA)
simulation model for the footpad sensor.
6.1
Material Testing
The material properties of three types of polyurethane rubber with different durImeter were characterized. The true stress-strain curve was obtained for each type of
material from testing using a Instron (5944) machine. The specimen for each of the
tested material were molded first prior to testings. Each one of the tested material
were molded to desired geometry as test specimen. The specimen is "I" shaped, where
the Intron machine will grip onto the two end of the "I" during testing.
71
Figure 6-1: Material specimen for characterizing the material property of molded
polyurethane rubber. The image shows a material specimen molded out of VytaFlex
10 liquid resin (made by Smooth-On).
Figure 6-1 shows one of the molded specimen made from VytaFlex 10. While
keeping the outer geometry the same, the specimen were varied by thickness, and
three thickness were chosen: 3mm, 6mm, and 9mm. For each tested material there
were two completely identical specimen tested on the Instron machine. The specimen
were attached to the Instron machine firmly and no visual slippage was observed.
While testing, the Instron machine collects the extension of the tested specimen as
well as the resulted force from stretching. Figure C-1 shows a image of a under testing
specimen on the Inston machine.
5040
V
~30
-3mm
10_
0
0
_ 6mm
100
200
Extension (mm)
300
400
Figure 6-2: Plot of collected Instron data on VytaFlex 10: extension of the specimen
versus the resulted force.
As shown in Figure 6-2, the data collected from Instron were plotted; extension of
72
the specimen versus the resulted force. Specimen with three different thickness were
tested and plotted in different colors. Each identical specimen were tested twice and
plotted to shown the repeatability of the Instron measurements. Figure 6-2 shows
that under the same amount of extension, the thickest specimen results in the largest
force. This is in agreement with the physical principle that the stiffness of the material
increases as its thickness increases. Moreover, as comparing the measurements made
on identical specimen, the measured results has very small variation.
The true stress and strain were then calculated from the measurements obtained
from Instron testing using Equation 6.1 and 6.2.
dl
Sln((6.1)
_F
F-
(6.2)
In Equation 6.1, 1 denote for the current length of the tested specimen under
tension and lo represent the original length of the specimen without any loading ondition. In Equation 6.2, F represent the force resulted from stretching the specinen
and A denotes for the actual cross sectional area of tested sample. A number o, assumptions were used to obtain the true stress and true strain of the tested specim ns:
" because the tested materials are polyurethane rubbers, thus the materials, are
assumed to be perfectly incompressible (total volume of the tested specimen is
always conserved)
" the cross sectional area along the length of the "I" shaped specimen is cons ant
(not considering the two ends of the "I" griped by the Instron machine), bec use
there is no visible necking of the tested specimen
" the effects of material fatigue on Instron measurements are negligible prior to
the fracture of the testing specimen
With the assumptions listed above, the true stress and true strain of each of the
tested specimen can be obtained. The calculated true stress and true stain values are
73
plotted in Figure 6-3. As shown, the true stress strain data overlaps across all the
tested specimens, there is hardly any observable variation between specimens. Thus,
the elastomer's material property from cured liquid resin is quite consistent. Material
characterization data on the other two tested material (VytaFlex 60 and EcoFlex 10,
made by Smooth-On) are included in Appendix D.
5
4-
1
3,
-3mm
1 ---
0
0
6mm
0.5
1
1.5
True Strain
2
2.5
Figure 6-3: Calculated true stress strain values plotted for VytaFlex 10.
From the material characterization data, the range and sensitivity of the footpad
sensor can be further optimized.
Furthermore, footpad sensor behavior could be
simulated and compared against empirical findings.
74
Chapter 7
Conclusion
The custom designed impact tester is sufficient to be used for the footpad sensor's
dynamic characterization.
Through the experimental characterization, the custom
designed impact tester was shown to meet all the specified functional requirements.
The designed and fabricated impact tester was able to produce a range of impact
conditions in terms of varying the impact velocity and the magnitude of impact.
Furthermore, the impact tester was able to produce a named impact condition repetitively. The reference force platform measurements were also validated prior to be
used for characterizing the footpad sensor.
The footpad sensor prototype was tested dynamically using the custom developed
impact tester. The previously developed static ANN model was applied to the footpad
sensor's outputs obtained under dynamic condition and found to be highly imprecise
(ratio between peak static ANN prediction and peak reference force measurements
was 0.21).
Therefore, a dynamic ANN model was developed to better predicate
the impact outputs of the footpad sensor. Such dynamically trained ANN model
was able to capture the impact response of the footpad sensor and achieve a ratio
of 0.88 between peak dynamic ANN prediction and peak reference force measured.
Four additional dynamic testing trials were carried out to verify the performance of
the developed dynamic ANN model and achieved RMSE
=
3.17% for a maximum
reference force reading of 3000N.
The newly designed footpad was able to detect ground contact accurately and
75
precisely. Moreover, the sensor was able to capture multiple ground contacts consecutihely and its outputs agree well with reference force measured by the force platform.
ThE developed footpad sensor was integrated with the legs of MIT Cheetah robot as
designed. Compare to the preceding iteration, the new design includes a fiberglass
enforced polyurethane rubber shell to improve its durability under running condition
when installed to the Cheetah robot. The size of the footpad sensor was also reduc d to better attach to the Cheetah robot's leg. This new footpad sensor design
was fabricated and secured to the Cheetah robot's leg for hopping experiments. As
suggested by the experimental results, the newly designed footpad sensor was capable
Df
capturing the hoping dynamics and agree well when compared to the reference
force measurements. No damage nor performance degrading of the developed footpad
senSor was observed at the end of the experimentation.
Three different kinds of polyurethane elastomer materials cured from liquid resins
were characterized and true stress/strain data were obtained. From the experimental
res lts, the elastomer's material property were consistent after molding and curing.
The obtained material information will be used for FEA simulations of the footpad
sensor's behavior under loads in future studies.
Overall, the newly developed footpad sensor was functional and can be characterized using the custom designed impact tester. The original developed static model
was shown to be... Moreover, the composite footpad force sensor was able to detect
ground reaction force accurately and precisely. The footpad sensor's range and sensitivity will be better toned via modeling of the footpad sensor's performance and
corparison with experimental findings in future investigations.
7.
Future Work
Future work on optimizing the footpad sensor's performance for the MIT Cheetah
robot includes resolving the footpad sensor signal saturation that was currently obserted; characterizing the newly designed footpad sensor both statically and dynamicallr; construct FEA simulation model for the footpad sensor; and conduct additional
76
integrated experimentation with the Cheetah robot to understand the footpad sensor's behavior overtime.
To avoid footpad sensor signal saturation, a stiffer polyurethane elastomer filling
will be explored and tested. Alternatively, the pressure sensor placement within the
footpad sensor can also be adjusted to ensure the loads are more evenly spread across
all the embedded pressure sensors.
Furthermore, the developed footpad sensor will be characterized both dynamically
and statically and ANN models will be developed accordingly. The obtained dynamic
ANN model will also be verified when attached to the Cheetah robot and the accuracy
of the developed model will be quantified. To further improve the ANN models for
the footpad sensor, the sampling rate will be increased for both the reference force
measurements and the footpad sensor outputs. The duration of sampling for the
footpad sensor will also be improved by expanding the onboard memory of the mbed
microcontroller.
FEA simulation for the designed footpad sensor will be developed utilizing the
material property information outline in Chapter 6. The established FEA simulation
will be verified by comparing modeled results with empirical findings. After validation, the FEA model will be used to optimize the pressure sensor layout within the
footpad sensor to improve its accuracy and range.
Finally, the developed footpad sensor will be used for more field tests with MIT
Cheetah robot. The footpad sensor's performance over time will be characterized nd
quantified namely its durability, drift over time, and hysteresis if any. Various Che tah
robot's running conditions will also be testing with the footpad sensor integrated such
as walking, running, galloping, etc. besides just hopping.
77
78
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80
Appendices
81
82
Appendix A
Dynamic ANN Model Verification
1200
-Ref
1000-
Force
-Dynamic
ANN
800
600
g
400
-1.
o
A
-l
200
-200'0
-
0
200
400
600
Time (ms)
800
1000
Figure A-i: Comparison between reference force measurements and predicted results
from dynamically developed ANN model. The carriage was dropped from 20cm with
mdropping carriage = 1.14kg. RMSE = 2.47%.
83
1000
-Ref
800-
Force
-Dynamic
ANN
-
600
400
-_k
200
O M ;
-
'
-
-
g
0
-200'
0
200
400
600
Time (ms)
800
1000
Figure A-2: Comparison between reference force measurements and predicted results
from dynamically developed ANN model. The carriage was dropped from 20cm with
mdroppingcarriage =
1.14kg. RMSE = 3.50%.
1200
-Ref
1000-
Force
-Dynamic
ANN
800
8 600g 4002000
-200
0
200
400
600
Time (ms)
800
1000
Figure A-3: Comparison between reference force measurements and predicted results
from dynamically developed ANN model. The carriage was dropped from 30cm with
mdropping carriage=1.14kg.
RMSE
=
3.57%.
84
Appendix B
Backplate Fabrication
Figure B-1: Degassing the wetted 3D printed mold and remaining resin in vacuum
chamber. The image shows the air escaping from the mixed Task 4 resin and causing
the resin to foam.
85
Figure B-2: A close up view for the 3D printed mold failure after demolding.
86
Appendix C
Instron Testing
Figure C-1: Instron testing of a VytaFlex 60 specimen.
87
88
Appendix D
Material Testing Results
D.1
EcoFlex 10
50-
/
4030-
r
/
-,
(
0
,-
10
U
0
/
-0o
ff
100
-- 6mm
200
300
Extension (mm)
400
500
Figure D-1: Plot of collected Instron data on EcoFlex 10: extension of the specimen
versus the resulted force.
89
5-3mm
-- 6mm
4
~9num
I-
3
I.
it
Ji
2-|
10
0
/$
0.5
1
1.5
2
2.5
True Strain
Figure D-2: Calculated true stress strain values plotted for EcoFlex 10.
Though there is only one trial of data for each experimental condition, the true
stress and strain curves are well overlapped across various specimens.
D.2
VytaFlex 60
600---3mm
500-
6mm
400
200-100
0
0
50
100
150
200
Extension (mm)
250
300
Figure D-3: Plot of collected Instron data on VytaFlex 60: extension of the specimen
versus the resulted force.
90
40 r
-
30
.7
//
10-
0
0
/
-
20
-3mm
6mm
0.5
1
1.5
True Strain
2
2.5
Figure D-4: Calculated true stress strain values plotted for VytaFlex 60.
The disagreement between calculated true stress and true stain data could be a
result of errors introduced from the calculation assumptions. A list of assumptions
used while calculating the true stress and true strain were outlined in Section 6.1.
91