Design, Development, and Dynamic
Characterization of Multi-Axis Force Sensing AMC M
MASSACHUSETTS INSTITUTEComposite Footpad
OF TECHNOLOGYby
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Guangtao Zhang
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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 charac-terization of the footpad sensor.
In order to characterize the developed footpad sensor dynamically, a custom im-pact 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.
Thesis Supervisor: Sangbae Kim Title: Assistant Professor
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.
Contents
1 Introduction 17
2 Previous Work 21
2.1 Compliant Footpad Sensor . . . .... . . . 21
2.2 Static Characterization ... ... . .. . . . 23
3 Impact Testing 25 3.1 Impact Tester Design. . . . ... . . . 25
3.2 Impact Tester Fabrication . . . ... 27
3.3 Characterization . . . .... . . . . 29
3.3.1 Reference Force Reading Validity . . . .. . . . .. 30
3.3.2 Repeatability . . . ... . . . 37
3.3.3 Operational Range... . . . 41
4 Dynamic Characterization 43 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
5 Footpad Sensor for Cheetah Robot 53 5.1 Design . . . . .. .. .. ....53
5.2.1 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 . . . . 67
6 Material Characterization 71 .1 M aterial Testing . . . . ... .. .. 71 7 onclusion 75 7.1 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 . . . .. . . . 89 D.2 VytaFlex 60 . . . .
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]. . . . . 22 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
2-3 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]. . . . .. . . . . . . 23 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. 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
-3 Close up view of the footpad sensor being attached to the impact tester. The force platform was placed right underneath the footpad sensor. 29
3-4 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
informa-tion 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 mdroing carriage = 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 mdroing carriage = 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 Dropping Height and their linearly fitted functions. . . . .. 39 3-13 Peak impact force measured using the reference force platform
plot-ted 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. . . . . 41 4-1 Footpad sensor's voltage outputs plotted against time when dropped
from 10cm and mdrWing carriage = 1.14kg. The measured reference
4-2 Comparison between reference force measurements and predicted re-sults from the previously developed static ANN model [13]... ... 46 4-3 A zoomed in view for the comparison between reference force
measure-ments 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 4-5 Zoomed in view of Figure 4-4. . . . . .49
4-6 Comparison between reference force measurements and predicted re-sults from dynamically developed ANN model. The carriage was dropped from 10cm with mdrping carriage = 1.14kg. . . . . 50 5-1 CAD rendering of the assembly between the newly designed footpad
sensor onto the Cheetah robot's leg. . . . . . . . 54
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. . . . . .. 55 5-3 Assembly rendering for the newly designed footpad sensor. Shown
from left to right: fiberglass enforced polyurethane rubber shell (yel-low body), PCB assembly (green body), elastomer filling (transparent body), and a polyurethane plastic backplate (violet body). .... 56
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
elas-tom 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
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 resin while curing. . . . .. . . . .. .63
-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. The pressure sensors are shown with top ports removed . . . . . .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
5-20 Image shows the saturation of the footpad sensor outputs. . . . . 70
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). . . . . 72
6-2 Plot of collected Instron data on VytaFlex 10: extension of the speci-men versus the resulted force . . . . .. 72
A-1 Comparison between reference force measurements and predicted
re-sults from dynamically developed ANN model. The carriage was dropped from 20cm with mdropping carriage = 1.14kg. RMSE = 2.47%. ... 83
A-2 Comparison between reference force measurements and predicted
re-sults from dynamically developed ANN model. The carriage was dropped from 20cm with mdropping carriage = 1.14kg. RMSE = 3.50%. ... 84 A-3 Comparison between reference force measurements and predicted
re-sults from dynamically developed ANN model. The carriage was dropped from 30cm with mdropping carriage = 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 resin and causing the resin to foam. . . . ... . . . . . 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 D-1 Plot of collected Instron data on EcoFlex 10: extension of the specimen
versus the resulted force. . . . . 89 D-2 Calculated true stress strain values plotted for EcoFlex 10. . . . . 90 D-3 Plot of collected Instron data on VytaFlex 60: extension of the
speci-men versus the resulted force. . . . ... . ... . . 90
List of Tables
4.1 Number of experimental trials for dynamic testing of the footpad sensor prototype. . . . .. 5.1 Mapping between pressure sensor groups and sensor layout. ...
44
Chapter 1
Introduction
Ground reaction force measurements are critical for designing a well-performed con-troller for a quadruped robot, especially when running at high speeds [1]. To monitor the reaction forces generated when the robot pushes against its environmental bound-aries, 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 op-erate 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 informa-tion 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.
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 proof-of-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.
contact as well as impact forces, characterization of the sensors impact response was performed. The multi-axis force sensing composite footpad was dynamically char-acterized by recording the sensor's outputs when impacting a referencing force mea-suring 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 de-veloped 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 im-provement 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.
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 under-standing 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 pro-totype is shown in Figure 2-2. After submerging each of the pressure sensor within
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 out-put 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 calcu-lated 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].
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.
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
Chapter 3
Impact Testing
Testing under static conditions alone cannot offer sufficient understanding and veri-fication 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
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
Lp~--JFootpad
Sensor
-- .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 iden-tical 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 characteriza-tion 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.
3.2
Impact Tester Fabrication
Aluminum structural framing parts (made by 80/20) were used for the ease of fabri-cation. 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.
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.
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.
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 verifica-tion. 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 track-ing software (Tracker 4.82) to obtain the position of the dropptrack-ing 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
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 20- -3.49kg 15 -10 5-0 0 0.5 1 1.5 2 Time(s)
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
acceler-ation 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.
25 r W2 0 p4 20 15 10 5 0 0 -0.5 1 Time (s)
Position data for 1.14kg
Quadratic fit
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 =
0 1 0mgm 0 0 0.2 0.4 0.6 Time (s) 0.8 1 1.2
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.
1000-0 800- 0 0 600- 0 * 400- 0 0 200 ni-i -200'-0 0 *0 m 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 experi-ment 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 1.5 r 1 0.5 0 U .0 >0 -0.5 F -1 -1 5
-*
0
.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 0 400 200-0o 00000 0 00000 -200 0.09 0.095 0.1 0.105 0.11 0.115 0.12 Time (s)
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 Fpak.
1
J = 1timpactFeak (3.2)
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
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 = 1027N.
1000 0 Reference Force 800 600 400 00 2000
0
--- ---00000 -200 ' 0.09 0.095 0.1 0.105 0.11 0.115 0.12 Time (s)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 drop-ping carriage leaves the force platform, however, the measuring surface itself is also
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, mdropping carriage= 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 = 2mdropping carriage (Vafter - 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
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 de-termined 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
2.5 -0 1.14kg * 3.49kg 0-W 1.5 0 1 0.1 0.15 0.2 0.25 0.3 0.35 Initial Dropping Height (m)
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 consider-ing 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 er-rors. 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. The linear fit for data collected when mdropping carriage = 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
to overcome more frictional losses and accelerate at a slightly higher acceleration than a lighter dropping carriage.
2.5-o 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 Dropping Height 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
3-13 shows, the captured peak impact forces were plotted against the initial dropping
height of the carriage. Again, blue circles are data collected when mdropping carriage =
1.14kg and peak impact forces observed when mdropping carriage = 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.
3uuu 0 1.14kg 3.49kg 2500 2000 1500 A4 1000-500 0.1 0.15 0.2 0.25 0.3 0.35 Initial Dropping Height (m)
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.
3000 -0 1. 14kg 920-* 3.49kg 2500 1500 - 1000-500 0.1 0.15 0.2 0.25 0.3 0.35 Initial Dropping Height (m)
Figure 3-14: 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 R2 = 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
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.
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 dynami-cally 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 sen-sor. 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
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.
Mdrappng carriage =1. 14kg mndrppng carriage =3.49kg
Dropped Height = 10cm
Dropped Height = 20cm
Dropped Height = 30cm
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 ana-lyzed 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
3 3
4 3
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.
6 1000 -1 -2 4- -3 500 -4 -5 6 7 9 -IRef Force 0 ' ' ' ' ''500 0 50 100 150 200 250 300 350 400 Time (ms)
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
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 2000 1000 0 -Ref Force -Static ANN 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Index
Figure 4-2: Comparison between reference force measurements and predicted results from. the previously developed static ANN model [13].
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 Force 800 -Static ANN 600 a400-0 100 150 200 250 Index
Figure 4-3: A zoomed in view for the comparison between reference force measure-ments 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.RMSE= 2 (giyi)2 (4.1)
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 2000 1000 0 -Ref Force -Dynamic ANN Static ANN 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Index
Figure 4-4: Comparison between reference force measurements, predicted results from the previously developed static ANN model [13], and dynamically developed ANN
model.
As Figure 4-4 shows, the reference force measurements, the static ANN model pre-dictions, 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.
800- -Ref Force -Dynamic ANN -Static ANN 600-0400 200-100 120 140 160 Index
Figure 4-5: Zoomed in view of Figure 4-4.
