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Shishir N. Y. Kolathaya Postdoctoral scholar Mechanical and Civil Engineering California Institute of Technology HISTORY OF WALKING ROBOTS Seminar Bombay, Aug 9
Shishir N. Y. KolathayaPostdoctoral scholar
Mechanical and Civil EngineeringCalifornia Institute of Technology
HISTORY OF WALKING ROBOTS
SeminarBombay, Aug 9
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1960’s 1980’s
2000’s 2000’s
There are quite a few working bipeds today!
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Traditional Methods: Zero Moment Point (ZMP)Spring Loaded Inverted Pendulums (SLIP)
Approaches used for bipedal walking
Modern Methods: Passivity based controlHybrid Zero Dynamics (HZD)
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Outline of the talk
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1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
Our approaches for walking
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
History of methods for walking
Outline of the talk
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1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
Our approaches for walking
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
History of methods for walking
Zero Moment Point (ZMP)
10Vukobratovic et. al, IEEE Transactions on Bio‐Med 1969
Capture points
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Jerry Pratt
Pratt et. al, IEEE International Conference on Humanoid Robots 2006
Outline of the talk
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1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
Our approaches for walking
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
History of methods for walking
Spring Loaded Inverted Pendulums (SLIP)
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Marc Raibert
Raibert, IEEE Journal of Robotics and Automation 1986
Outline of the talk
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1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
Our approaches for walking
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
History of methods for walking
Passivity based control
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Tad McGeer
McGeer, IJRR 1990
Slope change as a group action
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Slope angle of the plane
Robot configuration
Slope change is a group action
The dynamics undergo a controlled symmetrical transformation under the slope changeSpong et.al, TAC 2005
Outline of the talk
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1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
Our approaches for walking
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
History of methods for walking
Hybrid zero dynamics
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Jessy Grizzle
Grizzle et.al, CDC 2003
Zero dynamics <> Underactuated systems
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Hybrid zero dynamics <> Underactuated systems
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Hybrid zero dynamics <> Underactuated systems
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Tracking control:Actual outputs and desired outputs:
linear combination of joint anglesdesired polynomial trajectory
Example:
Control Objective:Drive the actual behavior of the robot to the desired behavior:
Hybrid Zero Dynamics14Grizzle et al., TAC 2001 & TAC 2003
Ames, ROMOCO 2011
Hybrid zero dynamics <> Underactuated systemsou
tputs
time
Hybrid zero dynamics <> Underactuated systems
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Tracking control:Actual outputs and desired outputs:
linear combination of joint anglesdesired polynomial trajectory
Example:
Tracking control:Actual outputs and desired outputs:
linear combination of joint anglesdesired polynomial trajectory
Hybrid zero dynamics <> Underactuated systems
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Example:
Output dynamics
Passive dynamics
Gait design Control design
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We have progressed from this
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To this…
Outline of the talk
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1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
Our approaches for walking
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
History of methods for walking
Gait design <> Trajectory Optimization
29We need fast trajectory optimization: Limit cycle in simulation does not
imply limit cycle in experiment.
Trajectory Optimization
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1. Single shooting method: >2 hours, solution not found2. Multiple shooting method: 13 hours, solution found
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Optimization performance
3. Direct collocation: <1 min, solution found
Single shooting
Multiple shooting
Trajectory Optimization
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Trajectory Optimization
36We need fast trajectory optimization for testing different gaits.
Outline of the talk
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1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
1. Gait design:Direct collocation based trajectory optimization
2. Controller design:Input‐to‐state stabilizing controllers
Our approaches for walking
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
1. Zero Moment Point (ZMP)2. Spring Loaded Inverted Pendulums (SLIP)3. Passivity based control4. Hybrid zero dynamics (HZD)
History of methods for walking
Controller design plays an important part!
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Nov 2013Dec 2011
Jun 2016Jun 2015
AMBER1 AMBER2 PROXI DURUS DURUS‐2DP Voltage Control PD current control PD current control PD current
control+Regulators, Time based parameterization
PD current control,Time+state based parameterization
2011 2013 2014 2015 2016
Controller design plays an important part!
39Increasing complexity!
40Design time
Deployment lifetime
Controller design plays an important part!
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Returning to basics!
Watch how the hip is always maintained at a constant height.
Returning to basics!
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Take the derivative and substitute for
Assuming constant center of mass height and low
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Returning to basics!
Black: Negative feedback for amplifiers.
Zames: Input/output stability. Operator theory.
Harold Black George ZamesAmplifier
Returning to basics!
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Preliminaries on ISS
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Preliminaries on ISS
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Eduardo Sontag
Aleksandr LyapunovGeorge Zames
Input/output stability for linear systems
Input to state stability for nonlinear systems
Lyapunov stability for nonlinear systems
Preliminaries on ISS
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Properties of ISS
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How to obtain ISSing controllers?
Linear feedback laws
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Hybrid invariance
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Stabilizing controller
= Output stability
Yadukumar et. al, WAFR 2010.
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Phase uncertainty
79Kolathaya et. al, ACC 2016
DURUS‐2D Running with ISS based controllers
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Conclusions
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Made a significant step toward bridging the gap between theory and experiment
• Gait design: Demonstrated fast gait generation via collocation methods.
• Controller design: Constructed ISSingcontrollers to address modeling and phase based uncertainties.
Next steps: Food and agriculture
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Challenges• Hybrid system model• Underactuation• Soft contact with trunk
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Robots in agriculture
Robots in agriculture
Farming and mining applications will be the first to receive self‐driving tech in India, because the driving patterns are far simpler – no humans and other vehicles in your path to worry about. They’re also quick to adopt new technologies. Plus, these industries are key drivers of our country’s economy.‐‐ Dr. Roshy John
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Thank you!
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Acknowledgements• NSF, DARPA• SRI Robotics, National Instruments• Miso Robotics
