history of walking robots - syscon | homethere are quite a few working bipeds today! 5. 6. ......
TRANSCRIPT
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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
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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
8
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
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Outline of the talk
9
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
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Zero Moment Point (ZMP)
10Vukobratovic et. al, IEEE Transactions on Bio‐Med 1969
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Capture points
11
Jerry Pratt
Pratt et. al, IEEE International Conference on Humanoid Robots 2006
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Outline of the talk
12
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
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Spring Loaded Inverted Pendulums (SLIP)
13
Marc Raibert
Raibert, IEEE Journal of Robotics and Automation 1986
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Outline of the talk
14
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
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Passivity based control
15
Tad McGeer
McGeer, IJRR 1990
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Slope change as a group action
16
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
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Outline of the talk
17
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
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Hybrid zero dynamics
18
Jessy Grizzle
Grizzle et.al, CDC 2003
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Zero dynamics <> Underactuated systems
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Hybrid zero dynamics <> Underactuated systems
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Hybrid zero dynamics <> Underactuated systems
21
Tracking control:Actual outputs and desired outputs:
linear combination of joint anglesdesired polynomial trajectory
Example:
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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
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Hybrid zero dynamics <> Underactuated systems
23
Tracking control:Actual outputs and desired outputs:
linear combination of joint anglesdesired polynomial trajectory
Example:
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Tracking control:Actual outputs and desired outputs:
linear combination of joint anglesdesired polynomial trajectory
Hybrid zero dynamics <> Underactuated systems
24
Example:
Output dynamics
Passive dynamics
Gait design Control design
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We have progressed from this
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To this…
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Outline of the talk
28
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
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Gait design <> Trajectory Optimization
29We need fast trajectory optimization: Limit cycle in simulation does not
imply limit cycle in experiment.
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Trajectory Optimization
30
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1. Single shooting method: >2 hours, solution not found2. Multiple shooting method: 13 hours, solution found
31
Optimization performance
3. Direct collocation: <1 min, solution found
Single shooting
Multiple shooting
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Trajectory Optimization
32
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Trajectory Optimization
36We need fast trajectory optimization for testing different gaits.
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Outline of the talk
37
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
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Controller design plays an important part!
38
Nov 2013Dec 2011
Jun 2016Jun 2015
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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!
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40Design time
Deployment lifetime
Controller design plays an important part!
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41
Returning to basics!
Watch how the hip is always maintained at a constant height.
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Returning to basics!
42
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
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Returning to basics!
44
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Preliminaries on ISS
45
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Preliminaries on ISS
46
Eduardo Sontag
Aleksandr LyapunovGeorge Zames
Input/output stability for linear systems
Input to state stability for nonlinear systems
Lyapunov stability for nonlinear systems
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Preliminaries on ISS
47
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Properties of ISS
64
How to obtain ISSing controllers?
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Linear feedback laws
66
Hybrid invariance
+
Stabilizing controller
= Output stability
Yadukumar et. al, WAFR 2010.
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Phase uncertainty
79Kolathaya et. al, ACC 2016
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DURUS‐2D Running with ISS based controllers
84
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Conclusions
86
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.
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Next steps: Food and agriculture
93
Challenges• Hybrid system model• Underactuation• Soft contact with trunk
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95
Robots in agriculture
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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!
99
Acknowledgements• NSF, DARPA• SRI Robotics, National Instruments• Miso Robotics