motion planning of extreme locomotion maneuvers using multi-contact dynamics and numerical...
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![Page 1: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/1.jpg)
Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and
Numerical Integration
The Human Center Robotics Laboratory (HCRL)The University of Texas at Austin
Luis Sentis and Mike Slovich
Humanoids 2011,Bled, SloveniaOctober 28th, 2011
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Luis Sentis
What Are Extreme Maneuvers (EM)?(Generalization of recreational free-running)
Tackles discrete surfaces and near-vertical terrains
Needed for humanoids, assistive devices and biomechanical studies
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Luis Sentis
Objectives of the research
• Develop new dynamical models and numerical techniques to predict, plan and analyze EM
• Develop whole-body adaptive torque controllers to execute the motion plans and the desired multi-contact behaviors
• Build a nimble bipedal robot to verify the methods
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Luis Sentis
State of the art
• Rough terrain still dominated by methods that do not taking into account friction characteristics
• No generalization of gait to discrete terrains with near-vertical surfaces
• Multicontact dynamics are largely overlooked
• Linearization is too commonly used instead of tackling the full nonlinear problems
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Luis Sentis
Our approach to EM• Model multicontact and single-contact dynamics
• Develop geometric path dependencies
• Use path dependencies to reduce dimensionality of the dynamic problems
• Derive set of rules for feasible geometric paths
• Given step conditions, use numerical integration to predict the nonlinear behavior in forward and backward times
• Choose as the contact planning strategy the intersections in state space of maneuvering curves
• Conduct comparative analysis with a human
![Page 6: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/6.jpg)
Luis Sentis
Let’s start with multicontact dynamics
Hands and feet are in contact
Only feet are in contact
acom
fr(RF)
fr(LF)
ft
fracom
ftmn
In IROS’09, TRO’10 we presented the Virtual Linkage Modeland the Multi-Contact / Grasp Matrix for humanoids
![Page 7: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/7.jpg)
Luis Sentis
Model for single-contact dynamics(established area of research)
Non-linear pendulum dynamics (balance of inertial-gravitational-reaction moments)
passive hinge
actuated linear motor
-
cop = center of pressure (contact point)
x
z
y
The form of the model is:
)0(v
Solving multivariate NL systems is difficult
![Page 8: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/8.jpg)
Luis Sentis
Resort to modeling arbitrary geometric paths
x
z
Geometric dependencies are model as:
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Luis Sentis
Dimensional Reduction of Models
Using the previous dependencies the actuated non-linear pendulum becomes
The model becomes now an ODE:
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Luis Sentis
Given the piecewise linear model analyze feasible geometric paths
FALL!!
0xcomv 0
xcomv0
is angle of attack
)0(vmotorf
0
00
passive
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Luis Sentis
Example: design of geometric path
GOOD! UNFEASIBLE
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Luis Sentis
If we consider non-linear geometric paths, dynamics are non-linear
![Page 13: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/13.jpg)
Luis Sentis
Then, prediction by Numerical Integration
Time perturbation is:
Reduction of single contact dynamics(Non linear behavior):
Consider discrete solutions (Taylor expansion):
State space solution:
Establishing geometric dependencies:
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Luis Sentis
Examples:(Forward/Backward Propagation)
00
00
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Luis Sentis
Solving the multicontact behavior
FRICTIONCONE
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Luis Sentis
Planning of contact transitions
FWD
FWD
BWDSearch-based to reach apex with zero velocity
Apex
Apex
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Luis Sentis
Entire leaping planning strategy
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Luis Sentis
Results and Comparison with Human
HUMAN
PLANNERHUMAN
PLANNER
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Luis Sentis
Movie
![Page 20: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/20.jpg)
Luis Sentis
Details design of Hume
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Luis Sentis
Design setpoint
CoM Path
Rough Terrain
0.4 m
![Page 22: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/22.jpg)
Luis Sentis
Questions
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Luis Sentis
Supporting slides
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Luis Sentis
How is that possible?
g
In the absence of forces -> parabola
)0(v0mf
![Page 25: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/25.jpg)
Luis Sentis
0xcoma
g
)0(v
Angle of attack negative0
0mf
![Page 26: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/26.jpg)
Luis Sentis
0xcomag
)0(v
Angle of attack positive
0
0mf
Mg
mf
totalf
0mf
Details on forces
![Page 27: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/27.jpg)
Luis Sentis
Side and Front of Hume
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Luis Sentis
Mechatronics
![Page 29: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/29.jpg)
Luis Sentis
Unused slides
![Page 30: Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration The Human Center Robotics Laboratory (HCRL) The](https://reader034.vdocuments.us/reader034/viewer/2022050714/56649f425503460f94c619c8/html5/thumbnails/30.jpg)
Luis Sentis
Let’s start with multicontact dynamics
Hands and feet are in contact
Only feet are in contact
acom
fr(RF)
fr(LF)
In IROS’09, TRO’10 we presented the Virtual Linkage Modeland the Multi-Contact / Grasp Matrix for humanoids
ft
fracom
ftmn