Post on 10-Feb-2016
description
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
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
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
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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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
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
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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
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Resort to modeling arbitrary geometric paths
x
z
Geometric dependencies are model as:
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Dimensional Reduction of Models
Using the previous dependencies the actuated non-linear pendulum becomes
The model becomes now an ODE:
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Given the piecewise linear model analyze feasible geometric paths
FALL!!
0xcomv 0
xcomv0
is angle of attack
)0(vmotorf
000
passive
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Example: design of geometric path
GOOD! UNFEASIBLE
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If we consider non-linear geometric paths, dynamics are non-linear
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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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Examples:(Forward/Backward Propagation)
00
00
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Solving the multicontact behavior
FRICTIONCONE
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Planning of contact transitions
FWD
FWD
BWDSearch-based to reach apex with zero velocity
Apex
Apex
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Entire leaping planning strategy
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Results and Comparison with Human
HUMAN
PLANNERHUMAN
PLANNER
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Movie
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Details design of Hume
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Design setpoint
CoM Path
Rough Terrain
0.4 m
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Questions
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Supporting slides
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How is that possible?
g
In the absence of forces -> parabola
)0(v0mf
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0xcoma
g
)0(v
Angle of attack negative0
0mf
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0xcomag
)0(v
Angle of attack positive0
0mf
Mg
mf
totalf
0mf
Details on forces
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Side and Front of Hume
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Mechatronics
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Unused slides
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