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

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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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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

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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