9 th IEEERAS International Conference on Humanoid Robots December 8 2009 Modeling and Control of Periodic Humanoid Balance Using the Linear Biped Model Introduction 2 Motivation 3 Simple models for complex systems ID: 797131
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Benjamin StephensCarnegie Mellon University9th IEEE-RAS International Conference on Humanoid RobotsDecember 8, 2009
Modeling and Control of Periodic Humanoid Balance Using the Linear Biped Model
Slide2Introduction2
Slide3Motivation3
Simple models for complex systemsMake complex robot control easier
Models for human balance control
Achieve stable balance on force-controlled robot
Slide4Force Controlled Balance4
How to handle perturbations when using low-impedance control on a torque-controlled humanoid robot
Slide5Force Controlled Balance5
How to handle perturbations when using low-impedance control on a torque-controlled humanoid robot
Slide6Sarcos Humanoid Robot6
Hydraulic ActuatorsForce Feedback Joint Controllers33 major DOFs (Lower body = 14)
Total mass 94kg
Off-board pump (3000 psi)
Sarcos
Hydraulic Humanoid Robot
Slide7Contributions7
Linear biped model for force control of balanceSimple description of periodic balance control
Application of model to estimation and control of Humanoid robot
Slide8OutlineModeling BalanceControlling BalanceApplications to Humanoid Robot ControlConclusion
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Slide9Modeling Balance
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Slide10General Biped BalanceAssumptions:Zero vertical accelerationNo torque about COM
Constraints:COP within the baseof support
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REFERENCE:
Kajita
, S.;
Tani
, K., "Study of dynamic biped locomotion on rugged terrain-derivation and application of the linear inverted pendulum mode,"
ICRA 1991
Slide11General Biped Balance Stability11
COM Position
COM Velocity
Linear constraints on the COP define a linear stability region for which the ankle strategy is stable
REFERENCE:
Stephens, “Humanoid Push Recovery,” Humanoids 2007
Slide12The Linear Biped ModelContact force is distributed linearly to the two feet.
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Slide13The Linear Biped ModelBiped dynamics resemble two superimposed linear inverted pendulums.
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Slide14The Double Support Region14
We define the “Double Support Region” as a fixed fraction of the stance width.
Slide15Dynamics of Double Support15
The dynamics during double support simplify to a simple harmonic oscillator
LIPM Dynamics
Slide16Controlling Balance
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Slide17Phase Space of LiBM
Location of feet
Double Support Region
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Slide18Periodic BalanceGoal: Balance while moving in a cyclic motion, returning to the cycle if perturbed.
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Slow Swaying
Fast Swaying
Marching in Place or Walking
Slide19Orbital Energy ControlOrbital Energy:Solution is a simple harmonic oscillator:We control the energy:
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Slide21Energy Control Trajectories
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Slide24Application to Humanoid Balance
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Slide25Humanoid Applications25
Linear Biped Model predicts gross body motion and determines a set of forces that can produce that motion
State Estimation
Combine sensors to predict important features, like center of mass motion.
Feed-Forward Control
Perform force control to generate the desired ground contact forces.
Slide26Center of Mass Filtering26
A (linear) Kalman Filter can combine multiple measurements to give improved position and velocity center of mass estimates.
Joint Kinematics
Hip
Accelerometer
Feet
Force Sensors
Kalman
Filter
Periodic Humanoid Balance
CoM
State
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Slide28Feed-Forward Force Control28
LiBM can be used for feedforward control of a complex biped system.
Full-body inverse dynamics can be reduced
to force control of the COM with respect
to each foot
Additional controls are applied to bias
towards a home pose and to keep the
torso vertical.
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Slide3030
Slide3131
Slide3232
Impulsive Push
Limit Cycle
Slide33Robot Experiments33
Slide34Future Work34
3D Linear Biped ModelRobot BehaviorsFoot PlacementPush Recovery
Walking
Robust Control/Estimation
Push Force Estimation
Robust control of
LiBM
Slide35Conclusion35
Linear biped model for force control of balanceSimple description of periodic behaviors and balance control
Applied to estimation and control of humanoid robot
Slow Swaying
Fast Swaying
Marching in Place or Walking
Joint Kinematics
Hip
Accel
Force Sensors
Kalman
Filter
Periodic Humanoid Balance
CoM
State
Thank you. Questions?
Slide36Thank you36
Questions?Special thanks to supporters:National Science Foundation
Quality of Life Technology Engineering Research Center
Slide37The Linear Biped ModelContact force is distributed linearly to the two feet.
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