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Benjamin Stephens Carnegie Mellon University Benjamin Stephens Carnegie Mellon University

Benjamin Stephens Carnegie Mellon University - PowerPoint Presentation

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Benjamin Stephens Carnegie Mellon University - PPT Presentation

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

humanoid control force linear control humanoid linear force biped balance robot periodic double estimation controlled support dynamics model center

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Presentation Transcript

Slide1

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

Slide2

Introduction2

Slide3

Motivation3

Simple models for complex systemsMake complex robot control easier

Models for human balance control

Achieve stable balance on force-controlled robot

Slide4

Force Controlled Balance4

How to handle perturbations when using low-impedance control on a torque-controlled humanoid robot

Slide5

Force Controlled Balance5

How to handle perturbations when using low-impedance control on a torque-controlled humanoid robot

Slide6

Sarcos Humanoid Robot6

Hydraulic ActuatorsForce Feedback Joint Controllers33 major DOFs (Lower body = 14)

Total mass 94kg

Off-board pump (3000 psi)

Sarcos

Hydraulic Humanoid Robot

Slide7

Contributions7

Linear biped model for force control of balanceSimple description of periodic balance control

Application of model to estimation and control of Humanoid robot

Slide8

OutlineModeling BalanceControlling BalanceApplications to Humanoid Robot ControlConclusion

8

Slide9

Modeling Balance

9

Slide10

General Biped BalanceAssumptions:Zero vertical accelerationNo torque about COM

Constraints:COP within the baseof support

10

REFERENCE:

Kajita

, S.;

Tani

, K., "Study of dynamic biped locomotion on rugged terrain-derivation and application of the linear inverted pendulum mode,"

ICRA 1991

Slide11

General 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

Slide12

The Linear Biped ModelContact force is distributed linearly to the two feet.

12

Slide13

The Linear Biped ModelBiped dynamics resemble two superimposed linear inverted pendulums.

13

Slide14

The Double Support Region14

We define the “Double Support Region” as a fixed fraction of the stance width.

Slide15

Dynamics of Double Support15

The dynamics during double support simplify to a simple harmonic oscillator

LIPM Dynamics

Slide16

Controlling Balance

16

Slide17

Phase Space of LiBM

Location of feet

Double Support Region

17

Slide18

Periodic BalanceGoal: Balance while moving in a cyclic motion, returning to the cycle if perturbed.

18

Slow Swaying

Fast Swaying

Marching in Place or Walking

Slide19

Orbital Energy ControlOrbital Energy:Solution is a simple harmonic oscillator:We control the energy:

19

Slide20

20

Slide21

Energy Control Trajectories

21

Slide22

22

Slide23

23

Slide24

Application to Humanoid Balance

24

Slide25

Humanoid 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.

Slide26

Center 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

Slide27

27

Slide28

Feed-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.

Slide29

29

Slide30

30

Slide31

31

Slide32

32

Impulsive Push

Limit Cycle

Slide33

Robot Experiments33

Slide34

Future Work34

3D Linear Biped ModelRobot BehaviorsFoot PlacementPush Recovery

Walking

Robust Control/Estimation

Push Force Estimation

Robust control of

LiBM

Slide35

Conclusion35

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?

Slide36

Thank you36

Questions?Special thanks to supporters:National Science Foundation

Quality of Life Technology Engineering Research Center

Slide37

The Linear Biped ModelContact force is distributed linearly to the two feet.

37