balancing and walking control of a torque controlled humanoid … · compliance control ext q u m...

1

Humanoids 29/11/2012

Balancing and walking control of a torquecontrolled humanoid robot

Dr.-Ing. Christian OttResearch Group on „Dynamic Control of Legged Humanoid Robots“

DLR - Institute for Robotics and Mechatronics

Folie 2

Compliant ManipulationJoint torque sensing & control for manipulation

Robustness: Passivity Based Control

Performance:Joint Torque Feedback

(noncollocated)

MotorDynamics

Rigid-BodyDynamics

TorqueControl

Environ-ment

ComplianceControl

extq

um

Folie 3

Compliant Manipulation

Robustness: Passivity Based Control

Performance:Joint Torque Feedback

(noncollocated)

MotorDynamics

Rigid-BodyDynamics

TorqueControl

Environ-ment

ComplianceControl

extq

um

Folie 4

Folie 5

Beyond Compliant Manipulation

DLR-Biped [Humanoids 2010]Joint torque sensing & control for manipulation

Folie 7

DLR-Biped

Experimental biped walking machine [Humanoids 2010]

• 6 DOF / leg

• ~50 kg

• Drive technology of the DLR arm

• Newly designed lower leg

• Slim foot design: 19 x 9,5cm

• Sensors:- joint torque sensors- force/torque sensors in the feet- IMU in the trunk

• Developed within 10 month by student projects.

• Allow for position controlled walking (ZMP) and joint torque control!

Folie 9

Torque controlled humanoid Robot

Very recent development1) preliminary version: May 20122) full version: December 2012 (estimated)

Research interests: Whole body motion/dynamicsMulti-contact interaction

Weigth: ~68kg / 75kg (complete)

Modified hip kinematics:compact design for locating thetotal COM close to the hip joints

(TORO)

Folie 10

Bipedal Robot Model

rF lF

lT

l

Tbl

rT

r

Tbr

bb

bb

qx

xqx FqJ

qJFqJ

qJqxg

qx

qxqCqx

qMqMqMqM

)(0

)(

0)()(

0),(),,(

)()()()(

l

r

qq

q

6bx

Properties for control:• Underactuated• Varying unilateral constraints

(single support, double support, edge contact)

• Constraints on the state & control

Folie 11

l

Tl

Tbl

rT

r

Tbr

bb

bb

qx

xqx FqJ

qJFqJ

qJqxg

qx

qxqCqx

qMqMqMqM

)(0

)(

0)()(

0),(),,(

)()()()(

pf p p

c

Mg

lríiT

i

FqJ

Iu

MgqqCq

cqM

M

, )ˆ(00

0)ˆ,ˆ(ˆ0

ˆ)(ˆ00

p

q

),( c

bx

Bipedal Robot Model

system structure with decoupled COM dynamics.[Space Robotics], [Wieber 2005, Hyon et al. 2006]

Folie 14

l

Tl

Tbl

rT

r

Tbr

bb

bb

qx

xqx FqJ

qJFqJ

qJqxg

qx

qxqCqx

qMqMqMqM

)(0

)(

0)()(

0),(),,(

)()()()(

pf p p

c

Mg

lríiT

i

FqJ

Iu

MgqqCq

cqM

M

, )ˆ(00

0)ˆ,ˆ(ˆ0

ˆ)(ˆ00

p

q

lri

ifMgcM,

),( c

bx

iMgcL Conservation of angular momentum:

Conservation of momentum:

On a flat ground:

)( MgcMpMgcLp

Bipedal Robot Model

Folie 15

l

Tl

Tbl

rT

r

Tbr

bb

bb

qx

xqx FqJ

qJFqJ

qJqxg

qx

qxqCqx

qMqMqMqM

)(0

)(

0)()(

0),(),,(

)()()()(

pf p p

c

Mg

lríiT

i

FqJ

Iu

MgqqCq

cqM

M

, )ˆ(00

0)ˆ,ˆ(ˆ0

ˆ)(ˆ00

),( c

bx

On a flat ground: the center of pressure = ZMP

)( MgcMpMgcLp

Bipedal Robot Model

Folie 16

Current Research Interests

Walking Control Compliant Balancing

Folie 17

State of the Art Walking Control

Footstep Generation

Pattern Generation

cx

pZMP-COMStabilizer

dxInverse

KinematicsPosition Control

dq

e.g. Preview Control [Kajita, 2003]

Model Predictive Control [Wieber, 2006]

realtime

State of the art walking control for fully actuated robots

1. Pattern Generator for desired CoM and ZMP motion2. ZMP based Stabilizer

e.g. [Choi et al., 2007]

Folie 18

Control Approach: Capture PointDefinition of the “Capture Point” (Pratt 2006, Hof 2008):

Point to step in order to bring the robot to stand.

constp

0

0* xxp

ptxtxttx ))cosh(1()0()sinh()0()cosh()(

ptx )(

c

p *p

cc ,

Computation of the Capture Point:

zg

)(2 pxx

)( MgcMpMgcLp

constzcMcL

0

0

py

px

ZMP

Folie 19

Capture Point Dynamics

xx

Coordinate transformation: ),(),( xxx

)(2 pxx p

xx

COMcapturepoint

xp

System structure: Cascaded system

exp. stableopen loopunstable

Folie 20

Capture Point Dynamics

xx

Coordinate transformation: ),(),( xxx

)(2 pxx p

xx

System structure: Cascaded system

COMcapturepoint

xp

exp. stableCP control

[Englsberger, Ott, et. al., IROS 2011]

Folie 21

COM

ZMP

Capture Point • COM velocity alwayspoints towards CP

• ZMP „pushes away“the CP on a line

• COM follows CP

Shifting the Capture Point

Folie 22

COM

ZMP

Capture Point

Shifting the Capture Point

Folie 25

COM kinematics

Capture Point Control

xx ,

pCP control

[Englsberger, Ott, et. al., IROS 2011]

ZMPControl

RobotDynamics

CP

qTrajectoryGenerator d

ZMP projection

Folie 26

COM kinematics

Capture Point Control

xx ,

pCP control

[Englsberger, Ott, et. al., IROS 2011]

ZMPControl

RobotDynamics

CP

qTrajectoryGenerator d

ZMP projection

MPC [SYROCO 2012]

Folie 27

COM kinematics

Capture Point Control

xx ,

pCP control

[Englsberger, Ott, et. al., IROS 2011]

ZMPControl

RobotDynamics

CP

qTrajectoryGenerator d

ZMP projection

MPC [SYROCO 2012]

Folie 28

Applications

1) Vision based walkingstereo vision (Hirschmüller)visual SLAM (Chilian, Steidel)online footstep planning, collaboration with N. Perrin (IIT)

Folie 29

Folie 30

Applications

2) Optimized swingfoot trajectories: collaboration with H. Kaminaga (Univ. Tokyo)

stride length: 70 cmspeed: 0.5 m/skinematically optimized swingfoot trajectory

stride length: 70 cmspeed: 0.5 m/skinematically optimized torso motion(no angular momentum conversation! slippery)

[Kaminaga et al., Humanoids 2012, Sat. Dec. 1st, 14:00]

Folie 31

Extension to nonlinear models

)(2 pxx

xx

pxx

00

)(txx

MzLpx

zzgx

)(

Simplified model General model

)(tzz

ztMLp

ztzgx

zzt

zz

ztz

ttx

)(

0

)(

0

2)(

2)(

)()(

pt

xtttx

ˆ)(

0)(0)()(

Feedback linearization timevarying cascaded

dynamics

)()(

tzgt

[Englsberger & Ott, Humanoids 2012]

Poster I-19

Folie 32

Current Research Interests

Walking Control Compliant Balancing

Use of the Capture Point

… simplifies control

… simplifies motion planning

Folie 33

Motivation for compliant control

completely stiff fully compliantcompliant control

Folie 35

Balancing & Posture Control

Compliant COM control [Hyon & Cheng, 2006]

Trunk orientation Control

)()( dDdPCOM ccKccKMgF

Mg

extF

COMF

HIPT

)3(SOR

)(),(dR

RHIP DKRVT

extT

),( HIPCOMd TFW Desired wrench:

IMU measurements

Folie 36

Balancing & Posture Control

Compliant COM control [Hyon & Cheng, 2006]

Trunk orientation Control

)()( dDdPCOM ccKccKMgF

)(),(dR

RHIP DKRVT

),( HIPCOMd TFW Desired wrench:

IMU measurements

dW

extFMg

Folie 37

Force distribution: Similar problems!

oFo

f1 f2

W

f1 f2

Fo

Grasping and Balancing

Folie 38

Force Distribution in Grasping

F

FGGFGFGWO

1

111Net wrench acting on the object:

TPiOi AdG

Grasp Map

if

)3(seFC

Well studied problem in grasping: Find contact wrenches such that a desired net wrench on the object is achieved.

FCFC

)3(se

friction cone

Folie 40

Force distribution

HIPT

COMF

f

fGGWd

1

1

ii

ii Rp

RG

ˆ

3if

Relation between balancing wrench & contact forces

Constraints:• Unilateral contact: (implicit handling of ZMP constraints)• Friction cone constraints

0, zif

Formulation as a constraint optimization problem

Cf

23

22

21minarg CCTHIPCFCOMC ffGTfGFf

T

F

GG

321

Folie 41

Contact force control via joint torques

ifMgcM

3if

c

lríiT

i

FqJ

Iu

MgqqCq

cqM

M

, )ˆ(00

0)ˆ,ˆ(ˆ0

ˆ)(ˆ00

iT

i fqJ )ˆ(

Multibody robot model:COM as a base coordinate system structure with decoupled COM dynamics.

[Space Robotics], [Wieber 2005, Hyon et al. 2006]

Passivity based compliance control(well suited for balancing)

Folie 42

ForceDistribution

Torque based balancing

Force Mapping

TorqueControl

RobotDynamics

Object ForceGeneration

IMU

cf

q

for orientation control and COM computation

Folie 43

Uncertain Foot Contact

[Ott, Roa, Humanoids 2011, best paper award]

Folie 47

Experiments on a Perturbation Platform

Leg perturbation setup

Movable elastic platform

Experimental evaluation of the robustness with respectto disturbances (frequency & amplitude) at the foot

Folie 48

Out of phase disturbance

synchronous disturbance2mm, up to 8 Hz

Folie 49

Current Research Interests

Walking Control Compliant Balancing

Use of the Capture Point

… simplifies control

… simplifies motion planning

Joint torque sensing

… enables compliant controlindependently from precise foot-ground contact information.

Folie 50

Summary

Compliance control for elastic robots based on joint torque sensingWalking control based on the Capture PointExtension of torque based compliance control to lower body balancing

OutlookCombination of torque based balancing and CP based walking

realize robust walking on uneven terrain

Multi-contact interaction using articulated upper body

Folie 51

Thank you very much foryour attention!

christian.ott@dlr.de

Dr. MaximoRoa

JohannesEnglsberger

AlexanderWerner

GianlucaGarofalo

Dr. Christian Ott

Dr. Andrei Herdt