christian ott german aerospace center (dlr) · development and control of compliant humanoid robots...

Development and Control of Compliant HumanoidRobots at DLRChristian OttGerman Aerospace Center (DLR)

> Humanoids 2014 > Christian Ott > 18.11.2014DLR.de • Chart 1

1) Design & Control of compliant robots Torque Controlled Robots

Elastic Robots

2) Control of humanoid robots Compliant Control

Bipedal Walking

Overview


τq

Motor

Elasticity

Segment

m

m

ext

qKB

qKqgqqqCqqM

)(

)()(),()(

Robot Model with Torque Sensors> Humanoids 2014 > Christian Ott > 18.11.2014DLR.de • Chart 3

τq

Motor

Elasticity

Segment

m

Joint torquesensor

Light-weight robotwith elastic joints

Movementaccuracy

activevibration damping

Safe human-robot-interaction

compliancecontrol

collisionreaction

Disturbance ObserverIdentification

Advantages of Torque Sensing

Torque Control


τq

Motor

Elasticity

Segment

m

Joint torquesensor


Movementaccuracy



compliancecontrol

collisionreaction



Torque Control


τq

Motor

Elasticity

Segment

m

Joint torquesensor


Movementaccuracy



compliancecontrol

collisionreaction



Torque Control

fm

qfext

B

qgqqqCqqM

,)(),()(


τq

Motor

Elasticity

Segment

m

Joint torquesensor


Movementaccuracy



compliancecontrol

collisionreaction



Torque Control


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

> Humanoids 2014 > Christian Ott > 18.11.2014DLR.de • Chart 8 [Ott & Albu-Schäffer, TRO 2008]

Compliant ManipulationJoint torque sensing & control for manipulation



(noncollocated)

MotorDynamics

Rigid-BodyDynamics

TorqueControl

Environ-ment

ComplianceControl

extq

um


)(q

)(q

qqV

ext

)(Equilibrium:

Compensation of the static effects of K Allows to fulfill requirements on the link side accuracy! Computation of by contraction analysis!

extqKqg )()(

)(q

[Ott & Albu-Schäffer, TRO 2008]

Compliant Manipulation



(noncollocated)

MotorDynamics

Rigid-BodyDynamics

TorqueControl

Environ-ment

ComplianceControl

extq

um


)(q

[Ott & Albu-Schäffer, TRO 2008]

11> Humanoids 2014 > Christian Ott > 18.11.2014

Folie 12

Humanoid Robots at DLR

Anthropomorphic Hand-Arm System

Legged HumanoidJoint torque sensing & control

Bimanual (Humanoid) Manipulation

• Compliant actuation

• Antagonistic actuation for fingers

• Variable stiffness actuation in arm

• Robustness to shocks and impacts

Space Qualified Joint Technology

ROKVISS

PAGE 12

• Antropomorphic design: Size, kinematics, force and dynamics of human arm and hand

• Actuation principle: Variable stiffness in all joints (3 types)

• 27 DoF• 50 motors• 108 position sensors

Antropomorphic Hand/Arm System


Antagonistic finger actuationTendon driven fingers

4 x FloatingSpring Joint

3 x BAVS (Bi‐directionalantagonism)

20 x Antagonistic

[Grebenstein, Albu-Schäffer et al, ICRA 2011]

Floating Spring Joint (4 DoF)• big motor for positioning • small motor to change stiffness • one single spring

Bidirectional Antagonism with Variable Stiffness Actuation (3 DoF)

• 2 equivalent motors • asymmetric cam disc shape• redundant joint actuation

Antagonism (20 DoF Hand): • 2 equivalent motors • in-tendon progressive spring

mechanism

Types of actuation


Motivation for physical compliance


Robustness Performance

1) Modal decoupling (link side)

2) Use torque feedback to achievedecoupling in M, K, and B

3) SISO design in decoupled coordinates

Control Challenges: Vibration Damping


m

ext

qKB

qKqgqqqCqqM

)(

)()(),()(

[Petit, Albu-Schäffer, ICRA 2011]

uBBBBI ddm11

1

1

QQK

QMQMT

QT

KMBd

0,0 QM

qQQ

q 1

1

1) Modal Decoupling (link side)

2) Use torque feedback to achievedecoupling in M, K, and B

3) SISO design in decoupled coordinates

Control Challenges: Vibration Damping


m

ext

qKB

qKqgqqqCqqM

)(

)()(),()(

[Petit, Albu-Schäffer, ICRA 2011]

uBBBBI ddm11

1

1

QQK

QMQMT

QT

KMBd

0,0 QM

qQQ

q 1

1

Compliance ( ) given as a seriesinterconnection of active and passive stiffnesselements

1) Use physical springs in the joints to set desiredstiffness as close as possible

2) Use active compliance to realize precise Cartesiancompliance

solve a matrix nearness problem

Control Challenges: Stiffness Design


pa CCC

1 KC

pdes CC min

0withmin aapdes CCCC

[Petit, Albu-Schäffer, IROS 2011]

Utilizes variabilityof the stiffness!


Elastic Robots


Bipedal Walking

Overview


Bipedal Walking Robots at DLR

DLR-Biped(2010-2012)

TORO, preliminary version (2012)

TORO (2013)TOrque controlled humanoid RObot

• Joint torque sensing & control

• Small foot size: 19 x 9,5 cm

• IMU in head & trunk

• FTS in feet for position based control

• Sensorized head (stereo vision & kinect)

• Simple prosthetic hands (iLIMB)

[Ott

et a

l, H

uman

oids

2010

]

[Eng

lsbe

rger

et a

l, H

uman

oids

2014

]


Motivation for compliant control

completely stiff fully compliantcompliant control


Balancing & Posture Control

Trunk orientation Control

)()( dDdPCOM ccKccKMgF

Mg

extF

COMF

HIPT

)3(SOR

)(),(dR

RHIP DKRVT

extT

c

IMU measurements

Compliant COM control [Hyon & Cheng, 2006]

> Humanoids 2014 > Christian Ott > 18.11.2014DLR.de • Chart 23 [Ott & Roa, Humanoids 2011]

Balancing & Posture ControlCompliant COM control [Hyon & Cheng, 2006]



Mg

extF

COMF

HIPT

)3(SOR

)(),(dR

RHIP DKRVT

extT

),( HIPCOMd TFW Desired wrench:

IMU measurements


Balancing & Posture ControlCompliant COM control [Hyon & Cheng, 2006]



)(),(dR

RHIP DKRVT

),( HIPCOMd TFW Desired wrench:

IMU measurements

dW

extFMg


Force distribution: Similar problems!

Grasping & Balancing> Humanoids 2014 > Christian Ott > 18.11.2014DLR.de • Chart 26

Force distribution: How to realize a desired force/torque on the COM via the available contact points. A similar problem has been solved also in robot grasping by constrained optimization!

[Ott & Roa, Humanoids 2011]

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

Cf

T

F

GG


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


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)


Experiments using the lower body


Experiments using whole body



Elastic Robots


Bipedal Walking

Overview


Folie 33

Walking Stabilization

c

p

xx ,

)(2 pxx

COMcapturepoint

xp

exp. stableopen loopunstable

(Pratt 2006, Hof 2008)

),(

),(

x

xx

xx

1

)( xx )( p

Template model:

[Englsberger, Ott, IROS 2013]

PAGE 33

Folie 34

Walking Stabilization

c

p

xx ,

)(2 pxx

COMcapturepoint

xp

exp. stable

(Pratt 2006, Hof 2008)

),(

),(

x

xx

xx

1

)( xx )( p

Template model:

CP control


PAGE 34

Folie 35

COM kinematics

Capture Point Control

xx ,

pCP control

[Englsberger, Ott, et. al., IROS-2011, ICRA-2012, at-2012]

ZMPControl

RobotDynamics

CP

qTrajectoryGenerator d

ZMP projection

MPC [SYROCO 2012]

)( p

PAGE 35

Folie 36

MPC [SYROCO 2012]

COM kinematics

Capture Point Control

xx ,

pCP control

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

ZMPControl

RobotDynamics

CP

qTrajectoryGenerator d

ZMP projection

Collaboration with Nicolas Perrin

PAGE 36

Folie 37

Extension to 3D walking

2D 3D

Capture Point (CP) „Divergent Component of Motion“ (DCM) [Takenaka]

ZMP (steers CP)

Virtual Repellent Point(steers DCM)

COM dynamics:(not a template model)

Fxm

extFmg

DCM dynamics:


PAGE 37

Folie 38

Extension to 3D walking

2D 3D

Capture Point (CP) „Divergent Component of Motion“ (DCM) [Takenaka]

ZMP (steers CP)

Virtual Repellent Point(steers DCM)

COM dynamics:(not a template model)

Fxm

extFmg

DCM dynamics:

[Englsberger, Ott, IROS 2013]vrpr

PAGE 38

39

CMP

eCMP

Enhanced Centroidal Moment Pivot point (eCMP)

Virtual Repellent Point (VRP)

> Humanoids 2014 > Christian Ott > 18.11.2014

Folie 40

DCM Tracking Control

DCM dynamics Desired closed loop

Tracking control:

Required leg force:

PAGE 40


Elastic Robots


Bipedal Walking

Overview


Thank you very much

for your attention!


christian ott german aerospace center (dlr) · development and control of compliant humanoid robots...

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