Control Approaches for Walking and Running

Christian Ott, Johannes EnglsbergerGerman Aerospace Center (DLR)

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 1

1) Humanoid robot TORO

2) Walking Control Capture Point

Divergent Component of Motion (3D)

3) Running

Overview

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 2

Folie 3

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 3

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

]

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 4

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 5

6 UT > 07.07.2015

1) Humanoid robot TORO

2) Walking Control Capture Point

Divergent Component of Motion (3D)

3) Running

Overview

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 7

Folie 8

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 8

Folie 9

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

[Englsberger, Ott, IROS 2013]

PAGE 9

Folie 10COM

ZMP

Capture Point

• COM velocity always points towards CP

• ZMP „pushes away“ the CP on a line

• COM follows CP

Using Capture Point for Walking

p

xx

xx

Folie 11

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 11

Folie 12

Position based ZMP Control

COM kinematics

xx ,

pCP control

ZMPControl

RobotDynamics

CP

qTrajectoryGenerator d

ZMP projection

)(2 pxx dp

Desired ZMP implies a desired force acting on the COM:

)(2dd pxMF

Position based force control [Roy&Whitcomb,2002]:

)( FFkx dfd )(2dfd ppMkx

Position based ZMP Control

MPC [SYROCO 2012]

Folie 13

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 13

Folie 14

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]

PAGE 14

Folie 15

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 15

16

Virtual Repellent Point (VRP)

17

CMP

torque

CoPeCMP

18

DCM trajectory generation

19DCM trajectory generation

Folie 20

DCM Tracking Control

DCM dynamics Desired closed loop

Tracking control:

Required leg force:

PAGE 20

OpenHRP

21> Humanoids 2015 > Christian Ott > 02.11.2015

> Humanoids 2015 > Christian Ott > 02.11.2015 22

point mass simulation(prismatic inverted pendulum model) 

23[Englsberger, Ott, IROS 2013]> Humanoids 2015 > Christian Ott > 02.11.2015

1) Humanoid robot TORO

2) Walking Control Capture Point

Divergent Component of Motion (3D)

3) Running

Overview

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 24

Humanoids 2015 Interactive Presentation by J. Englsberger

SLIP Template ModelDLR.de • Chart 25

i

i

FF

ilk xxxx

f

10

0gffx mm LRG

Existence of stable limit cycles can be shown

Vertical ground reaction force resembles human data

Mathematical model:

Poincare Map

Vertical ground reaction force

Conceptual biomechanical model: single mass, mass‐less legs, conservative

> Humanoids 2015 > Christian Ott > 02.11.2015

Human experiments as motivation

3rd order polynomial

2nd order polynomial

DLR.de • Chart 26

Force and motion encoding (during stance)

vertical horizontal

force 2nd order 3rd order

CoM position 4th order 5th order

five parameters six parameters

DLR.de • Chart 27

Fxm

• 28

Preview / Planning

design parameters- touch-down height- apex height- time of stance

Flight Dynamics> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 29

Vertical planning (five parameters)> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 30

Vertical planning=> achieving apex height

DLR.de • Chart 31

+ force ray focusing(quadratic)

??

Horizontal planning (six parameters)DLR.de • Chart 32

• 33

Force ray focusing

least deviation/variance(=> CoP …)

• 34

Minimizing variance ….

Minimizing variance ….DLR.de • Chart 35

• 36

scalar, but difficult to evaluate (non‐linearities)

Minimizing variance(mean square deviation)….

Leg Force evaluation

DLR.de • Chart 37

• 38

Typical force profiles

Deviation from point-foot (if not projected)

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 40

1) Walking Control based on the Capture Point

2) Extension to 3D

3) Running via polynomial leg force design

4) Implementation requires leg force control

Summary

> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 41