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DLR.de Chart 1 > Humanoids 2015 > Christian Ott > 02.11.2015 Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de Chart 2 > Humanoids 2015 > Christian

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Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR)

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

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1) Humanoid robot TORO 2) Walking Control

 Capture Point  Divergent Component of Motion (3D)

3) Running Overview

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

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Humanoid Robots at DLR

Anthropomorphic Hand-Arm System Legged Humanoid Joint 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

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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 al, Humanoids 2010] [Englsberger et al, Humanoids 2014]

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

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

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6 UT > 07.07.2015

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1) Humanoid robot TORO 2) Walking Control

 Capture Point  Divergent Component of Motion (3D)

3) Running Overview

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

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Walking Stabilization

c p  x x  ,

) (

2

p x x    

COM capture point

 x p

  • exp. stable
  • pen loop

unstable (Pratt 2006, Hof 2008)

) , ( ) , (  x x x  

x x    1   ) ( x x      ) ( p      

Template model:

[Englsberger, Ott, IROS 2013]

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Walking Stabilization

c p  x x  ,

) (

2

p x x    

COM capture point

 x p

  • exp. stable

(Pratt 2006, Hof 2008)

) , ( ) , (  x x x  

x x    1   ) ( x x      ) ( p      

Template model:

CP control

[Englsberger, Ott, IROS 2013]

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COM 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 x x                 x x   

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COM kinematics

Capture Point Control

 x x  , p

CP control

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

ZMP Control Robot Dynamics CP

q

Trajectory Generator

d

ZMP projection

MPC [SYROCO 2012]

) ( p      

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Position based ZMP Control

COM kinematics

 x x  , p

CP control ZMP Control Robot Dynamics CP

q

Trajectory Generator

d

ZMP projection

) (

2

p x x     

d

p

Desired ZMP implies a desired force acting on the COM:

) (

2 d d

p x M F   

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

) ( F F k x

d f d

   ) (

2 d f d

p p M k x    

Position based ZMP Control

MPC [SYROCO 2012]

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MPC [SYROCO 2012]

COM kinematics

Capture Point Control

 x x  , p

CP control

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

ZMP Control Robot Dynamics CP

q

Trajectory Generator

d

ZMP projection

Collaboration with Nicolas Perrin

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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)

F x m   

ext

F mg

DCM dynamics:

[Englsberger, Ott, IROS 2013]

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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)

F x m   

ext

F mg

DCM dynamics:

[Englsberger, Ott, IROS 2013]

vrp

r

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16

Virtual Repellent Point (VRP)

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17

CMP torque CoP eCMP

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DCM trajectory generation

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DCM trajectory generation

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DCM Tracking Control

DCM dynamics Desired closed loop Tracking control: Required leg force:

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OpenHRP

21 > Humanoids 2015 > Christian Ott > 02.11.2015

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> Humanoids 2015 > Christian Ott > 02.11.2015 22

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point mass simulation

(prismatic inverted pendulum model)

23

[Englsberger, Ott, IROS 2013]

> Humanoids 2015 > Christian Ott > 02.11.2015

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1) Humanoid robot TORO 2) Walking Control

 Capture Point  Divergent Component of Motion (3D)

3) Running Overview

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

Humanoids 2015 Interactive Presentation by J. Englsberger

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SLIP Template Model

DLR.de • Chart 25

 

i i

F F i

l k x x x x f             1

g f f x m m

L R G

    

 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

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Human experiments as motivation

3rd order polynomial 2nd order polynomial

DLR.de • Chart 26

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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

F x m   

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  • 28

Preview / Planning design parameters

  • touch-down height
  • apex height
  • time of stance
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Flight Dynamics

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

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Vertical planning (five parameters)

> Humanoids 2015 > Christian Ott > 02.11.2015 DLR.de • Chart 30

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Vertical planning => achieving apex height

DLR.de • Chart 31

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+ force ray focusing (quadratic)

??

Horizontal planning (six parameters)

DLR.de • Chart 32

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Force ray focusing least deviation/variance (=> CoP …)

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Minimizing variance ….

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Minimizing variance ….

DLR.de • Chart 35

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scalar, but difficult to evaluate (non‐linearities)

Minimizing variance (mean square deviation)….

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Leg Force evaluation

DLR.de • Chart 37

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Typical force profiles

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Deviation from point-foot (if not projected)

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

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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 > 02.11.2015 DLR.de • Chart 41