Control Approaches for Walking and Running Christian Ott, Johannes - PowerPoint PPT Presentation

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 Ott > 02.11.2015 Overview 1) Humanoid robot TORO 2) Walking Control  Capture Point  Divergent Component of Motion (3D) 3) Running

Humanoid Robots at DLR Legged Humanoid Joint torque Bimanual (Humanoid) Manipulation sensing & control ROKVISS • Compliant actuation • Antagonistic actuation for fingers • Variable stiffness actuation in arm • Robustness to shocks and impacts Space Qualified Joint Technology Anthropomorphic Hand-Arm System Folie 3 PAGE 3

DLR.de • Chart 4 > Humanoids 2015 > Christian Ott > 02.11.2015 Bipedal Walking Robots at DLR • 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) [Englsberger et al, Humanoids 2014] • Simple prosthetic hands (iLIMB) [Ott et al, Humanoids 2010] TORO (2013) DLR-Biped TORO, preliminary version TOrque controlled (2010-2012) (2012) humanoid RObot

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

UT > 07.07.2015 6

DLR.de • Chart 7 > Humanoids 2015 > Christian Ott > 02.11.2015 Overview 1) Humanoid robot TORO 2) Walking Control  Capture Point  Divergent Component of Motion (3D) 3) Running

Walking Stabilization [Englsberger, Ott, IROS 2013]      2 x ( x p ) Template model: x  , x 1  ( x , x )     x x    c ( x , )            p ( ) x ( x )  p  p x (Pratt 2006, Hof 2008) capture COM point open loop exp. stable unstable Folie 8 PAGE 8

Walking Stabilization [Englsberger, Ott, IROS 2013]      2 x ( x p ) Template model: x  , x 1  ( x , x )     x x    c ( x , )            p ( ) x ( x )  p  p x (Pratt 2006, Hof 2008) capture COM point exp. stable CP control Folie 9 PAGE 9

Using Capture Point for Walking  x           x x x         p • COM velocity always points towards CP Capture Point • ZMP „pushes away“ the CP on a line • COM follows CP ZMP COM Folie 10

Capture Point Control MPC [SYROCO 2012] p q Trajectory CP ZMP ZMP Robot  projection Generator control Control Dynamics d  x  , x COM CP kinematics       ( p ) Folie 11 [Englsberger, Ott, et. al., IROS-2011, ICRA-2012, at-2012] PAGE 11

Position based ZMP Control MPC [SYROCO 2012] p q Trajectory CP ZMP ZMP Robot  projection Generator control Control Dynamics d  x  , x COM CP kinematics Desired ZMP implies a desired force acting on the COM:         2 p 2 x ( x p ) F M ( x p ) d d d Position based force control Position based ZMP Control [Roy&Whitcomb,2002]:     2   x k M ( p p )  x k ( F F ) d f d d f d Folie 12

Collaboration with Nicolas Perrin Capture Point Control MPC [SYROCO 2012] p q Trajectory CP ZMP ZMP Robot  projection Generator control Control Dynamics d  x  , x COM CP kinematics Folie 13 [Englsberger, Ott, et. al., IROS 2011] PAGE 13

Extension to 3D walking 2D 3D Capture Point (CP) „Divergent Component of Motion“ (DCM) [Takenaka] ZMP Virtual Repellent Point (steers CP) (steers DCM) m    DCM dynamics: x F COM dynamics: (not a template model) mg  F ext [Englsberger, Ott, IROS 2013] Folie 14 PAGE 14

Extension to 3D walking 2D 3D Capture Point (CP) „Divergent Component of Motion“ (DCM) [Takenaka] ZMP Virtual Repellent Point (steers CP) (steers DCM) m    DCM dynamics: x F COM dynamics: (not a template model) mg  F ext r vrp [Englsberger, Ott, IROS 2013] Folie 15 PAGE 15

Virtual Repellent Point (VRP) 16

torque eCMP CoP CMP 17

DCM trajectory generation 18

DCM trajectory generation 19

DCM Tracking Control Desired closed loop DCM dynamics Tracking control: Required leg force: Folie 20 PAGE 20

OpenHRP > Humanoids 2015 > Christian Ott > 21 02.11.2015

> Humanoids 2015 > Christian Ott > 22 02.11.2015

point mass simulation (prismatic inverted pendulum model) > Humanoids 2015 > Christian Ott > [Englsberger, Ott, IROS 2013] 23 02.11.2015

DLR.de • Chart 24 > Humanoids 2015 > Christian Ott > 02.11.2015 Overview 1) Humanoid robot TORO 2) Walking Control  Capture Point  Divergent Component of Motion (3D) 3) Running Humanoids 2015 Interactive Presentation by J. Englsberger

DLR.de • Chart 25 > Humanoids 2015 > Christian Ott > 02.11.2015 SLIP Template Model Conceptual biomechanical model: single mass, mass ‐ less legs, conservative Vertical ground reaction force Mathematical model:      m x f f m g G R L 0     Poincare Map   l    0 f k 1 x x   i  F i x x   F i  Existence of stable limit cycles can be shown  Vertical ground reaction force resembles human data

2nd order polynomial 3rd order polynomial Human experiments as motivation DLR.de • Chart 26

DLR.de • Chart 27 Force and motion encoding (during stance) vertical horizontal 2nd order 3rd order force m    x F 4th order 5th order CoM position six parameters five parameters

Preview / Planning • 28 - touch-down height design parameters - apex height - time of stance

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

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

DLR.de • Chart 31 Vertical planning => achieving apex height

DLR.de • Chart 32 Horizontal planning (six parameters) ?? + force ray focusing (quadratic)

Force ray focusing • 33 least deviation/variance (=> CoP …)

Minimizing variance …. • 34

Minimizing variance …. DLR.de • Chart 35

Minimizing variance (mean square deviation)…. • 36 scalar, but difficult to evaluate (non ‐ linearities)

DLR.de • Chart 37 Leg Force evaluation

Typical force profiles • 38

Deviation from point-foot (if not projected)

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

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