Control Approaches for Walking and Running

Transcription

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

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

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

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

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

6 6 UT >

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

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

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

10 Using Capture Point for Walking x x p x x Capture Point COM velocity always points towards CP ZMP pushes away the CP on a line COM follows CP ZMP COM Folie 10

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

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

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

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

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

16 Virtual Repellent Point (VRP) 16

17 torque ecmp CoP CMP 17

18 DCM trajectory generation 18

19 DCM trajectory generation 19

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

21 OpenHRP > Humanoids 2015 > Christian Ott >

22 > Humanoids 2015 > Christian Ott >

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

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

25 DLR.de Chart 25 > Humanoids 2015 > Christian Ott > SLIP Template Model Conceptual biomechanical model: single mass, mass less legs, conservative Vertical ground reaction force Mathematical model: m x G f R f L m g 0 f i l k 0 1 x x x x Fi F i Poincare Map Existence of stable limit cycles can be shown Vertical ground reaction force resembles human data

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

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

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

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

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

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

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

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

34 34 Minimizing variance.

35 DLR.de Chart 35 Minimizing variance.

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

37 DLR.de Chart 37 Leg Force evaluation

38 38 Typical force profiles

39 Deviation from point-foot (if not projected)

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

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