Humanoid Walking Control using the Capture Point Christian Ott and Johannes Englsberger Institute of Robotis and Mehatronis German Aerospae Center (DLR e.v.) hristian.ott@dlr.de
Joint torque sensing & ontrol for manipulation Compliant Manipulation Environment ext Rigid-Body Dynamis q Motor Dynamis Compliane Control u Torque Control m Robustness: Passivity Based Control Performane: Joint Torque Feedbak (nonolloated)
Compliant Manipulation Environment ext Rigid-Body Dynamis q Motor Dynamis Compliane Control u Torque Control m Robustness: Passivity Based Control Performane: Joint Torque Feedbak (nonolloated)
Beyond Compliant Manipulation Joint torque sensing & ontrol for manipulation DLR-Biped [Humanoids 2010] Anthropomorphi Hand-Arm System [Grebenstein, Albu-Shäffer et al, Humanoids 2010] Compliant atuation Antagonisti atuation for fingers Variable stiffness atuation in arm Robustness to shoks and impats
From Manipulating to Walking walking on arms
Experimental biped walking mahine [Humanoids 2010] 6 DOF / leg ~50 kg Drive tehnology of the DLR arm Newly designed lower leg Slim foot design: < 10m Sensors: - joint torque sensors - fore/torque sensors in the feet - IMU in the trunk Developed within 10 month by student projets. Allow for position ontrolled walking (ZMP) and joint torque ontrol! DLR-Biped
First experiments with DLR-Biped First experiment at Automatia Fair in 06-2010: ZMP preview ontrol [Kajita, 2003] Current approah: Walking ontrol based on the Capture Point [Englsberger, Ott, Roa, et al. IROS 2011]
Current Researh Interests Compliant Balaning Control [Humanoids 2011, Tomorrow 9:50-10:10] Walking Control IRT Humanoid (U. Tokyo)
Walking Control State of the art walking ontrol for fully atuated robots Pattern Generator for desired CoM and ZMP motion ZMP based Stabilizer realtime Footstep Generation Pattern Generation x p ZMP-COM Stabilizer x d Inverse Kinematis q d Position Control e.g. Preview Control [Kajita, 2003] Model Preditive Control [Wieber]
Objetive Goal: Simple, robust and flexible ontrol framework for bipedal walking, whih - is not restrited to either position or torque ontrol - allows for higher level ontrol strategies like push reovery and online step planning Approah: Use Linear Inverted Pendulum and Capture Point (Pratt et al 2006, Hof 2008) as starting point. Why to use Capture Point for walking? - Simplifies planning (pattern generation) - Extension to push reovery & online step adaptation
Linear Inverted Pendulum (LIP) Assumptions one-mass model (robot modeled as point mass orresponding to the COM) COM at onstant height z Base joint of pendulum is torque-free
where ) ( 2 p x x z g with p 2 2 0 0 1 0 T x x p t t t t t t t ) sinh( ) osh( 1 ) osh( ) sinh( ) sinh( 1 ) osh( ) ( 0 Linear Inverted Pendulum (LIP)
Capture Point Definition: The Capture Point (CP) is the point on the floor where the robot has to plae the ZMP to ome to a omplete rest (=> COM over foot) x t p x x,0, 0 osh( t) sinh( t) p posh( t) p x x tanh( t t,0, 0 ) 1 Capture Point [1] x x g z [1] Pratt et al., 2006
Capture Point Dynamis Capture Point x x x ( x ) x x x 2 ( x p) x x p ( p)
Derivation of Capture Point ontrol (CPC) ( p) x ( x ) solution in time CP COM ( t dt ) motivates e * dt * dt ( t) (1 e Capture Point Control ) p Idea: only stabilizing the unstable part of the dynamis p d 1 e e * dt * dt 1 1 b d 1 b b
Capture Point ontrol (CPC) Capture Point Control 1 p d 1b b 1b CP COM Closed loop dynamis 0 1 b 0 d 1 b * dt with b e 10 dt dt 0 0 stable x and T
Basi CP shift Capture Point COM veloity always points towards CP ZMP pushes away the CP on a line COM follows CP ZMP COM
Foot to foot shift of CP predefined footprints desired end-of-step CPs at onstant offset from foot enters desired ZMPs alulated aording to CP ontrol law only single support phase onsidered for planning, whereas ontrol an handle double support
CP pattern generators End of step referene (CPS) stepwise onstant desired end-of-step Capture Points linear dereasing time until desired arrival Traking referene (CPT) p d 1 e e * dt * dt desired Capture Point follows a referene trajetory (ideal LIP) (shifted by dt) time until desired arrival is held onstant (design parameter)
Predefined footprints Control loop x x Planning of end-of-step CPs Sheduling for CPS or CPT ontrol al CP dt CP ontrol p d 1 e e * dt * dt p d support polygon projetion p p p ZMP ontrol robot
Projetion of ZMP desired ZMPs projeted to support polygon if needed tilting avoidane by expliit limitation of the ZMP to the support polygon
Simulations
Experiments
Summary and Conlusions System struture: COM and CP have first order dynamis (COM follows CP (stable), ZMP pushes CP (unstable)) CP ontrol motivated by the solution in time of CP dynamis CP ontrol stabilizes the unstable part of the dynamis effetive and simple tool for design of feedbak ontrollers for bipedal walking robots => basis for push reovery and online step planning Robustness an be shown analytially, in simulation and experiments
Outlook Push reovery / online step adjustment Consider projetion of ZMP to support polygon in the ontroller design Extension of CP ontrol to more general models (3D COM motion )
Thankyouverymuh foryourattention! hristian.ott@dlr.de johannes.englsberger@dlr.de