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1
Humanoids 29/11/2012
Balancing and walking control of a torquecontrolled humanoid robot
Dr.-Ing. Christian OttResearch Group on „Dynamic Control of Legged Humanoid Robots“
DLR - Institute for Robotics and Mechatronics
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Folie 2
Compliant ManipulationJoint torque sensing & control for manipulation
Robustness: Passivity Based Control
Performance:Joint Torque Feedback
(noncollocated)
MotorDynamics
Rigid-BodyDynamics
TorqueControl
Environ-ment
ComplianceControl
extq
um
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Folie 3
Compliant Manipulation
Robustness: Passivity Based Control
Performance:Joint Torque Feedback
(noncollocated)
MotorDynamics
Rigid-BodyDynamics
TorqueControl
Environ-ment
ComplianceControl
extq
um
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Folie 4
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Folie 5
Beyond Compliant Manipulation
DLR-Biped [Humanoids 2010]Joint torque sensing & control for manipulation
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Folie 7
DLR-Biped
Experimental biped walking machine [Humanoids 2010]
• 6 DOF / leg
• ~50 kg
• Drive technology of the DLR arm
• Newly designed lower leg
• Slim foot design: 19 x 9,5cm
• Sensors:- joint torque sensors- force/torque sensors in the feet- IMU in the trunk
• Developed within 10 month by student projects.
• Allow for position controlled walking (ZMP) and joint torque control!
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Folie 9
Torque controlled humanoid Robot
Very recent development1) preliminary version: May 20122) full version: December 2012 (estimated)
Research interests: Whole body motion/dynamicsMulti-contact interaction
Weigth: ~68kg / 75kg (complete)
Modified hip kinematics:compact design for locating thetotal COM close to the hip joints
(TORO)
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Folie 10
Bipedal Robot Model
rF lF
lT
l
Tbl
rT
r
Tbr
bb
bb
qx
xqx FqJ
qJFqJ
qJqxg
qx
qxqCqx
qMqMqMqM
)(0
)(
0)()(
0),(),,(
)()()()(
l
r
q
6bx
Properties for control:• Underactuated• Varying unilateral constraints
(single support, double support, edge contact)
• Constraints on the state & control
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Folie 11
l
Tl
Tbl
rT
r
Tbr
bb
bb
qx
xqx FqJ
qJFqJ
qJqxg
qx
qxqCqx
qMqMqMqM
)(0
)(
0)()(
0),(),,(
)()()()(
pf p p
c
Mg
lríiT
i
FqJ
Iu
MgqqCq
cqM
M
, )ˆ(00
0)ˆ,ˆ(ˆ0
ˆ)(ˆ00
p
q
),( c
bx
Bipedal Robot Model
system structure with decoupled COM dynamics.[Space Robotics], [Wieber 2005, Hyon et al. 2006]
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Folie 14
l
Tl
Tbl
rT
r
Tbr
bb
bb
qx
xqx FqJ
qJFqJ
qJqxg
qx
qxqCqx
qMqMqMqM
)(0
)(
0)()(
0),(),,(
)()()()(
pf p p
c
Mg
lríiT
i
FqJ
Iu
MgqqCq
cqM
M
, )ˆ(00
0)ˆ,ˆ(ˆ0
ˆ)(ˆ00
p
q
lri
ifMgcM,
),( c
bx
iMgcL Conservation of angular momentum:
Conservation of momentum:
On a flat ground:
)( MgcMpMgcLp
Bipedal Robot Model
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Folie 15
l
Tl
Tbl
rT
r
Tbr
bb
bb
qx
xqx FqJ
qJFqJ
qJqxg
qx
qxqCqx
qMqMqMqM
)(0
)(
0)()(
0),(),,(
)()()()(
pf p p
c
Mg
lríiT
i
FqJ
Iu
MgqqCq
cqM
M
, )ˆ(00
0)ˆ,ˆ(ˆ0
ˆ)(ˆ00
),( c
bx
On a flat ground: the center of pressure = ZMP
)( MgcMpMgcLp
Bipedal Robot Model
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Folie 16
Current Research Interests
Walking Control Compliant Balancing
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Folie 17
State of the Art Walking Control
Footstep Generation
Pattern Generation
cx
pZMP-COMStabilizer
dxInverse
KinematicsPosition Control
dq
e.g. Preview Control [Kajita, 2003]
Model Predictive Control [Wieber, 2006]
realtime
State of the art walking control for fully actuated robots
1. Pattern Generator for desired CoM and ZMP motion2. ZMP based Stabilizer
e.g. [Choi et al., 2007]
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Folie 18
Control Approach: Capture PointDefinition of the “Capture Point” (Pratt 2006, Hof 2008):
Point to step in order to bring the robot to stand.
constp
0
0* xxp
ptxtxttx ))cosh(1()0()sinh()0()cosh()(
ptx )(
c
p *p
cc ,
Computation of the Capture Point:
zg
)(2 pxx
)( MgcMpMgcLp
constzcMcL
0
0
py
px
ZMP
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Folie 19
Capture Point Dynamics
xx
Coordinate transformation: ),(),( xxx
)(2 pxx p
xx
COMcapturepoint
xp
System structure: Cascaded system
exp. stableopen loopunstable
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Folie 20
Capture Point Dynamics
xx
Coordinate transformation: ),(),( xxx
)(2 pxx p
xx
System structure: Cascaded system
COMcapturepoint
xp
exp. stableCP control
[Englsberger, Ott, et. al., IROS 2011]
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Folie 21
COM
ZMP
Capture Point • COM velocity alwayspoints towards CP
• ZMP „pushes away“the CP on a line
• COM follows CP
Shifting the Capture Point
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Folie 22
COM
ZMP
Capture Point
Shifting the Capture Point
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Folie 25
COM kinematics
Capture Point Control
xx ,
pCP control
[Englsberger, Ott, et. al., IROS 2011]
ZMPControl
RobotDynamics
CP
qTrajectoryGenerator d
ZMP projection
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Folie 26
COM kinematics
Capture Point Control
xx ,
pCP control
[Englsberger, Ott, et. al., IROS 2011]
ZMPControl
RobotDynamics
CP
qTrajectoryGenerator d
ZMP projection
MPC [SYROCO 2012]
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Folie 27
COM kinematics
Capture Point Control
xx ,
pCP control
[Englsberger, Ott, et. al., IROS 2011]
ZMPControl
RobotDynamics
CP
qTrajectoryGenerator d
ZMP projection
MPC [SYROCO 2012]
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Folie 28
Applications
1) Vision based walkingstereo vision (Hirschmüller)visual SLAM (Chilian, Steidel)online footstep planning, collaboration with N. Perrin (IIT)
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Folie 29
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Folie 30
Applications
2) Optimized swingfoot trajectories: collaboration with H. Kaminaga (Univ. Tokyo)
stride length: 70 cmspeed: 0.5 m/skinematically optimized swingfoot trajectory
stride length: 70 cmspeed: 0.5 m/skinematically optimized torso motion(no angular momentum conversation! slippery)
[Kaminaga et al., Humanoids 2012, Sat. Dec. 1st, 14:00]
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Folie 31
Extension to nonlinear models
)(2 pxx
xx
pxx
00
)(txx
MzLpx
zzgx
)(
Simplified model General model
)(tzz
ztMLp
ztzgx
zzt
zz
ztz
ttx
)(
0
)(
0
2)(
2)(
)()(
pt
xtttx
ˆ)(
0)(0)()(
Feedback linearization timevarying cascaded
dynamics
)()(
tzgt
[Englsberger & Ott, Humanoids 2012]
Poster I-19
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Folie 32
Current Research Interests
Walking Control Compliant Balancing
Use of the Capture Point
… simplifies control
… simplifies motion planning
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Folie 33
Motivation for compliant control
completely stiff fully compliantcompliant control
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Folie 35
Balancing & Posture Control
Compliant COM control [Hyon & Cheng, 2006]
Trunk orientation Control
)()( dDdPCOM ccKccKMgF
Mg
extF
COMF
HIPT
)3(SOR
)(),(dR
RHIP DKRVT
extT
),( HIPCOMd TFW Desired wrench:
IMU measurements
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Folie 36
Balancing & Posture Control
Compliant COM control [Hyon & Cheng, 2006]
Trunk orientation Control
)()( dDdPCOM ccKccKMgF
)(),(dR
RHIP DKRVT
),( HIPCOMd TFW Desired wrench:
IMU measurements
dW
extFMg
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Folie 37
Force distribution: Similar problems!
oFo
f1 f2
W
f1 f2
Fo
Grasping and Balancing
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Folie 38
Force Distribution in Grasping
F
FGGFGFGWO
1
111Net wrench acting on the object:
TPiOi AdG
Grasp Map
if
)3(seFC
Well studied problem in grasping: Find contact wrenches such that a desired net wrench on the object is achieved.
FCFC
)3(se
friction cone
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Folie 40
Force distribution
HIPT
COMF
f
fGGWd
1
1
ii
ii Rp
RG
ˆ
3if
Relation between balancing wrench & contact forces
Constraints:• Unilateral contact: (implicit handling of ZMP constraints)• Friction cone constraints
0, zif
Formulation as a constraint optimization problem
Cf
23
22
21minarg CCTHIPCFCOMC ffGTfGFf
T
F
GG
321
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Folie 41
Contact force control via joint torques
ifMgcM
3if
c
lríiT
i
FqJ
Iu
MgqqCq
cqM
M
, )ˆ(00
0)ˆ,ˆ(ˆ0
ˆ)(ˆ00
iT
i fqJ )ˆ(
Multibody robot model:COM as a base coordinate system structure with decoupled COM dynamics.
[Space Robotics], [Wieber 2005, Hyon et al. 2006]
Passivity based compliance control(well suited for balancing)
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Folie 42
ForceDistribution
Torque based balancing
Force Mapping
TorqueControl
RobotDynamics
Object ForceGeneration
IMU
cf
q
for orientation control and COM computation
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Folie 43
Uncertain Foot Contact
[Ott, Roa, Humanoids 2011, best paper award]
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Folie 47
Experiments on a Perturbation Platform
Leg perturbation setup
Movable elastic platform
Experimental evaluation of the robustness with respectto disturbances (frequency & amplitude) at the foot
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Folie 48
Out of phase disturbance
synchronous disturbance2mm, up to 8 Hz
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Folie 49
Current Research Interests
Walking Control Compliant Balancing
Use of the Capture Point
… simplifies control
… simplifies motion planning
Joint torque sensing
… enables compliant controlindependently from precise foot-ground contact information.
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Folie 50
Summary
Compliance control for elastic robots based on joint torque sensingWalking control based on the Capture PointExtension of torque based compliance control to lower body balancing
OutlookCombination of torque based balancing and CP based walking
realize robust walking on uneven terrain
Multi-contact interaction using articulated upper body
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Folie 51
Thank you very much foryour attention!
Dr. MaximoRoa
JohannesEnglsberger
AlexanderWerner
GianlucaGarofalo
Dr. Christian Ott
Dr. Andrei Herdt