Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running...
Transcript of Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running...
Control Approaches for Walking and Running
Christian Ott, Johannes EnglsbergerGerman Aerospace Center (DLR)
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 1
1) Humanoid robot TORO
2) Walking Control Capture Point
Divergent Component of Motion (3D)
3) Running
Overview
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 2
Folie 3
Humanoid Robots at DLR
Anthropomorphic Hand-Arm System
Legged HumanoidJoint 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
PAGE 3
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 a
l, H
uman
oids
2010
]
[Eng
lsbe
rger
et a
l, H
uman
oids
2014
]
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 4
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 5
6 UT > 07.07.2015
1) Humanoid robot TORO
2) Walking Control Capture Point
Divergent Component of Motion (3D)
3) Running
Overview
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 7
Folie 8
Walking Stabilization
c
p
xx ,
)(2 pxx
COMcapturepoint
xp
exp. stableopen loopunstable
(Pratt 2006, Hof 2008)
),(
),(
x
xx
xx
1
)( xx )( p
Template model:
[Englsberger, Ott, IROS 2013]
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Folie 9
Walking Stabilization
c
p
xx ,
)(2 pxx
COMcapturepoint
xp
exp. stable
(Pratt 2006, Hof 2008)
),(
),(
x
xx
xx
1
)( xx )( p
Template model:
CP control
[Englsberger, Ott, IROS 2013]
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Folie 10COM
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
xx
xx
Folie 11
COM kinematics
Capture Point Control
xx ,
pCP control
[Englsberger, Ott, et. al., IROS-2011, ICRA-2012, at-2012]
ZMPControl
RobotDynamics
CP
qTrajectoryGenerator d
ZMP projection
MPC [SYROCO 2012]
)( p
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Folie 12
Position based ZMP Control
COM kinematics
xx ,
pCP control
ZMPControl
RobotDynamics
CP
qTrajectoryGenerator d
ZMP projection
)(2 pxx dp
Desired ZMP implies a desired force acting on the COM:
)(2dd pxMF
Position based force control [Roy&Whitcomb,2002]:
)( FFkx dfd )(2dfd ppMkx
Position based ZMP Control
MPC [SYROCO 2012]
Folie 13
MPC [SYROCO 2012]
COM kinematics
Capture Point Control
xx ,
pCP control
[Englsberger, Ott, et. al., IROS 2011]
ZMPControl
RobotDynamics
CP
qTrajectoryGenerator d
ZMP projection
Collaboration with Nicolas Perrin
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Folie 14
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)
Fxm
extFmg
DCM dynamics:
[Englsberger, Ott, IROS 2013]
PAGE 14
Folie 15
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)
Fxm
extFmg
DCM dynamics:
[Englsberger, Ott, IROS 2013]vrpr
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Virtual Repellent Point (VRP)
17
CMP
torque
CoPeCMP
18
DCM trajectory generation
19DCM trajectory generation
Folie 20
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
> Humanoids 2015 > Christian Ott > 02.11.2015 22
point mass simulation(prismatic inverted pendulum model)
23[Englsberger, Ott, IROS 2013]> Humanoids 2015 > Christian Ott > 02.11.2015
1) Humanoid robot TORO
2) Walking Control Capture Point
Divergent Component of Motion (3D)
3) Running
Overview
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 24
Humanoids 2015 Interactive Presentation by J. Englsberger
SLIP Template ModelDLR.de • Chart 25
i
i
FF
ilk xxxx
f
10
0gffx mm LRG
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
Human experiments as motivation
3rd order polynomial
2nd order polynomial
DLR.de • Chart 26
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
Fxm
• 28
Preview / Planning
design parameters- touch-down height- apex height- time of stance
Flight Dynamics> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 29
Vertical planning (five parameters)> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 30
Vertical planning=> achieving apex height
DLR.de • Chart 31
+ force ray focusing(quadratic)
??
Horizontal planning (six parameters)DLR.de • Chart 32
• 33
Force ray focusing
least deviation/variance(=> CoP …)
• 34
Minimizing variance ….
Minimizing variance ….DLR.de • Chart 35
• 36
scalar, but difficult to evaluate (non‐linearities)
Minimizing variance(mean square deviation)….
Leg Force evaluation
DLR.de • Chart 37
• 38
Typical force profiles
Deviation from point-foot (if not projected)
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 40
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 > 02.11.2015DLR.de • Chart 41