christian ott, johannes englsberger german …...control approaches for walking and running...
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![Page 1: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/1.jpg)
Control Approaches for Walking and Running
Christian Ott, Johannes EnglsbergerGerman Aerospace Center (DLR)
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 1
![Page 2: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/2.jpg)
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
![Page 3: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/3.jpg)
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
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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
![Page 5: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/5.jpg)
> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 5
![Page 6: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/6.jpg)
6 UT > 07.07.2015
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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
![Page 8: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/8.jpg)
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
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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]
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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]
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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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16
Virtual Repellent Point (VRP)
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17
CMP
torque
CoPeCMP
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18
DCM trajectory generation
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19DCM trajectory generation
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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
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> Humanoids 2015 > Christian Ott > 02.11.2015 22
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point mass simulation(prismatic inverted pendulum model)
23[Englsberger, Ott, IROS 2013]> Humanoids 2015 > Christian Ott > 02.11.2015
![Page 24: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/24.jpg)
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
![Page 25: Christian Ott, Johannes Englsberger German …...Control Approaches for Walking and Running Christian Ott, Johannes Englsberger German Aerospace Center (DLR) DLR.de • Chart 1 > Humanoids](https://reader030.vdocuments.net/reader030/viewer/2022041018/5ecb6fb03b76e961d928ffbf/html5/thumbnails/25.jpg)
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
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Human experiments as motivation
3rd order polynomial
2nd order polynomial
DLR.de • Chart 26
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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
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• 28
Preview / Planning
design parameters- touch-down height- apex height- time of stance
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Flight Dynamics> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 29
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Vertical planning (five parameters)> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 30
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Vertical planning=> achieving apex height
DLR.de • Chart 31
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+ force ray focusing(quadratic)
??
Horizontal planning (six parameters)DLR.de • Chart 32
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• 33
Force ray focusing
least deviation/variance(=> CoP …)
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• 34
Minimizing variance ….
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Minimizing variance ….DLR.de • Chart 35
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• 36
scalar, but difficult to evaluate (non‐linearities)
Minimizing variance(mean square deviation)….
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Leg Force evaluation
DLR.de • Chart 37
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• 38
Typical force profiles
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Deviation from point-foot (if not projected)
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> Humanoids 2015 > Christian Ott > 02.11.2015DLR.de • Chart 40
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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