Robotic and EVA/Robotic Servicing: Past Experiences, Future Promise
Multi-Contact Compliant Motion Control for Robotic...
Transcript of Multi-Contact Compliant Motion Control for Robotic...
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Multi-Contact Compliant Motion Controlfor Robotic Manipulators
Jaeheung Park?,Rui Cortesao??,
Oussama Khatib?
?Stanford AI Lab, Stanford University??University of Coimbra, ISR
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
1. System Setup
• PUMA560
• Two contacts with vertical boardand horizontal table
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
2. Motivation
Multi-Contact Formulation
• Our previous work1 developed a general multi-contact model, whichcannot be described by the Raibert-Craig model.2
• Extend the framework by modeling the stiffness of the environment.
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
2. Motivation
Multi-Contact Formulation
• Our previous work1 developed a general multi-contact model, whichcannot be described by the Raibert-Craig model.2
• Extend the framework by modeling the stiffness of the environment.
Force Control
A modified Kalman estimation(AOB) is well suited for our system.
• Uncertain input torque - additional input error state.
• Varying measurement noise - on-line variance calculation.
1Roy Featherstone, Stef Sonck Tiebaut, and Oussama Khatib. A general contact model fordynamically decoupled force/motion control, 1999.
2Raibert, M. H., and Craig, J. J. Hybrid Position/Force Control of Manipulators, ASME Jnl.Dynamic Systems, Measurement & Control, 1981
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
3. Multi-Contact Formulation
Multi-Contact model
fc = Nα
N =
[~n
~n×~l
]α : magnitude of
contact force
~n
~l
Contact Point
Operational Point
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
3. Multi-Contact Formulation
Multi-Contact model
fc = Nα
N =
[~n
~n×~l
]α : magnitude of
contact force
~n
~l
Contact Point
Operational Point
Projection Matrices
fc = Ωff
ϑt = Ωmϑ
ϑ velocity of the operational pointf force at the operational pointN spans contact normal space
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
4. Control
JTF Γ
Force Control
Motion Control
fc
f ∗
t
fc
q
f ∗
c
µo + po
Robotf ?
comm
Ωm
Ωf
Σ Λo Σ
Equations of Motion with Operational Space Formulation
Λo(x)ϑ + µo(x, ϑ) + po(x) + fc = F ,
F = f ?com + µo(x, ϑ) + po(x) + fc
f ?com = ΛoΩmf ∗t + ΛoΩff
∗c .
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Force control
With equations of motion in Contact Normal Space
ϑc = Ωff?c
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Force control
With equations of motion in Contact Normal Space
ϑc = Ωff?c
and a spring model
fc,i = ks,iϑc,i,
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Force control
With equations of motion in Contact Normal Space
ϑc = Ωff?c
and a spring model
fc,i = ks,iϑc,i,
The system transfer function can be derived as
G(s) =ks,ie
−sTd
s(s + K2).
Td system input delayK2 additional damping
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Force control Design
fc,dL1 G(s)
rkΣ
- -
fc
Lr Observer
Σ
pk
xk
Lr a full state feedback gain obtained by Pole Placement MethodL1 a scaling factor to compute reference inputfc contact forcefc,d desired contact forcerk reference inputxk state estimatepk input error estimate
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Noise Variance(Rk) Estimation
• The discrete time first order high-pass filter
αf (z) = Gf (z)α(z),
Gf (z) the filter with a zero at 3[Hz] and a pole at 60[Hz]α(z) the measured contact force for each contact force space
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Noise Variance(Rk) Estimation
• The discrete time first order high-pass filter
αf (z) = Gf (z)α(z),
Gf (z) the filter with a zero at 3[Hz] and a pole at 60[Hz]α(z) the measured contact force for each contact force space
• The estimation of the measurement noise, R(ti)
R(ti) =1
N
i∑j=i−N+1
[αf (tj)− αf ][αf (tj)− αf ]T,
where αf is the mean of the filtered force over a time window.
• 50 samples have been used in the experiments.
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
5. Results
Experiment for Analysis
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Measured and Estimated forces in contact with the table.
(a) Measured force of the first contact. z direction.
(b) Estimated force of the first contact. z direction.
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Measured and Estimated forces in contact with the vertical board.
(a) Measured force of the second contact. y direction.
(b) Estimated force of the second contact. y direction.
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Noise Variance Estimations.
(a) Noise Covariance Estimation for the first contact force.
(b) Noise Covariance Estimation for the second contact force.
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Wrist translational motion in x direction.
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
6. Movie
Linear/Angular Motion with Contacts ( 90/120 degree )
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
Without/With online calculation of Noise Variance, Rk
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
7. Conclusion
Multi-Contact Formulation
• Extend our previous work(multi-contact motion/force control forrigid contact) to deal with compliant contact.
• This new formulation sets up dynamic equation for contact forcecontrol.
Force Control
• Apply a modified Kalman filter estimator(AOBs).
• On-line noise Estimation.
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System Setup
Motivation
Multi-Contact Formulation
Control
Results
Movie
Conclusion
Future Works
8. Future Work
• More experiments with different stiffness environment.
• Implement on-line stiffness estimation strategy.
• Multi-contact with multi-link.