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SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION. Andreu Fargas-Marquès Ramon Costa-Castelló Luis Basañez Institut d’Organització i Control de Sistemes Industrials Universitat Politècnica de Catalunya Barcelona-SPAIN. SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION. - PowerPoint PPT Presentation
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SPATIAL IMPEDANCE CONTROL IN COORDINATED
MANIPULATION
Andreu Fargas-Marquès Ramon Costa-Castelló
Luis Basañez
Institut d’Organització i Control de Sistemes Industrials
Universitat Politècnica de Catalunya
Barcelona-SPAIN
ImplementationExperimental Setup
Equation Discretization
Impedance FormulationError Definition
Potential Energy
Complete Formulation
Introduction
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Experimental Results
Conclusions
Introduction
Internal forces sources– inaccurate modeling– lack of synchronization
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Goal– Keep internal forces under control– Position controlled Manipulators– Decoupled controllers
Coordinated Manipulation may apply undesired forces over manipulated object
Introduction Previous Works
– Impedance over n(Kosuge et al
1997),(Ferreti et al 2000)
– Impedance over nx SO(3)
(Natale et al, 1999)
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Impedance Control– Impedance control is a control
strategy to manage the interaction with an unstructured environment.
Proposed approach– Impedance over SE(3)
ImplementationExperimental Setup
Equation Discretization
Impedance FormulationError Definition
Energy Study
Complete Formulation
Introduction
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Experimental Results
Conclusions
Impedance Formulation Classical Formulation
– Mass + Spring + Damping
System Behaviour:– Motion Equation
– Energy formulation
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
f Kx Bv Ma
xK x2
1v Mv
2
1 TT
UTEt
wii=100 kg (kg.m), bii=266 N.s/m (N.s/rad), kii=711N/m (N/rad)
SE(3) Formulation – End effector position and orientation can be seen as an
SE(3) element.
– Homogenous matrix (4x4)
Position
Rotation Matrix
Impedance FormulationSPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
)3(10
pRH hh SE
)3( R h SO
3hp
Error Definition
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
To be consistent with SE(3), E should be defined in terms of the group operation.
– Exploits group structure
– Inertial Frame Independent
101 dr
Tdr
Td
rd
ppRRRHHE
Complete Formulation
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Spatial Impedance defined over the error (E). Energies:
– Kinetic Energy
– Potential Energy v Wv
2
1 e
TeT
Kee 2
1 TU
(E) loge
6T
SE(3)
γβαzyx eeeeee
Complete Formulation
Newton Law over SE(3)
Complete Formulation
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
exteev fKe Bv vWe
extev fvWe
wii=100 kg (kg.m), bii=266 N.s/m (N.s/rad), kii=711N/m (N/rad)
Complete Formulation
Internal Forces
Complete Scheme
Steady State
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
mmm e K f
mmext
mmext
eK eK 0f
eK - eK f
ImplementationExperimental Setup
Equation Discretization
Impedance FormulationError Definition
Energy Study
Complete Formulation
Introduction
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Experimental Results
Conclusions
Implementation Control Scheme
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Steps– Impedance Generator Impedance equations
discretization– PD controller design
Experimental Setup
1 JR3 Force Sensors
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Crimson Elan SGI Workstation
2 Stäubli RX-90 Robots
Equation Discretization
Problem:– Impedance equations over SE(3) are nonlinear– Robots are seen as discrete time systems (T=48 ms)
Proposed Approach– Online-Integration Method– Integrator: P-2/PC-3/C-3 - R.M. Howe [Howe, 1991]
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
3)(2161
Te
Equation Discretization
Ex:– wii=100 kg (kg.m), bii=266 N.s/m (N.s/rad), kii=711N/m (N/rad).
– fext= 1 N (N.m)
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
ImplementationExperimental Setup
Equation Discretization
Impedance FormulationError Definition
Energy Study
Complete Formulation
Introduction
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Experimental Results
Conclusions
Experimental ResultsSPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Individual Manipulation- Impedance Generator
Experimental ResultsSPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Individual Manipulation- Impedance Generator
Experimental Results
1 Robot Impedance Behaviour– wii=100 kg (kg.m), bii=266 N.s/m (N.s/rad), kii=711N/m (N/rad).
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Experimental ResultsSPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
COORDINATED MANIPULATION
Experimental ResultsSPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
COORDINATED MANIPULATION
Experimental Results COORDINATED MANIPULATION
– wii=1000 kg (kg.m), bii=4000 N.s/m (N.s/rad), kii=4000 N/m (N/rad).
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
X axis trajectory Multi axis trajectory
ImplementationExperimental Setup
Equation Discretization
Impedance FormulationError Definition
Energy Study
Complete Formulation
Introduction
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
Experimental Results
Conclusions
Conclusions Impedance behaviour defined over SE(3). On-line Integration Methodology to compute trajectory
in Real Time. Validated in a real Experimental Setup. (Preliminary
Results)
Future works: – Both arms under impedance behaviour.– Saturation Effects Study– Discretization Equations– Adaptative Behaviours– Haptic Manipulation
SPATIAL IMPEDANCE CONTROL IN COORDINATED MANIPULATION
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