Advertisement

Optimal Efficiency of a Robot Environment Interaction Task in a Matching Impedance Approach

  • G. A. Ombede
  • J. P. Simon
  • M. Betemps
  • A. Jutard
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 361)

Abstract

This paper investigates a matched impedance approach using scattering waves in robot manipulators task in contact with the environment. Given that the dynamic performance of robot in constrained situations is very dependent on the environment parameters, matched conditions are established to optimize the power transferred on a fixed configuration. Simulations show that on matched conditions, the coupled robot-environment consume maximum power supplied.

Keywords

Contact Force Optimal Efficiency Inertia Matrix Inertia Tensor Fixed Configuration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Ac

Controller-actuator gain (diagonal matrix)

B

Force / velocity relation

Bc

Damping matrix of controller actuator

Be

Damping matrix of environment

Br

Damping matrix of the robot

Cc

Input torque

Ce

Environment torque

F

Contact force

Fe

Environment contact force

g(θ)

Robot gravity terms

I(θ)

Inertia tensor in actuator coordinates

J(θ)

Jacobian

K

Force / displacement relation

Kc

Stiffness matrix of controller actuator

Ke

Stiffness matrix of environment

Kr

Stiffness matrix of the robot

L1,L2

Link lengths

M

Inertia tensor in end point coordinates

Mc

Inertia matrix of controller actuator

Me

Inertia matrix of environment

Mr

Inertia matrix of the robot

Rc

real part of Zc

Re

real part of Ze

Rr

real part of Zr

Rre

real part of Zre

Rp

Real part of Zp

S

Power wave scattering matrix

Ve

Environment velocity

Vin

Nominal velocity input

X

End point position

Xc

Imaginary part of Zc

Xe

Imaginary part of Ze

Xr

Imaginary part of Zr

Xre

Imaginary part of Zre

Zc

Controller-actuator impedance

Ze

Environment impedance

Zp

Diagonal matrix of internal impedance of the circuit

Zr

Robot impedance

Zre

coupling robot-environment impedance

θ

Actuator position or angle

θ12

Absolute joint angle

θin

Desired joint position

θe

Environment equilibrium position in joint frame

Ωin

Joint velocity input

Ωe

Environment velocity

τint

Interface torque

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Goldenberg A. A.,“ Implementation of force and impedance control in Robot manipulators”, IEEE Int. Conf. on Robotic and Automation, Philadelphia,1988.Google Scholar
  2. [2]
    HOGAN N. “ Impedance Control: An Approach to Manipulation”, ASME Journal of Dynamic Systems, Measurement and Control, Vol 107, 1985, pp 1–24CrossRefMATHGoogle Scholar
  3. [3]
    Raibert M. H., Craig J. J. “ Hybrid Position/ Force Control of Manipulators”, ASME Journal of Dynamic Systems, Measurement and Control, Vol 102, 1981, pp 418–432Google Scholar
  4. [4]
    Simon J.P., Betemps M., Jutard A., “Matching Impedance Model of a constrained robot-environment task using scattering S matrix”, IFACS-IMACS-IEEE International Workshop on Motion Control for Intelligent Automation, Vol 2, pp 31–37, Perugia Italy 27–29 October 1992.Google Scholar
  5. [5]
    Simon J.P., Betemps M., Jutard A., “Application to the Wave Scatter Theory to the Impedance Model of a Robot ”, INRIA–SIAM Int. Conf. on Mathematical and Numerical Aspect of propagation Phenomena, Strasbourg, April 23–26, 1991Google Scholar
  6. [6]
    Simon J.P., Betemps M. “An Active Compliant Parallel Link Manipulator” IEEE–IES Int Workshop on Sensorial Integration for Industrial Robots, Zaragoza, Nov 22–24 1989Google Scholar
  7. [7]
    Kurokawa K.,“ Power Waves and Scattering Matrix”, IEEE on Transaction Microwaves Theory and Techiques. March 1965.Google Scholar
  8. [8]
    Oswald J. “ Sur la repartition de l’énergie dans les réseaux linéaires” Câbles et Transmissions, Octobre 1958, pp 303–326Google Scholar
  9. [9]
    Rivier E., Sardos R. “La matrice S”, Edition Masson 1982Google Scholar

Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • G. A. Ombede
    • 1
  • J. P. Simon
    • 1
  • M. Betemps
    • 1
  • A. Jutard
    • 1
  1. 1.National Institute of Applied Sciences of LyonVilleurbanneFrance

Personalised recommendations