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

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Theory and Practice of Robots and Manipulators

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 361))

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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.

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Abbreviations

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

θ1,θ2 :

Absolute joint angle

θin :

Desired joint position

θe :

Environment equilibrium position in joint frame

Ωin :

Joint velocity input

Ωe :

Environment velocity

τint :

Interface torque

References

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  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 418–432

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  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.

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Author information

Authors and Affiliations

  1. National Institute of Applied Sciences of Lyon, Villeurbanne, France

    G. A. Ombede, J. P. Simon, M. Betemps & A. Jutard

Authors
  1. G. A. Ombede
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  2. J. P. Simon
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  3. M. Betemps
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  4. A. Jutard
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Editor information

Editors and Affiliations

  1. Warsaw University of Technology, Polish

    A. Morecki

  2. Polytechnical University of Milan, Italy

    G. Bianchi

  3. Warsaw University of Technology, Polish

    K. Jaworek

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© 1995 Springer-Verlag Wien

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Ombede, G.A., Simon, J.P., Betemps, M., Jutard, A. (1995). Optimal Efficiency of a Robot Environment Interaction Task in a Matching Impedance Approach. In: Morecki, A., Bianchi, G., Jaworek, K. (eds) Theory and Practice of Robots and Manipulators. International Centre for Mechanical Sciences, vol 361. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2698-1_16

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  • DOI: https://doi.org/10.1007/978-3-7091-2698-1_16

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82697-3

  • Online ISBN: 978-3-7091-2698-1

  • eBook Packages: Springer Book Archive

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