The ROMIN inverse geometric model and the dynamic evaluation method


M.J. González-López, T. Recio
Dpto. Metemáticas, Estadística y Computación,
Facultad de Ciencias,
Universidad de Cantabria
Santander 39071, Spain

Dedicated to the memory of Mario Raimondo

Abstract

The inverse geometric model of a robot manipulator involves finding the joint angles for a given place (position and orientation) of the manipulator tip. This problem can be stated from an algebraic point of view in such a way that its solution consists of solving a system of polynomial equations with parametric coefficients in which the variables represent the joint angles and the parameters the place of the tip. The method of dynamic evaluation applied to the solution of polynomial systems with parametric coefficients provides a useful tool to attack this problem in practice because we get a finite collection of completely triangular systems (also with inequalities "not equal") whose union is equivalent to the original one. Several other symbolic computation methods for solving the same problem are discussed. The dynamic evaluation method has been applied to solve the inverse geometric model of the manipulator ROMIN, developed as part of a joint project between the University of Cantabria, the enterprise ENSA (Santander) and the Instituto de Automatica Industrial of Madrid, to perform manipulation tasks in high radioactivity zones of a nuclear plant. We also include a detailed description of the algorithm for this particular case, together with some numerical examples of its performance

Computer Algebra in Industry Edited by A.M. Cohen © 1993 John Wiley & Sons Ltd


Reproduced by permission of John Wiley & Sons Ltd, 1995

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