# 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

** Go to:**

Applications

*Computer Algebra in Industry*

webmaster@can.nl

Last Update: June 24, 1997.