Symbolic Elimination for Parallel Manipulators

Abstract

The forward kinematics problem of parallel robot consists in computing the position of a solid moving in the three-dimensional space with six points on it constrained to lie respectively on six given spheres. This problem can also be represented by a system of algebraic equations, and it is known to admit at most 40 complex solutions. Our approach consists in adding extra sensors, that give us more information, in order to reduce this bound. We propose a symbolic elimination method, based on the scheme of dialytic elimination. We prove that our method actually gives upper bounds on the number of solutions of the problem. Our implementation supplies us with the first general bounds on this problem with extra sensors.