Polynomial Invariants and SAGBI Bases for Multi-screws

Polynomial invariants for robot manipulators and their joints arise from the adjoint action of the Euclidean group on its Lie algebra, the space of infinitesimal twists or screws. The aim of this paper is to determine basic sets of generating polynomials for multiple screws. Techniques from the theory of SAGBI bases are introduced. As a result, a complete description is provided of the polynomial invariants for screw pairs and some results for screw triples are obtained. The invariants are shown to be related to Denavit-Hartenberg parameters.