On avoiding singularities in redundant robot kinematics

Abstract

SummaryFor redundant robot kinematics with a degree of redundancy 1 a self-motion vector field is examined whose equilibrium points lie at singular configurations of the kinematics, and whose orbits determine the self-motion manifolds. It is proved that the self-motion vector field is divergence-free. Locally, around singular configurations of corank 1, the self-motion vector field defines a 2-dimensional Hamiltonian dynamical system. An analysis of the phase portrait of this system in a neighbourhood of a singular configuration solves completely the question of avoidability or unavoidability of this configuration. Complementarily, sufficient conditions for avoidability and unavoidability are proposed in an analytic form involving the self-motion Hamilton function. The approach is illustrated with examples. A connection with normal forms of kinematics is established.