Redundancy Parametrization in Globally-Optimal Inverse Kinematics

Abstract

Redundancy resolution schemes based on the optimization of integral performance indices through calculus of variations do not provide a minimum parametrization of redundancy, i.e. the one with the minimum number of variables and differential equations, which is rather implicitly used in techniques based on dynamic programming. This communication investigates the possible minimum parametrizations and the conditions by which they become unrepresentative of the redundancy. Techniques are proposed to choose the right parametrization, depending on the manipulator kinematic characteristics and trajectory. While reducing the number of differential equations to be solved, they pave the way to the design of more effective redundancy resolution algorithms based on dynamic programming.