A New Perspective on O(n) Mass-Matrix Inversion for Serial Revolute Manipulators

Abstract

This paper describes a new algorithm for the efficient mass-matrix inversion of serial manipulators. Whereas several well-known O(n) algorithms already exist, our presentation is an alternative and completely different formulation that builds on Fixman’s theorem from the polymer physics literature. The main contributions here are therefore adding a new perspective to the manipulator dynamics literature and providing an alternative to existing algorithms. The essence of this theory is to consider explicitly the band-diagonal structure of the inverted mass matrix of a manipulator with no constraints on link length, offsets or twist angles, and then build in constraints by appropriate partitioning of the inverse of the unconstrained mass matrix. We present the theory of the partitioned mass matrix and inverse of the mass matrix for serial revolute manipulators. The planar N-link manipulator with revolute joints is used to illustrate the procedure. Numerical results verify the O(n) complexity of the algorithm. Exposure of the robotics community to this approach may lead to new ways of thinking about manipulator dynamics and control.