An O(n) geometric algorithm for manipulator forward dynamics

Abstract

In this paper we derive efficient recursive algorithms for the forward dynamic analysis of open chain manipulators based on the theory of Lie groups and Lie algebras. Starting with the geometric formulation of robot dynamics presented in Park et al. (1995), we show that the equations of motion admit a natural matrix factorization in which the robot parameters appear in a transparent manner. We then utilize a geometric version of Featherstone's (1987) articulated body inertia algorithm to re-derive Rodriquez et al.'s (1991, 1992) square factorization of the manipulator mass matrix and its inverse. We then demonstrate that an efficient O(n) recursive algorithm for forward dynamics is embedded in the structure of the inverse mass matrix factorization.