Analytical Expression for the Inverted Inertia Matrix of Serial Robots

Abstract

This paper presents the analytical derivation of the inertia matrix and its inverse for an open-loop, serial-chain mbot. The derivation allows one to write a recursiveforward-dynamics algorithmforsimulation purposes whose computational complexity is of order a, i.e., O(n) n being the degrees offreedom of the robot under study The proposed methodology is based on the Gaussian elimination of the inertia matrix, in contrast to, say, Kalmanftltering; which is proposed elsewhere. The derivation is illustrated with a three-degrees-of-freedom planar robot.