Fast dynamic simulation of highly articulated robots with contact via Θ(n 2) time dense generalized inertia matrix inversion

Abstract

The generalized inertia matrix and its inverse are used extensively in robotics applications. While construction of the inertia matrix requires Θ(n 2) time, inverting it traditionally employs algorithms running in time O(n 3). We describe an algorithm that reduces the asymptotic time complexity of this operation to the theoretical minimum: Θ(n 2). We also present simple modifications that reduce the number of arithmetic operations (and thereby the running time). We compare our approach against fast Cholesky factorization both theoretically (using number of arithmetic operations) and empirically (using running times). We demonstrate our method to dynamically simulate a highly articulated robot undergoing contact, yielding an order of magnitude decrease in running time over existing methods. © 2012 Springer-Verlag Berlin Heidelberg.