Fast Implementation of Lemke’s Algorithm for Rigid Body Contact Simulation

We present a fast method for solving rigid body contact problems with friction, based on optimizations incorporated into Lemke’s algorithm for solving linear complementarity problems. These optimizations improve computation time in general and reduce the expected solution complexity from O(n 3 ) to nearly O(nm + m 3 ), where n and m are the number of contacts and rigid bodies. For a fixed number of bodies the expected complexity is therefore close to O(n) . Our method also improves numerical robustness, and removes the need to explicitly compute the large matrices associated with rigid body contact problems.