On the Existence of Solutions to Complementarity Formulations of Contact Problems with Friction

Complementarity formulations are a promising approach for solving dynamic multi-rigid-body contact problems. Here, we formulate the problem as a mixed linear complementarity problem (LCP). We introduce the notion of a disassemblable contact configuration and show that the matrix of the LCP for frictionless configurations is strictly copositive. As a result, in the case of dynamic friction, the matrix of the LCP for small friction coefficient values is also strictly copositive and the LCP again has a solution. 1 Introduction The dynamic multi-rigid-body contact problem is concerned with predicting the accelerations and contact forces of rigid bodies in contact. Work in several research areas, robotics and virtual reality (VR) especially, has led to strong recent interest in this problem. Virtual reality applications, for instance, need improved physical believability; existing systems typically exhibit glaringly apparent physical inconsistencies that are due to a poor treatment of cont..