The dynamic multi-rigid-body problem is concerned with predicting the accelerations and contact forces of several rigid bodies in contact. Recent advances in two major research areas have generated this interest: robotics simulation and virtual reality (VR).
The approach of clasical dynamics simulation is to consider this problem as a piecewise differential algebraic equation (DAE, see Haug [4]) using the sign of the constraint force as a test for deciding if the respective contact will break or not. This approach implicitly assumes that the contact forces are continuous with respect to time, an assumption that is reasonable for real systems but not justified theoretically if the bodies are rigid.
Robots acting in the real world must deal with various contact situations that are difficult to account for using DAEs, especially at rolling, sliding or breaking times. As a result of having a DAE structure, even advanced systems need as input the moments of the change in the contact structure in order to be able to carry out, motion planning, for instance [5]. This requirement places a difficult burden on the user.
VR reality applications need to improved physical believability. Many systems exhibit glaring inconsistencies that are obvious to the user due to a poor treatment of loss of contact and multiple contacts between objects.
The complementarity approach appears to provide a satisfactory solution to many of the problems encountered by such simulation systems.