Hybrid Complementarity Formulations for Robotics Applications

The focus of this paper is to review hybrid recursive-complementarity formulations for multibody systems characterized by a large number of bilateral constraints which are frequently encountered in robotics. Here, hybrid implies the use of complementarity contact models with recursive forward dynamics schemes. Such formulations have a common underlying structure which can be applied to multibody systems with a constrained tree-type topology. These common steps are pointed out. Theoretical formulation is given for systems using three important classes (O(n), O(n) and O(log(n))) of multibody algorithms. Further, numerical comparison for the efficiency is given for rigid multibody systems. The paper makes recommendations on the choice of hybrid complementarity formulations which would result in the most efficient simulation. The paper further gives a non-iterative approach to allow the use of explicit higher order integrators for frictionless contacts. The difficulties in extending this approach to allow for frictional contact are also discussed.