Towards random sampling with contact constraints

Random sampling strategies play critical roles in randomized motion planners, which are promising and practical for motion planning problems with many degrees of freedom (dofs). In this paper, we explore random sampling in a constrained configuration space-the contact configuration space between two polyhedra, motivated by the need for generating contact motion plans. Given a contact formation (CF) between two polyhedra A and B, our approach is to randomly generate configurations of A satisfying the contact constraints of the CF. Key to the approach is to guarantee that sampling happens only in the constrained space to be efficient, which has not been addressed in the literature. We have implemented a strategy for random sampling of configurations constrained by CF consisting of a single principal contact (PC) with good results. We plan to further extend the approach to CFs with multiple PCs, and apply the results to contact motion planning