Towards Random Sampling with Contact Constraints

Random sampling strategies play critical roles in ran-domized 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 connguration space { the contact connguration 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 conngurations 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 eecient, which has not been addressed in the literature. We have implemented a strategy for random sampling of conngurations constrained by CFs 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.