A method is presented to efficiently compute a collision free path for manipulators with polyhedral links moving among polyhedral obstacles. The method is based on an analytical representation of the boundaries of configuration space obstacles (CSOB), obtained by modeling the contacts between manipulator links and obstacle as higher kinematic pairs. The contact conditions and manipulator kinematics are expressed in terms of homogeneous transformations, providing analytic relations between the joint angles and the contact variables. The set of joint angles associated with permissible contact variables forms the boundary of the CSOB. Using these analytical relations, the free space is efficiently divided into free-cells. Each contiguous set of free-cells is then represented by a connected graph that is of polynomial complexity in the number of geometric features of the obstacles and links. The shortest collision-free path on the graph is found using a best-first search. Examples are presented which demonstrate the method for a two link planar manipulator.

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