A Kinematics-Based Probabilistic Roadmap Method for Closed Chain Systems

In this paper we consider the motion planning problem for closed chain systems with a mobile base. We propose an extension of the prmmethodology which uses the kinematics of the closed chain system to guide the generation and connection of closure congurations. In particular, we break the closed chains into a set of open chains, apply standard prm random sampling techniques and forward kinematics to one subset of the subchains, and then use inverse kinematics on the remaining subchains to enforce the closure constraints. This strategy preserves the PRM sampling philosophy, while addressing the fact that the probability that a random con guration will satisfy the closure constraints is zero, which has proven problematical in previous attempts to apply the PRM methodology to closed chain systems. Another distinguishing feature of our approach is that we adopt a two-stage strategy, both of which employ the prm framework. First, we disregard the environment, x the position and orientation of one link of the chain, and construct a kinematic roadmap which contains di erent self-collision-free closure con gurations. Next, we populate the environment with copies of the kinematic roadmap (nodes and edges), and then use rigid body planners to connect con gurations of the same closure type. This two-stage approach enables us to amortize the cost of computing and connecting closure con gurations. Our results in 3-dimensional workspaces show that good roadmaps for closed chains with many links can be constructed in a few seconds as opposed to the several hours required by the previous purely randomized approach. Figure 1: The Stanford Assistant Mobile Manipulator [13]. (Photo Courtesy of Prof. Oussama Khatib.)