Motion Planning Algorithms for General Closed-Chain Mechanisms

Kinematic loop-closure constraints significantly increase the difficulty of motion planning for articulated mechanisms. Configurations of closed-chain mechanisms do not form a single manifold, easy to parameterize, as the configurations of open kinematic chains. In general, they are grouped into several subsets with complex topology than cannot be globally parameterized. This paper presents a general approach for the extension of sampling-based motion planning algorithms to treat closed-chain mechanisms. The basic principle consists in separating configuration variables into two sets: active variables and passive variables. The planner directly acts on the active variables while the passive ones are obtained by solving loop-closure equations. Configurations of complex closed-chain mechanisms are computed by an algorithm called RLG that combines random sampling with simple geometrical operations. The practical efficiency of the extended planners is shown through several applications in robotics as well as in other domains such as graphic animation and computational biology.