Complete Path Planning for Closed Kinematic Chains with Spherical Joints

We study the path planning problem, without obstacles, for closed kinematic chains with n links connected by spherical joints in space or revolute joints in the plane. The configuration space of such systems is a real algebraic variety whose structure is fully determined using techniques from algebraic geometry and differential topology. This structure is then exploited to design a complete path planning algorithm that produces a sequence of compliant moves, each of which monotonically increases the number of links in their goal configurations. The average running time of this algorithm is proportional to n3. While less efficient than the O(n) algorithm of Lenhart and Whitesides, our algorithm produces paths that are considerably smoother. More importantly, our analysis serves as a demonstration of how to apply advanced mathematical techniques to path planning problems. Theoretically, our results can be extended to produce collisionfree paths, paths avoiding both link

• Type: Journal
• Year: 2002
• Where: IJRR
• Authors: Jeffrey C. Trinkle, R. James Milgram
• Keywords: Algorithm, IJRR 2002, Kinematic Chains, Planning Problems