Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
I. Streinu , Dept. of Comput. Sci., Smith Coll., Northampton, MA, USA
We propose a combinatorial approach to plan noncolliding motions for a polygonal bar-and-joint framework. Our approach yields very efficient deterministic algorithms for a category of robot arm motion planning problems with many degrees of freedom, where the known general roadmap techniques would give exponential complexity. It is based on a novel class of one-degree-of-freedom mechanisms induced by pseudo triangulations of planar point sets, for which we provide several equivalent characterization and exhibit rich combinatorial and rigidity theoretic properties. The main application is an efficient algorithm for the Carpenter's rule problem: convexify a simple bar-and-joint planar polygonal linkage using only non self-intersecting planar motions. A step in the convexification motion consists in moving a pseudo-triangulation-based mechanism along its unique trajectory in configuration space until two adjacent edges align. At that point, a local alteration restores the pseudo triangulation. The motion continues for O(n/sup 2/) steps until all the points are in convex position.
manipulator kinematics; path planning; deterministic algorithms; computational complexity; graph theory; combinatorial approach; planar noncolliding robot arm motion planning; polygonal bar-and-joint framework; deterministic algorithms; 1DOF mechanisms; exponential complexity; one-degree-of-freedom mechanisms; pseudo triangulations; rule problem; non-self-intersecting planar motions; planar point sets; graph theory
I. Streinu, "A combinatorial approach to planar non-colliding robot arm motion planning," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 443.