Document Type
Conference Proceeding
Publication Date
12-1-2000
Publication Title
Annual Symposium on Foundations of Computer Science - Proceedings
Abstract
We propose a combinatorial approach to plan non-colliding 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(n2) steps until all the points are in convex position.
First Page
443
Last Page
453
ISSN
02725428
Recommended Citation
Streinu, Ileana, "Combinatorial Approach to Planar Non-Colliding Robot Arm Motion Planning" (2000). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/287
Comments
Archived as published.