Proceedings ArticleDOI
A combinatorial approach to planar non-colliding robot arm motion planning
Ileana Streinu
- pp 443-453
TLDR
A combinatorial approach to plan noncolliding motions for a polygonal bar-and-joint framework based on a novel class of one-degree-of-freedom mechanisms induced by pseudo triangulations of planar point sets that yields very efficient deterministic algorithms for a category of robot arm motion planning problems with many degrees of freedom.Abstract:
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.read more
Citations
More filters
Assembling and Disassembling Planar Structures with Divisible and Atomic Components.
TL;DR: In this article, a lower bound on the number of pieces that the divisible part must be cut into to separate the parts using a sequence of rigid-body motions is presented.
Dissertation
Morphing Parallel Graph Drawings
TL;DR: The problem of morphing between pairs of parallel planar drawings of a graph, keeping all intermediate drawings planar and parallel with the source and target drawings, is studied and an efficient algorithm that computes a parallel morph is given.
Journal ArticleDOI
Pseudo-Simplicial Complexes from Maximal Locally Convex Functions
Franz Aurenhammer,Hannes Krasser +1 more
TL;DR: This approach is based on the concept of maximal locally convex functions on polytopal domains and describes pseudo-simplicial complexes in ℝd as generalizations of pseudo-triangulations inℝ2.
Proceedings ArticleDOI
Pre-triangulations and liftable complexes
TL;DR: The concept of pre-triangulations is introduced and discussed, a relaxation of triangulations that goes beyond the well-established class of pseudo-Triangulations.
Journal Article
Parallel-redrawing mechanisms, pseudo-triangulations and kinetic planar graphs
TL;DR: The main result is that they are (essentially) pseudo-triangulation mechanisms: pointed pseudo-trian- gulations with a convex hull edge removed, which have potential applications in morphing of more complex shapes than just simple polygons.
References
More filters
Journal ArticleDOI
Probabilistic roadmaps for path planning in high-dimensional configuration spaces
TL;DR: Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).
Book
The complexity of robot motion planning
TL;DR: John Canny resolves long-standing problems concerning the complexity of motion planning and, for the central problem of finding a collision free path for a jointed robot in the presence of obstacles, obtains exponential speedups over existing algorithms by applying high-powered new mathematical techniques.
Journal ArticleDOI
On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
Jacob T. Schwartz,Micha Sharir +1 more
TL;DR: In this paper, a decision method for finding a continuous motion connecting two given positions and orientations of the whole collection of bodies is presented. But it is not shown that this problem can be solved in polynomial time.
Book
Handbook of convex geometry
Peter M. Gruber,Jörg M. Wills +1 more
TL;DR: This handbook should be useful for mathematicians working in other areas, as well as for econometrists, computer scientists, crystallographers, physicists and engineers who are looking for geometric tools for their own work.
Related Papers (5)
Topologically sweeping visibility complexes via pseudotriangulations
Michel Pocchiola,Gert Vegter +1 more