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
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Book ChapterDOI
Flat-State Connectivity of Linkages under Dihedral Motions
Greg Aloupis,Erik D. Demaine,Vida Dujmović,Jeff Erickson,Stefan Langerman,Henk Meijer,Joseph O'Rourke,Mark H. Overmars,Michael A. Soss,Ileana Streinu,Godfried T. Toussaint +10 more
TL;DR: This work explores which classes of linkages have the property that each pair of their flat states--that is, their embeddings in R2 without self-intersection--can be connected by a continuous dihedral motion that avoids self-Intersection throughout.
Journal ArticleDOI
Enumerating Non-crossing Minimally Rigid Frameworks
TL;DR: In this article, an algorithm for enumerating all non-crossing generically minimally rigid bar-and-joint frameworks on a given generic set of n points is presented.
Journal ArticleDOI
LineUp: Computing Chain-Based Physical Transformation
TL;DR: A novel method that can generate a sequence of physical transformations between 3D models with different shape and topology is introduced and it is found that collision-free motion sequence can always be generated when using a straight line as the intermediate configuration of transformation.
Proceedings ArticleDOI
Simplex-Tree Based Kinematics of Foldable Objects as Multi-body Systems Involving Loops
Li Han,Lee Rudolph +1 more
TL;DR: This paper presents two sets of new parameters for single-vertex rigid fold kinematics, like the parameters in the triangle-tree prototype, each has a geometrically meaningful and computationally tractable constraint formulation, and each endows the configuration space with a nice geometry.
Lifting planar graphs to realize integral 3-polytopes and topics in pseudo-triangulations
TL;DR: In this paper, the Delaunay triangulation of a simple polygon is used to construct a lifted pseudo-triangulation, which is then used to obtain a maximal locally convex surface.
References
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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.
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