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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Proceedings ArticleDOI
Locked and unlocked smooth embeddings of surfaces
TL;DR: It is shown that every star-shaped or spiral-shaped domain is unlocked: a continuous motion unfolds it to aflat embedding, and disks with two holes can have locked embeddings that are topologically equivalent to a fl at embedding but cannot reach a ﰂat embedded by continuous motion.
Minimum weight pseudo-triangulations (Extended abstract)
TL;DR: An O(n log n)-time algorithm is presented that produces a pseudo-triangulation of weight O(wt(M(S) · log n) which is shown to be asymptotically worst- case optimal, i.e., there exists a point set S for which every pseudo- triangulation has weight Ω(log n · wt(M (S)))), where wt is the weight of a minimum spanning tree of S.
Journal ArticleDOI
Unfolding H-convex Manhattan Towers
TL;DR: A new grid unfolding without refinement of a new sub-class of polycubes that is called Manhattan towers with an H-convex base is proposed and an extension of this algorithm to Up-and-Down Orthoterrains is also possible.
Proceedings Article
On the Number of Pseudo-Triangulations of Certain Point Sets.
TL;DR: In this article, a monotonicity conjecture on the number of pseudo-triangulations of any planar point set was proposed and checked on two prominent families of point sets, namely double circle and double chain.
Dissertation
Kinematic and dynamic modeling of Nanostructured Origami
TL;DR: Barraham et al. as mentioned in this paper presented a methodology for modeling the dynamics of two classes of origami: accordion origami and single-vertex origami, and the forward dynamics and equilibrium analysis of a useful bridge structure and the corner cube origami are simulated.
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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