Multiple shooting approach for computing approximately shortest paths on convex polytopes
نویسندگان
چکیده
منابع مشابه
Computing Approximate Shortest Paths on Convex Polytopes1
The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R3, two points s, t ∈ P , and a parameter ε > 0, it computes a path between s and t on P whose lengt...
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The Holt-Klee Condition states that there exist at least d vertex-disjoint strictly monotone paths from the source to the sink of a polytopal digraph consisting of the set of vertices and arcs of a polytope P directed by a linear objective function in general position. Studying these paths has the potential to provide new insight into a long standing problem, that of designing a polynomial-time...
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We use the idea of the Direct Multiple Shooting Method (presented by H. G. Bock in Proceedings of the 9th IFAC world congress Budapest, Pergamon Press, 1984, for solving optimal control problems) to introduce an algorithm for solving some approximate shortest path problems in motion planning. The algorithm is based on a direct multiple shooting discretization that includes a collinear condition...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2017
ISSN: 0377-0427
DOI: 10.1016/j.cam.2016.10.026