Topological complexity and efficiency of motion planning algorithms
نویسندگان
چکیده
منابع مشابه
Topological Complexity of Motion Planning
In this paper we study a notion of topological complexity TC(X) for the motion planning problem. TC(X) is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, TC(X) is the minimal number k such that there are k different “motion planning rules”, each defined on an open subset of X×X, so that each rule is continuous in the source a...
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Topological Complexity of Motion Planning and Massey Products
We employ Massey products to find sharper lower bounds for the Schwarz genus of a fibration than those previously known. In particular we give examples of non-formal spaces X for which the topological complexity TC(X) (defined to be the genus of the free path fibration on X) is greater than the zero-divisors cup-length plus one.
متن کاملTopological Complexity of Collision-free Motion Planning on Surfaces
The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik–Schnirelmann category of X. Given a mechanical system with configuration space X, the invariant TC(X) measures the complexity of all possible motion planning algorithms designed for the system. In this paper, we compute th...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2018
ISSN: 0213-2230
DOI: 10.4171/rmi/1039