Computing the Number of Connected Components of Spaces Defined by Generic Non-linear Inequalities
Автор: Interval methods in control engineering
Загружено: 2025-03-23
Просмотров: 39
Описание:
Speaker:
Hugo Rémin (Université Angers, France)
Abstract:
Topological spaces are used in almost all branch of modern mathematics, it is of importance in robotics as the free configuration space of a robot is a topological space. Thus knowing underlying topological properties on the free configuration space can be used in motion planning.
In this talk, our focus is on computing the number of path-connected components of spaces defined by generic non-linear inequalities. With our approach we are able to guarantee whether a trajectory between two configurations is feasible or not. Previous research includes formal methods limited to semi-algebraic sets and, most relevant to this paper, an algorithm on the same spaces as our focus running in O(2^{2n}) time using star domains and interval analysis. Here we show that by using contractibility over star domain a substantial improvement on the time complexity can be accomplished. An algorithm is presented with a time complexity of O(2^{n}) and the results are shown on examples.
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