Topological complexity and efficiency of motion planning algorithms
Algebraic Topology
2019-01-08 v1 Differential Geometry
Metric Geometry
Abstract
We introduce a variant of Farber's topological complexity, defined for smooth compact orientable Riemannian manifolds, which takes into account only motion planners with the lowest possible "average length" of the output paths. We prove that it never differs from topological complexity by more than , thus showing that the latter invariant addresses the problem of the existence of motion planners which are "efficient".
Cite
@article{arxiv.1607.00703,
title = {Topological complexity and efficiency of motion planning algorithms},
author = {Zbigniew Błaszczyk and José Carrasquel},
journal= {arXiv preprint arXiv:1607.00703},
year = {2019}
}