Configuration spaces and robot motion planning algorithms

Michael Farber*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


These notes survey topological problems relevant to the motion planning problem of robotics and include some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible for discontinuities in algorithms for robot navigation. Then we present explicit motion planning algorithms for coordinated collision free control of many particles moving in Euclidean spaces or on graphs. These algorithms are optimal in the sense that they have minimal number of regions of continuity. Moreover, we describe in full detail the topology of configuration spaces of two particles on a tree and use it to construct some top-dimensional cohomology classes in configuration spaces of n particles on a tree.

Original languageEnglish
Title of host publicationCombinatorial and Toric Homotopy
Subtitle of host publicationIntroductory Lectures
PublisherWorld Scientific Publishing Co. Pte Ltd
Number of pages41
ISBN (Electronic)9789813226579
ISBN (Print)9789813226562
StatePublished - 1 Jan 2017
Externally publishedYes


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