Work

Topology of Parametrized Motion Planning Algorithms

Year: 2021

Type: article

Abstract: We introduce and study a new concept of parametrized topological complexity: a topological invariant motivated by the motion planning problem of robotics. In the parametrized setting, a motion planning algorithm has a high degree of universality and flexibility and can function under a variety of external conditions (such as positions of obstacles). We explicitly compute the parametrized topological complexity of obstacle-avoiding collision-free motion of many particles (robots) in 3-dimensional space. Our results show that the parametrized topological complexity can be significantly higher than the standard (nonparametrized) invariant.

Source: SIAM Journal on Applied Algebra and Geometry

DOI: 10.1137/20m1358505

Authors: Daniel C. Cohen, Michael Farber, Shmuel Weinberger

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Louisiana State University, Leverhulme Trust, Engineering and Physical Sciences Research Council

Award: G4732012811

OpenAlex ID: W3084922497

FWCI: 5.633

Cites: 8

Cited by: 21

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