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Sequential motion planning of non-colliding particles in Euclidean spaces


Authors: Jesús González and Mark Grant
Journal: Proc. Amer. Math. Soc. 143 (2015), 4503-4512
MSC (2010): Primary 55R80, 55S40; Secondary 55M30, 68T40
Published electronically: June 5, 2015
MathSciNet review: 3373948
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Abstract: In terms of Rudyak's generalization of Farber's topological complexity of the path motion planning problem in robotics, we give a complete description of the topological instabilities in any sequential motion planning algorithm for a system consisting of non-colliding autonomous entities performing tasks in space whilst avoiding collisions with several moving obstacles. The Isotopy Extension Theorem from manifold topology implies, somewhat surprisingly, that the complexity of this problem coincides with the complexity of the corresponding problem in which the obstacles are stationary.


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Additional Information

Jesús González
Affiliation: Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Av. IPN 2508, Zacatenco, México City 07000, México
Email: jesus@math.cinvestav.mx

Mark Grant
Affiliation: School of Mathematics & Statistics, Newcastle University, Herschel Building, Newcastle upon Tyne NE1 7RU, United Kingdom
Email: mark.grant@newcastle.ac.uk

DOI: https://doi.org/10.1090/proc/12443
Keywords: Robot motion planning, higher topological complexity, sectional category, configuration spaces, moving obstacles
Received by editor(s): October 2, 2013
Received by editor(s) in revised form: January 9, 2014
Published electronically: June 5, 2015
Additional Notes: The first author was supported by Conacyt Research Grant 221221.
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2015 American Mathematical Society