Sequential motion planning of non-colliding particles in Euclidean spaces
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- by Jesús González and Mark Grant PDF
- Proc. Amer. Math. Soc. 143 (2015), 4503-4512 Request permission
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.References
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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
- MR Author ID: 794577
- Email: mark.grant@newcastle.ac.uk
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4503-4512
- MSC (2010): Primary 55R80, 55S40; Secondary 55M30, 68T40
- DOI: https://doi.org/10.1090/proc/12443
- MathSciNet review: 3373948