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Navigation functions for focally admissible surfaces

Filippidis, Ioannis and Kyriakopoulos, Kostas J. (2013) Navigation functions for focally admissible surfaces. In: 2013 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 994-999. ISBN 978-1-4799-0177-7.

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This work presents a sharper condition for the applicability of Navigation Functions (NF). The condition depends on the placement of the destination with respect to the focal surfaces of obstacles. The focal surface is the locus of centers of principal curvatures. If each obstacle encompasses at least one of its focal surfaces, then the world is navigable using a Koditschek-Rimon NF (KRNF). Moreover, the Koditschek-Rimon (KR) potential is non-degenerate for all destinations which are not on a focal surface. So, for almost all destinations there exists a non-degenerate KR potential. This establishes a link between the differential geometry of obstacle surfaces and KRNFs. Channel surfaces (e.g. Dupin cyclides) and certain Boolean operations between shapes are examples of admissible obstacles. We also prove a weak converse result about the inexistence of a KRNF for obstacles with some concave point, for large tuning parameters. Finally, our results support non-trivial simulations in a forest, a pipeline and a cynlinder rig, with some notes about allowable types of non-smoothness.

Item Type:Book Section
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Filippidis, Ioannis0000-0003-4704-3334
Additional Information:© 2013 AACC.
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INSPEC Accession Number13808764
Record Number:CaltechAUTHORS:20131219-093533917
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Official Citation:Filippidis, I.; Kyriakopoulos, K.J., "Navigation functions for focally admissible surfaces," American Control Conference (ACC), 2013 , vol., no., pp.994,999, 17-19 June 2013 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43084
Deposited By: Tony Diaz
Deposited On:23 Dec 2013 20:03
Last Modified:03 Oct 2019 06:04

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