Navigation Functions for everywhere partially sufficiently curved worlds

We extend Navigation Functions (NF) to worlds of more general geometry and topology. This is achieved without the need for diffeomorphisms, by direct definition in the geometrically complicated configuration space. Every obstacle boundary point should be partially sufficiently curved. This requires...

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Bibliographic Details
Main Authors: Filippidis, I. F., Kyriakopoulos, K. J.
Format: Conference Proceeding
Language:English
Subjects:
Bismuth
Eigenvalues and eigenfunctions
Geometry
Level set
Navigation
Noise measurement
Planning
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Description
Summary:We extend Navigation Functions (NF) to worlds of more general geometry and topology. This is achieved without the need for diffeomorphisms, by direct definition in the geometrically complicated configuration space. Every obstacle boundary point should be partially sufficiently curved. This requires that at least one principal normal curvature be sufficient. A normal curvature is termed sufficient when the tangent sphere with diameter the associated curvature radius is a subset of the obstacle. Examples include ellipses with bounded eccentricity, tori, cylinders, one-sheet hyperboloids and others. Our proof establishes the existence of appropriate tuning for this purpose. Direct application to geometrically complicated cases is illustrated through nontrivial simulations.
ISSN:1050-4729
2577-087X
DOI:10.1109/ICRA.2012.6225105