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Paper WeA08.1

Filippidis, Ioannis (National Technical University of Athens), Kyriakopoulos, Kostas (National Technical Univ. of Athens)

Navigation Functions for Everywhere Partially Sufficiently Curved Worlds

Scheduled for presentation during the Regular Session "Motion Path Planning I" (WeA08), Wednesday, May 16, 2012, 08:30−08:45, Meeting Room 8 (Wacipi)

2012 IEEE International Conference on Robotics and Automation, May 14-18, 2012, RiverCentre, Saint Paul, Minnesota, USA

This information is tentative and subject to change. Compiled on October 24, 2017

Keywords Motion and Path Planning, Collision Avoidance

Abstract

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.

 

 

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