Navigation Functions for Convex Potentials in a Space With Convex Obstacles

Given a convex potential in a space with convex obstacles, an artificial potential is used to navigate to the minimum of the natural potential while avoiding collisions. The artificial potential combines the natural potential with potentials that repel the agent from the border of the obstacles. Thi...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2018-09, Vol.63 (9), p.2944-2959
Main Authors: Paternain, Santiago, Koditschek, Daniel E., Ribeiro, Alejandro
Format: Article
Language:English
Subjects:
Aerospace electronics
Barriers
Collision avoidance
control systems
Eigenvalues
Linear programming
mathematics
motion control
motion Planning
Navigation
nonlinear dynamical systems
nonlinear systems
Robot sensing systems
Trajectory
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Summary:Given a convex potential in a space with convex obstacles, an artificial potential is used to navigate to the minimum of the natural potential while avoiding collisions. The artificial potential combines the natural potential with potentials that repel the agent from the border of the obstacles. This is a popular approach to navigation problems because it can be implemented with spatially local information that is acquired during operation time. Artificial potentials can, however, have local minima that prevent navigation to the minimum of the natural potential. This paper derives conditions that guarantee artificial potentials to have a single minimum that is arbitrarily close to the minimum of the natural potential. The qualitative implication is that artificial potentials succeed when either the condition number-the ratio of the maximum and the minimum eigenvalue-of the Hessian of the natural potential is not large and the obstacles are not too flat, or when the destination is not close to the border of an obstacle. Numerical analyses explore the practical value of these theoretical conclusions.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2775046