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Navigation Functions for Convex Potentials in a Space with Convex Obstacles | | Santiago Paternain
; Daniel E. Koditschek
; Alejandro Ribeiro
; | | Date: |
2 May 2016 | | Abstract: | 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 given 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 -- as opposed to most other
approaches that require global knowledge of the environment. Artificial
potentials can, however, have local minima that prevent navigation to the
intended destination. This paper derives generic conditions that guarantee
artificial potentials with a single minimum that coincides with the minimum of
the natural potential. The qualitative implication of these general conditions
is that artificial potentials succeed when either the condition number of the
natural potential is not large and the obstacles do not have sharp corners or
when the destination is not close to the border of an obstacle. Numerical
analyses explore the practical value of these theoretical conclusions. | | Source: | arXiv, 1605.0638 | | Services: | Forum | Review | PDF | Favorites | |
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