1 research outputs found
Navigation of a Quadratic Potential with Ellipsoidal Obstacles
Given a convex quadratic potential of which its minimum is the agent's goal
and a space populated with ellipsoidal obstacles, one can construct a
Rimon-Koditschek artificial potential to navigate. These potentials are such
that they combine the natural attractive potential of which its minimum is the
destination of the agent with potentials that repel the agent from the boundary
of the obstacles. This is a popular approach to navigation problems since it
can be implemented with spatially local information that is acquired during
operation time. However, navigation is only successful in situations where the
obstacles are not too eccentric (flat). This paper proposes a modification to
gradient dynamics that allows successful navigation of an environment with a
quadratic cost and ellipsoidal obstacles regardless of their eccentricity. This
is accomplished by altering gradient dynamics with the addition of a second
order curvature correction that is intended to imitate worlds with spherical
obstacles in which Rimon-Koditschek potentials are known to work. Convergence
to the goal and obstacle avoidance is established from every initial position
in the free space. Results are numerically verified with a discretized version
of the proposed flow dynamics