Navigation Of A Quadratic Potential With Star Obstacles

The Rimon-Koditscheck potential is known to be a navigation function for sufficiently curved worlds. With global information, a diffeomorphism can be constructed to convert complex star worlds into sphere worlds so that the point agent can follow the negative gradient of the navigation function potential. Without global information, convergence guarantees only exist for sufficiently curved worlds or ellipsoidal worlds. This work closes the gap between local information and global information by extending convergence guarantees with local information to star worlds in general. 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 dynamic flow.