Obstacle avoidance for an extremum seeking system using a navigation function

The problem of autonomously steering a vehicle to a destination point, while avoiding obstacles, is considered. The vehicle is modeled as a single-integrator in the plane and it is assumed that the obstacles are unknown a priori. The control law is an extremum seeking algorithm, which steers the vehicle to the minimum of a navigation function. In this framework, obstacle avoidance and practical uniform convergence to a destination point for almost all initial conditions is proven. The theoretic results are illustrated using numerical examples.