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We propose a continuous feedback control strategy that steers a point-massvehicle safely to a destination, in a quasi-optimal manner, in sphere worlds.The main idea consists in avoiding each obstacle via the shortest path withinthe cone enclosing the obstacle and moving straight toward the target when thevehicle has a clear line of sight to the target location. In particular, almostglobal asymptotic stability of the target location is achieved intwo-dimensional (2D) environments under a particular assumption on theobstacles configuration. We also propose a reactive (sensor-based) approach,suitable for real-time implementations in a priori unknown 2D environments withsufficiently curved convex obstacles, guaranteeing almost global asymptoticstability of the target location. Simulation results are presented toillustrate the effectiveness of the proposed approach.

Safe and Quasi-Optimal Autonomous Navigation in Environments with Convex Obstacles