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