  We propose a hybrid feedback control strategy that safely steers a point-mass
robot to a target location optimally from all initial conditions in the
n-dimensional Euclidean space with a single spherical obstacle. The robot moves
straight to the target when it has a clear line-of-sight to the target
location. Otherwise, it engages in an optimal obstacle avoidance maneuver via
the shortest path inside the cone enclosing the obstacle and having the robot's
position as a vertex. The switching strategy that avoids the undesired
equilibria, leading to global asymptotic stability (GAS) of the target
location, relies on using two appropriately designed virtual destinations,
ensuring control continuity and shortest path generation. Simulation results
illustrating the effectiveness of the proposed approach are presented.
