  For a vehicle moving in an $n$-dimensional Euclidean space, we present a
construction of a hybrid feedback that guarantees both global asymptotic
stabilization of a reference position and avoidance of an obstacle
corresponding to a bounded spherical region. The proposed hybrid control
algorithm switches between two modes of operation: stabilization
(motion-to-goal) and avoidance (boundary-following). The geometric construction
of the flow and jump sets of the hybrid controller, exploiting a hysteresis
region, guarantees robust switching (chattering-free) between the stabilization
and avoidance modes. Simulation results illustrate the performance of the
proposed hybrid control approach for a 3-dimensional scenario.
