  In this paper we present a hybrid feedback approach to solve the navigation
problem of a point mass in the n-dimensional space containing an arbitrary
number of ellipsoidal shape obstacles. The proposed hybrid control algorithm
guarantees both global asymptotic stabilization to a reference and avoidance of
the obstacles. The intuitive idea of the proposed hybrid feedback is to switch
between two modes of control: stabilization and avoidance. The geometric
construction of the flow and jump sets of the proposed hybrid controller,
exploiting hysteresis regions, guarantees Zeno-free switching between the
stabilization and the avoidance modes. Simulation results illustrate the
performance of the proposed hybrid control approach for 2-dimensional and
3-dimensional scenarios.
