A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

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 stabilization and avoidance. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.