A Hybrid Controller for Obstacle Avoidance in an n-dimensional Euclidean Space
For robotic vehicles, this provides a provably stable hybrid control approach for obstacle avoidance, though it is an incremental extension of existing hybrid control methods.
The paper presents a hybrid feedback controller for a vehicle in n-dimensional space that ensures global asymptotic stabilization to a reference position while avoiding a bounded spherical obstacle, with simulation results in 3D.
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.