Obstacle Avoidance via Hybrid Feedback

TL;DR

This paper introduces a hybrid feedback control method for obstacle avoidance in n-dimensional space, ensuring global stabilization and obstacle avoidance through mode switching, with proven Zeno-free switching and simulation validation.

Contribution

It presents a novel hybrid control algorithm that guarantees obstacle avoidance and stabilization with hysteresis-based switching, avoiding Zeno phenomena.

Findings

Guarantees global asymptotic stabilization and obstacle avoidance.

Ensures Zeno-free switching between control modes.

Validated through simulations in 2D and 3D scenarios.

Abstract

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.