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

## TL;DR

This paper introduces a hybrid control method for vehicles in n-dimensional space that ensures both goal stabilization and obstacle avoidance through robust, chattering-free switching between modes.

## Contribution

It presents a novel hybrid feedback control strategy that guarantees global asymptotic stabilization and obstacle avoidance in n-dimensional Euclidean spaces.

## Key findings

- Guarantees robust switching without chattering.
- Ensures global asymptotic stabilization of the reference position.
- Demonstrates effectiveness through 3D simulation results.

## Abstract

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.