# Safe and Quasi-Optimal Autonomous Navigation in Sphere Worlds

## TL;DR

This paper introduces a continuous feedback control method for safe, quasi-optimal autonomous navigation of a point-mass vehicle in environments with spherical obstacles, ensuring almost global stability.

## Contribution

It presents a novel control strategy that combines shortest path obstacle avoidance with direct navigation, applicable in n-dimensional Euclidean spaces.

## Key findings

- Ensures safe navigation with almost global asymptotic stability.
- Effective in complex environments with multiple spherical obstacles.
- Validated through simulation results.

## Abstract

We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a desired destination, in a quasi-optimal manner, from almost all initial conditions in an n-dimensional Euclidean space cluttered with spherical obstacles. The main idea consists in avoiding each obstacle via the shortest path within the cone enclosing the obstacle, and moving straight towards the target when the vehicle has a clear line of sight to the target location. The proposed control strategy ensures safe navigation with almost global asymptotic stability of the equilibrium point at the target location. Simulation results, illustrating the effectiveness of the proposed approach, are presented.