Safe and Quasi-Optimal Autonomous Navigation in Environments with Convex Obstacles

TL;DR

This paper introduces a continuous feedback control method for safe, quasi-optimal autonomous navigation around convex obstacles, ensuring stability and real-time applicability in 2D environments.

Contribution

It presents a novel control strategy that combines shortest path navigation on obstacle cones with a reactive sensor-based approach for unknown environments.

Findings

Achieves almost global asymptotic stability in 2D environments.

Demonstrates effectiveness through simulation results.

Provides a real-time, sensor-based navigation method for convex obstacles.

Abstract

We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a destination, in a quasi-optimal manner, in sphere worlds. The main idea consists in avoiding each obstacle via the shortest path on the cone's surface enclosing the obstacle and moving straight toward the target when the vehicle has a clear line of sight to the target location. In particular, almost global asymptotic stability of the target location is achieved in two-dimensional (2D) environments under a particular assumption on the obstacles configuration. We also propose a reactive (sensor-based) approach, suitable for real-time implementations in a priori unknown 2D environments with sufficiently curved convex obstacles, guaranteeing almost global asymptotic stability of the target location. Simulation results are presented to illustrate the effectiveness of the proposed approach.