Guiding Vector Fields for Following Occluded Paths

TL;DR

This paper introduces a composite guiding vector field approach that enables mobile robots to follow desired paths while avoiding obstacles, even when the path is temporarily occluded, without global re-planning.

Contribution

It develops a novel vector field method with theoretical guarantees for path following and obstacle avoidance in 2D space, addressing deadlock and Zeno behaviors.

Findings

The vector field ensures collision-free path following.

The method guarantees convergence to the desired path.

Simulations validate the theoretical guarantees.

Abstract

Accurately following a geometric desired path in a two-dimensional space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to temporarily deviate from the path for obstacle/collision avoidance. In this paper, we develop a composite guiding vector field via the use of smooth bump functions, and provide theoretical guarantees that the integral curves of the vector field can follow an arbitrary sufficiently smooth desired path and avoid collision with obstacles of arbitrary shapes. These two behaviors are reactive since path (re)-planning and global map construction are not involved. To deal with the common deadlock problem, we introduce a switching vector field, and the Zeno behavior is excluded. Simulations are conducted to support the theoretical results.