Multiple Shooting Approach for Finding Approximately Shortest Paths for Autonomous Robots in Unknown Environments in 2D

TL;DR

This paper introduces a novel multiple shooting algorithm for approximately shortest path planning of autonomous robots in unknown 2D environments, improving computational efficiency over existing methods.

Contribution

The paper presents a new multiple shooting-based algorithm for path planning that accounts for environmental mapping and obstacle avoidance, with convergence guarantees.

Findings

The proposed method converges to the shortest path when the collinear condition holds.

The algorithm is faster than the rubber band technique in numerical experiments.

Implementation in Python demonstrates practical applicability.

Abstract

An autonomous robot with a limited vision range finds a path to the goal in an unknown environment in 2D avoiding polygonal obstacles. In the process of discovering the environmental map, the robot has to return to some positions marked previously, the regions where the robot traverses to return are defined as sequences of bundles of line segments. This paper presents a novel algorithm for finding approximately shortest paths along the sequences of bundles of line segments based on the method of multiple shooting. Three factors of the approach including bundle partition, collinear condition, and update of shooting points are presented. We then show that if the collinear condition holds, the exactly shortest paths of the problems are determined, otherwise, the sequence of paths obtained by the update of the method converges to the shortest path. The algorithm is implemented in Python and some numerical examples show that the running time of path-planning for autonomous robots using our method is faster than that using the rubber band technique of Li and Klette in Euclidean Shortest Paths, Springer, 53-89 (2011).