Modification of Hilbert's Space-Filling Curve to Avoid Obstacles: A Robotic Path-Planning Strategy

TL;DR

This paper presents an online algorithm that modifies Hilbert's space-filling curve to enable robotic exploration of regions with obstacles, ensuring complete coverage without prior knowledge of the environment.

Contribution

It introduces a novel obstacle-avoidance strategy for Hilbert's curve-based exploration, leveraging its fractal properties to guarantee full coverage.

Findings

Successfully explores regions with up to two side-by-side obstacles

Proves the validity of the modified curve for obstacle avoidance

Demonstrates the approach's effectiveness through theoretical analysis

Abstract

This paper addresses the problem of exploring a region using the Hilbert's space-filling curve in the presence of obstacles. No prior knowledge of the region being explored is assumed. An online algorithm is proposed which can implement evasive strategies to avoid obstacles comprising a single or two blocked unit squares placed side by side and successfully explore the entire region. The strategies are specified by the change in the waypoint array which robot going to follow. The fractal nature of the Hilbert's space-filling curve has been exploited in proving the validity of the solution.