Minimum-Length Coverage Path Planning for Grid Environments with Approximation Guarantees
Megnath Ramesh, Frank Imeson, Baris Fidan, Stephen L. Smith
AI summary
Problem
Traditional rank-touring frameworks for coverage path planning minimize turns but lack theoretical guarantees on path length, often yielding suboptimal routes. This paper addresses the need for a provably efficient algorithm that minimizes path length in grid environments.
Approach
MLC-Approx modifies the standard rank-touring framework by strategically breaking and merging coverage sub-tours using double-edge and corner-junction strategies to minimize added path length while maintaining a provable approximation guarantee.
Key results
- Proves rank-touring framework has a (1 + 1.5γ) approximation factor for path length
- Proposes MLC-Approx algorithm achieving a (1.5 + ϵ) approximation guarantee for minimum-length coverage
- Introduces a lazy variant of MLC-Approx that matches its performance with faster runtime
- Validates MLC-Approx on real-world environment maps, showing superior path length and turn reduction compared to state-of-the-art baselines
Why it matters
Provides robotics researchers and service automation developers with a theoretically grounded, efficient algorithm for planning near-optimal coverage paths in complex environments.
Abstract
We focus on planning minimum-length robot paths to cover environments using the robot’s sensor or coverage (e.g., cleaning) tool. Many algorithms use the following framework: (i) compute a grid decomposition of the environment, (ii) partition the grid to be covered by non-overlapping coverage lines (straight- line paths), and (iii) compute a cost-minimizing tour of the coverage lines to get a coverage path. While this framework aims to minimize turns in the path, it does not yield guarantees on the resulting path length. In this paper, we show that this framework guarantees a coverage path of length (1+1.5γ) times the optimal, where γ > 1 is the approximation factor to solve the metric traveling salesman problem (metric-TSP). Following this, we propose the Minimum Length Coverage Approx (MLC- Approx) approach that modifies this framework to achieve an approximation factor of (1.5 + ε), where ε ≪1 depends on the number of coverage lines. Instead of computing a tour of the coverage lines, MLC-Approx merges minimum-length sub-tours of coverage lines while minimizing the turns added by the merges. We also propose a lazy variation of MLC-Approx that achieves the same result with faster empirical runtime. We validate MLC- Approx in simulations using maps of real-world environments and compare against state-of-the-art CPP approaches.