This paper tackles the multi-vehicle Coverage Path Planning (CPP) problem, crucial for applications like search and rescue or environmental monitoring. Due to its NP-hard nature, finding optimal solutions becomes infeasible with larger problem sizes. This motivates the development of heuristic approaches that enhance efficiency even marginally. We propose a novel approach for exploring paths in a 2D grid, specifically designed for easy integration with the Quantum Alternating Operator Ansatz (QAOA), a powerful quantum heuristic. Our contribution includes: 1) An objective function tailored to solve the multi-vehicle CPP using QAOA. 2) Theoretical proofs guaranteeing the validity of the proposed approach. 3) Efficient construction of QAOA operators for practical implementation. 4) Resource estimation to assess the feasibility of QAOA execution. 5) Performance comparison against established algorithms like the Depth First Search. This work paves the way for leveraging quantum computing in optimizing multi-vehicle path planning, potentially leading to real-world advancements in various applications.

We study graph-based Multi-Robot Coverage Path Planning (MCPP) that aims to compute coverage paths for multiple robots to cover all vertices of a given 2D grid terrain graph $G$. Existing graph-based MCPP algorithms first compute a tree cover on $G$ -- a forest of multiple trees that cover all vertices -- and then employ the Spanning Tree Coverage (STC) paradigm to generate coverage paths on the decomposed graph $D$ of the terrain graph $G$ by circumnavigating the edges of the computed trees, aiming to optimize the makespan (i.e., the maximum coverage path cost among all robots). In this paper, we take a different approach by exploring how to systematically search for good coverage paths directly on $D$. We introduce a new algorithmic framework, called LS-MCPP, which leverages a local search to operate directly on $D$. We propose a novel standalone paradigm, Extended-STC (ESTC), that extends STC to achieve complete coverage for MCPP on any decomposed graphs, even those resulting from incomplete terrain graphs. Furthermore, we demonstrate how to integrate ESTC with three novel types of neighborhood operators into our framework to effectively guide its search process. Our extensive experiments demonstrate the effectiveness of LS-MCPP, consistently improving the initial solution returned by two state-of-the-art baseline algorithms that compute suboptimal tree covers on $G$, with a notable reduction in makespan by up to 35.7\% and 30.3\%, respectively. Moreover, LS-MCPP consistently matches or surpasses the results of optimal tree cover computation, achieving these outcomes with orders of magnitude faster runtime, thereby showcasing its significant benefits for large-scale real-world coverage tasks.

We investigate time-optimal Multi-Robot Coverage Path Planning (MCPP) for both unweighted and weighted terrains, which aims to minimize the coverage time, defined as the maximum travel time of all robots. Specifically, we focus on a reduction from MCPP to Min-Max Rooted Tree Cover (MMRTC). For the first time, we propose a Mixed Integer Programming (MIP) model to optimally solve MMRTC, resulting in an MCPP solution with a coverage time that is provably at most four times the optimal. Moreover, we propose two suboptimal yet effective heuristics that reduce the number of variables in the MIP model, thus improving its efficiency for large-scale MCPP instances. We show that both heuristics result in reduced-size MIP models that remain complete (i.e., guaranteed to find a solution if one exists) for all MMRTC instances. Additionally, we explore the use of model optimization warm-startup to further improve the efficiency of both the original MIP model and the reduced-size MIP models. We validate the effectiveness of our MIP-based MCPP planner through experiments that compare it with two state-of-the-art MCPP planners on various instances, demonstrating a reduction in the coverage time by an average of 27.65% and 23.24% over them, respectively.