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 Rooted Min-Max Tree Cover (RMMTC). For the first time, we propose a Mixed Integer Programming (MIP) model to optimally solve RMMTC, 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., guarantee to find a solution if one exists) for all RMMTC 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 42.42% and 39.16% over them, respectively.

翻译：我们研究了无权重与带权重地形下的时间最优多机器人覆盖路径规划（MCPP），该问题旨在最小化覆盖时间（即所有机器人最大行程时间）。具体而言，我们关注从MCPP到根系最小-最大树覆盖（RMMTC）的归约。首次提出了基于混合整数规划（MIP）的模型来最优求解RMMTC，由此得到的MCPP解的可证明覆盖时间至多为最优值的四倍。此外，我们提出了两种次优但有效的启发式方法，通过减少MIP模型中的变量数量来提高大规模MCPP实例的求解效率。我们证明这两种启发式方法均能生成规模缩减的MIP模型，并且对所有RMMTC实例保持完备性（即保证存在解时一定能找到解）。进一步，我们探索利用模型优化热启动技术来提升原始MIP模型及缩减规模MIP模型的效率。通过将我们的基于MIP的MCPP规划器与两种现有最优规划器在多个实例上的实验对比，验证了其有效性：平均覆盖时间分别降低了42.42%和39.16%。