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.

翻译：我们研究了在无权重与有权重地形上的时间最优多机器人覆盖路径规划问题，其目标是最小化覆盖时间（定义为所有机器人最大旅行时间）。具体而言，我们聚焦于将多机器人覆盖路径规划问题归约为最小-最大有根树覆盖问题。首次提出了一种混合整数规划模型以最优求解最小-最大有根树覆盖问题，由此得到的覆盖规划解能够保证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高效的启发式方法，通过减少混合整数规划模型中的变量数量，从而提升其对大规模多机器人覆盖路径规划问题的求解效率。我们证明这两种启发式方法均能生成精简规模的混合整数规划模型，且对所有最小-最大有根树覆盖实例保持完备性（即若存在解则保证可找到）。进一步地，我们探索了模型优化热启动技术，以提升原始混合整数规划模型与精简规模模型的求解效率。通过将基于混合整数规划的覆盖规划器与两种当前最先进的覆盖规划器在多个实例上进行对比实验，验证了其有效性：覆盖时间分别平均降低了27.65%和23.24%。