This study explores the problem of Multi-Agent Path Finding with continuous and stochastic travel times whose probability distribution is unknown. Our purpose is to manage a group of automated robots that provide package delivery services in a building where pedestrians and a wide variety of robots coexist, such as delivery services in office buildings, hospitals, and apartments. It is often the case with these real-world applications that the time required for the robots to traverse a corridor takes a continuous value and is randomly distributed, and the prior knowledge of the probability distribution of the travel time is limited. Multi-Agent Path Finding has been widely studied and applied to robot management systems; however, automating the robot operation in such environments remains difficult. We propose 1) online re-planning to update the action plan of robots while it is executed, and 2) parameter update to estimate the probability distribution of travel time using Bayesian inference as the delay is observed. We use a greedy heuristic to obtain solutions in a limited computation time. Through simulations, we empirically compare the performance of our method to those of existing methods in terms of the conflict probability and the actual travel time of robots. The simulation results indicate that the proposed method can find travel paths with at least 50% fewer conflicts and a shorter actual total travel time than existing methods. The proposed method requires a small number of trials to achieve the performance because the parameter update is prioritized on the important edges for path planning, thereby satisfying the requirements of quick implementation of robust planning of automated delivery services.

翻译：中文摘要：本研究探讨了在概率分布未知的连续随机旅行时间下的多智能体路径规划问题。我们的目标是管理一群自动机器人，使其在行人与各类机器人共存的建筑环境（如办公楼、医院和公寓的配送服务）中提供包裹配送服务。在这些实际应用中，机器人穿越走廊所需时间通常呈现连续值且随机分布，同时关于旅行时间概率分布的先验知识十分有限。多智能体路径规划已被广泛研究并应用于机器人管理系统，但在上述环境中实现机器人自动化运行仍具挑战性。我们提出：（1）在线重规划方法，可在执行过程中动态更新机器人的行动方案；（2）参数更新方法，通过贝叶斯推理在观测到延迟时估算旅行时间的概率分布。我们采用贪心启发式算法在有限计算时间内获取解。通过仿真实验，我们从冲突概率和机器人实际旅行时间两个维度，将所提方法与现有方法进行实证比较。仿真结果表明，该方法能够规划出冲突至少减少50%且实际总旅行时间更短的路径。由于参数更新优先针对路径规划中的关键边，所提方法仅需少量试验即可达到预期性能，从而满足自动化配送服务快速实施鲁棒规划的工程需求。