## 1 Introduction  
In recent years, autonomous mobile robots have been widely employed in automatic factories [1], logistic centers [2], warehouses [3], and manufacturing systems [4], playing an increasingly important role in transportation, pickup, and delivery systems. Today, the demand for autonomous mobile robots that can collaborate with humans is rapidly increasing. Consequently, planning an optimal safe path for a mobile robot performing multiple pickup and delivery operations in human-shared environments has become a critical and urgent challenge. Path planning is widely recognized as one of the fundamental problems in robotic control. For a mobile robot performing multiple tasks, the control problem can generally be divided into two subproblems: the task scheduling problem, which determines the order in which tasks are executed, and the local path planning problem, which computes an optimal path to accomplish each individual task. The task scheduling problem determines the execution order of tasks, aiming to find an optimal sequence for visiting multiple goal locations. This is commonly formulated as the Vehicle Routing Problem (VRP) [5] or the Traveling Salesman Problem (TSP) [6], which have been extensively studied in static environments where the path cost between locations is fixed and known. However, the path cost in dynamic environments is uncertain and often time-varying. Local path planning focuses on computing a conflict-free path from a start location to a goal location while satisfying specific performance criteria such as minimizing travel distance, commonly referred to as the Shortest Path Planning (SPP) problem [7,8]. These two subproblems are deeply interdependent: the outcome of task scheduling directly influences local planning decisions; in turn, local path feasibility can affect task scheduling results. Moreover, both subproblems are significantly affected by the presence of stochastically moving humans in human-shared environments, which introduces uncertainty and increases the complexity of planning. As is well known, path planning in static environments has already been studied in considerable depth and various methods have been developed, including D* [9] and A* [10]. However, the path planning problem for a mobile robot designed with multiple pickup and delivery tasks is NP-hard and remains a significant challenge, particularly in dynamic environments. The primary difficulties arise from (1) controlling multiple tasks, and (2) dealing with environmental uncertainties, including dynamic obstacles and stochastic human behavior. To date, various methods have been developed to generate a global path for a mobile robot performing multiple tasks. To manage task sequences, syntactically co-safe Linear Temporal Logic (sCLTL)--a fragment of Linear Temporal Logic (LTL) [11]--has been widely applied for specifying and controlling multiple tasks formulated as scLTL expressions [12]. For example, [PERSON] et al. [13] employed scLTL to represent task specifications and combined it with the A* pathfinding algorithm. It has been proved that scLTL is efficient in task descriptions and control. In terms of path planning, real-time algorithms [14,15] are commonly used to ensure safe navigation by avoiding moving obstacles in dynamic environments. These methods typically adopt a hierarchical path planning framework; instead, a global planner provides guidance toward the goal, while a local planner is responsible for obstacle avoidance. Unfortunately, real-time path planning methods incur high computational costs due to continuous re-planning, and are unable to explicitly address environmental uncertainties at the planning level. Although real-time re-planning at each time step is widely regarded as the safest strategy for handling environmental uncertainties [16], it is often impractical in real-world scenarios such as warehouses, logistics centers, and automated factories.