## 2 Related Work  
In path planning, obstacle avoidance has traditionally been the primary requirement for mobile robots. Numerous efficient algorithms have been proposed for path planning and task assignment, including A*[10; 23], D*[9; 24], Reinforcement Learning (RL) [17; 25], and Monte Carlo Tree Search (MCTS) [26; 27]. However, as is widely known, although the A* algorithm is efficient for finding the shortest path in static environments, it struggles to address uncertainties in dynamic environments, with D* facing the same limitation. While the RL and MCTS methods are effective in both static and dynamic settings, unfortunately these approaches typically require extensive learning costs to derive an optimal policy by repeating trials. What is more, even in static environments they cannot provide any guarantees for the learned policy. These classic algorithms do not perform well when addressing uncertain factors, especially unpredictable obstacles such as human operators. When a human suddenly appearsin front of a mobile robot, the robot has to stop proactively to ensure human safety. Thus, more robust methods [28; 29; 30; 31] have been presented for environments requiring human-robot coexistence. [PERSON] et al. [28] proposed a safe RL controller with control barrier functions and utilized Gaussian Processes (GPs) to model the system dynamics and uncertainties. However, Gaussian functions encounter difficulties when modeling uncertainties with multiple peaks. [PERSON] et al. [29] proposed a framework that uses DRL as an enabling technology to enhance the intelligence and safety of robots in human-robot collaboration scenarios. [PERSON] et al. [30] presented a DRL approach to realize the real-time collision-free motion planning of an industrial robot for human-robot collaboration. [PERSON] et al. [31] proposed a Reachability-based Trajectory Safeguard (RTS) controller which leverages reachability analysis to ensure safety during training and operation. While these methods are efficient in human-robot collaboration, they are depended on online learning and cannot solve the issue of collisions at the planning level. A novel approach to collision avoidance based on human-robot interaction was proposed in [32], where the robot communicates its presence to nearby humans through voice messages. Upon approaching a certain distance, the human is required to provide feedback in order to complete the interaction process. [PERSON] et al. [33] presented a virtual force field-based mobile robot navigation algorithm in which both active and critical regions are used to deal with the uncertainty of human motion. The region sizes for the robot's navigation are calculated based on worst-case avoidance conditions. Although the above-mentioned methods have shown promising results, they all consider humans as fixed subjects in the physical workspace. Hybrid methods combining Global Path Planning (GPP) and Local Path Planning (LPP) [34] are widely applied in navigation, where LPP is used for real-time obstacle avoidance. For instance, this scheme is widely utilized in the field of autonomous driving [35]. Strictly speaking, this is a real-time planning system in which the re-planning mechanism is invoked when an unexpected obstacle is encountered. The main advantage is that it provides high safety assurance. However, this approach does not consider the future risk or uncertainties at the planning level. In an automated factory scenario where mobile robots work together with humans, a mobile robot usually needs to accomplish its tasks within a given time budget. Thus, such real-time planning systems encounter high cost while also easily becoming trapped in continuous re-planning, leading to low task success rates. Recently, numerous path planning methods that consider uncertain human actions have been proposed to handle human-robot interactions. [PERSON] et al. [36] presented a conflict-free speed alteration strategy for human safety.