## 2 Related Work
Although the superiority of this method was shown by comparing it with two existing methods, this method plans one-dimensional moving paths, which is unsuitable for an autonomous system. Similar works have made progress in the probabilistic prediction of human motion [37; 38] and robust sequential trajectory planning for multi-robot systems [39; 40]. However, fusing these techniques into a real-time planning system remains a challenge because of the difficulty encountered in joint planning and prediction for multiple robots and humans. [PERSON]'s research [41] introduced a scalable framework for robot navigation that accounts for high-order system dynamics and maintains safety in the presence of external disturbances, other robots, and nondeterministic intentional agents. However, this framework decomposes multi-agent pathfinding into a sequence of instances in which it is necessary to re-plan the paths at every time step for all agents [42; 43]. While such a framework maintains human safety, it does not account for the time budget of the robot or its task success rate. Consequently, this framework is difficult to realize in real-world applications. Table 1 summarizes and compares the related path planning methods discussed above. As described previously, shortest path planning methods such as A*, D*, and RRT* are not suitable for dynamic environments in which humans move randomly. Methods such as  
RL, FSA-MDP, and MCTS adopt learning schemes to obtain an optimal control policy, and are efficient in both static and dynamic environments. Moreover, these learning schemes include the possibility of addressing future risk in the learning phase through techniques such as stochastic simulations. Overall, RL is a good scheme, while MCTS suffers expensive computation cost. It is well known that real-time solutions are the safest approach to path planning which combines the two key components of global path planning and real-time obstacle avoidance. The real-time method is widely applied in navigation; however, it lacks risk foresight ability and cannot solve conflicts at the planning level. Above all, addressing risks at the planning level rather than relying on real-time methods is crucial for ensuring the safety of mobile robots working alongside humans while achieving a high task success rate. It has been proven that syntactically co-safe Linear Temporal Logic (scLTL), which is one fragment of linear temporal logic (LTL) [11], is efficient in terms of both task descriptions and control. Multiple tasks can be formulated using an scLTL formula [44; 45], offering efficient methodologies for managing multi-task scenarios and seamlessly integrating with path planning methods. For example, in [22] the authors investigated an RL approach merging MDP with scLTL and proposed an FSA-MDP algorithm to generate optimal paths against jamming attacks. Building upon this foundation, our primary aim is to generate safe and efficient plans that satisfy scLTL tasks for environments such as warehouses and automated factories where humans and robots must coexist or cooperate. Table 2 shows a comparison of the different methods. [PERSON] et al. [46] proposed a product MDP learner based on LTL for robots performing multiple tasks. However, their method only considers uncertainties in state transitions and does not address environmental uncertainties. The FSA-encoder-based MDP (Feb-MDP) [22] integrates scLTL and reinforcement learning, handling environmental uncertainties through real-time re-planning. However, this approach was designed for jamming attack scenarios, which differ significantly from human-robot interaction settings. DRL [47] and Plan-Seq-Learn [48] primarily focus on task sequencing for robotic manipulators, but lack mechanisms for handling environmental uncertainties. Furthermore, path planning for mobile robots in human-shared environments is fundamentally different from motion planning for manipulators. [PERSON] et al.