## 1 Introduction  
As the exploration of space continues to evolve, the Moon has emerged as a promising destination for scientific research and human settlement. In lunar missions, the transportation of personnel, equipment and resources plays a crucial role in facilitating exploration and enabling the successful execution of mission objectives. Advances in autonomous technologies have the potential to increase the ability to work on large-scale operations and minimize human risk through the use of autonomous rovers [1]. However, there is also the risk that if an autonomous system fails, the astronauts would have to spend valuable time rescuing the rover or taking over the tasks, which is considered a difficult failure to solve in an early stage lunar mission. The challenges and complexities associated with lunar transportation necessitate innovative solutions to optimize efficiency, ensure safety, and enhance mission productivity. One promising avenue for addressing these challenges lies in the collaboration between humans and robots [2]. By leveraging the complementary capabilities of both humans and robots, a dynamic human-robot function allocation system can be developed to optimize the allocation of transportation tasks, leading to increasedefficiency and improved adaptability to the variability of complex environments. This is especially the case in the resource-intensive, technologically risky and environmentally unstructured world of lunar surface operations [3]. In multi-human-robot lunar surface operations (LSO), astronauts are able to drive lunar rovers. When not driven by an astronaut, some vehicles might also function independently as robots, either teleoperated from the cabin or operated with supervised autonomy [4]. However, as the complexity of the environment and the task size expand, the function allocation efficiency is significantly suppressed. Due to the specificity of lunar mission scenarios, few studies have been found to construct human-robot task allocation methods for dynamic lunar missions. Fortunately, [PERSON] et al. proposed a task assignment method for lunar missions involving multiple agents that matches capabilities with specific functions, enabling a suitable assignment plan based on task decomposition and helping to address the unpredictable and changing nature of the lunar environment [5]. [PERSON] et al. leveraged an action graph to enhance the allocation of tasks and path planning for robots in dynamic environments, leading to faster and more efficient performance [6]. However, the aforementioned studies do not focus on optimizing lunar transportation, and the dynamic function allocation is still based on the predefined functions of each agent, whose capabilities will vary in different task scenarios and during the process of task implementation. Machine learning is extremely promising for solving dynamic task allocation [7]. A series of human-robot function allocation algorithms have been proposed, such as the market-based auction algorithm [8; 9], particle swarm optimization algorithm [10; 11], greedy algorithm [12], heuristic algorithm [13], queen bee-assisted genetic algorithm [14], and simulation-based learning techniques [15; 16]. [PERSON] et al. introduced a task allocation approach that takes into account both capacity and time, with the objective of enhancing the efficiency of task allocation and accommodating current tasks as they arise [17]. [PERSON] et al. have suggested an approach that takes into account transportation time and collision avoidance, aiming to reduce the number of robots required [18]. [PERSON] et al. suggested an algorithm for task allocation that optimizes the time required to complete the task [19]. [PERSON] et al. optimized the task allocation algorithm by conducting the maximum number of tasks [20]. [PERSON] et al. have suggested methods that take into account the effect of possible mission uncertainties on both the robot and the task, intending to generate task reallocation suggestions automatically [21].