# Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm
## 1 Introduction
Due to the strong similarity between the MRTA problem and the multiple traveling salesman problem, some researchers regard the MRTA problem as an example of the multiple traveling salesman problem. The traveling salesman problem is one of the standard combined discrete optimization problems. There are two methods for solving the TSP: Exact method and heuristic method. [PERSON] and [PERSON] [28] adopted multiple update rules and K-opt operations to improve the artificial bee colony algorithm, they used the characteristics of the exchange sequence to exchange the urban sequence (solution/path) of the problem, and created update rules of different solutions (path) for the algorithm to solve the travel agent problem. [PERSON] and [PERSON] et al. [29] proposed a centralized solution based on fuzzy logic algebra and combined with two goals: taking the minimum total travel distance of the traveling salesman and the maximum travel distance of any robot as the goal. [PERSON] et al. [30] combined the characteristics of particle swarm optimization, ant colony algorithm and 3-opt algorithm, and proposed a hybrid algorithm PSO-ACO-3-opt for solving standard TSPs. The task-planning method of the spacer-robot cluster will directly affect the efficiency of the entire system. Therefore, choosing the optimal robot cluster task-planning method becomes the key to effectively solve the task planning problem of the robot cluster system. The existing methods usually consider the task planning problem of robot clusters as a multiple traveling salesman problem and establish the shortest-path model of robot cluster task-planning. When using the shortest-path model to solve space maintenance tasks, there exist the following problems: (1) no modeling analysis of space-robot cluster task-planning problems under resource constraints; (2) no consideration of the maximum benefit of space maintenance when space resources are limited; (3) no considering the difficulty of solving large-scale planning problems. Based on the analysis of the current research situation, this study proposes a new space-robot cluster task-planning scheme for the maintenance of SSPS. First, the task planning of the space-robot cluster under limited energy is analyzed, and a task planning model of space-robot clusters is proposed with penalty function added, which is comprehensively optimal for the consideration of income and energy consumption. Then, the task-clustering method is used to cluster the maintenance tasks to reduce the problem size and reduce the problem solving time; finally, a modified differential evolution algorithm including multiple neighborhood operations, roulette, de-crossover, multiple groups and other strategies is proposed to solve the problem of task allocation and path planning of multi-robots, complete the mission planning of the space-robot cluster, and improve the maintenance efficiency. The rest of the paper is organized as follows: Section 2 introduces the background of basic space maintenance tasks and the theoretical basis of modeling. Section 3 proposes the modeling theory of space-robot cluster task-planning. In Section 4, a modified differential evolution algorithm is proposed, and the algorithm is described in detail. In Section 5, the accuracy and effectiveness of the proposed model and algorithm are verified by experiments, and the results are discussed. Section 6 presents the conclusion.