# Multirobot Task Planning Method Based on the Energy Penalty Strategy
## 1 Introduction  
With the continuous development of mobile robot technology, efficient cooperative control makes it possible for mobile robot clusters to complete complex tasks, thus providing an important tool or enabler for task planning [1, 2]. Such technology has been widely used in the industries of factory automation [3], warehouse [4], medical treatment [5], fire rescue [6], and so on.  
Multirobot task allocation (MRTA) decomposes a task into several subtasks under the constraint conditions of robot performance and load capacity, and coordinates the matching relationship between tasks and robots based on the principle of minimizing energy consumption and execution time. The goal is to obtain the optimal task allocation execution sequence and path for each robot to avoid task conflict, imbalance, and other problems and realize the reasonable allocation of resources. MRTA involves related technologies such as robot dynamic model [7], robot navigation [8] and environmental detection [9, 10], graph search method [11], architecture for multirobot coordination [12], and so on. At present, scholars pay more attention to the research of algorithm models and implementation methods, usually using centralized and distributed task allocation models and algorithms to solve MRTA problems [13, 14, 15]. Distributed task allocation models mainly include game theory [16], auction algorithm [17], competitive coordination [18], the MTSP(Multiple Traveling Salesman Problem) model [19; 20], and the VRP (Vehicle Routing Problem) model [21]. Many heuristic algorithms have been extensively applied in task sequence optimization and robot collaborative control, such as the neural network-based auction scheme [22], genetic algorithm for industrial plant inspection [13], and colony algorithm for agricultural machinery operation [23]. There are other methods that focus on obstacle avoidance path planning for robots to optimize task costs. [PERSON] et al. [24] proposed an optimal task decision method that indicates the optimal sequence and path for robots to complete certain tasks, thereby enabling warehouse robots to make optimal task decisions at minimum costs. An improved ant colony algorithm [25] coordinates the path of robots based on the priority of their residual power distribution. Because the APF (Artificial Potential Field) path planning algorithm can easily fall into the local minimum [26], [PERSON] et al. [27] integrated fuzzy logic into the APF algorithm to identify and avoid local minima. The A* algorithm usually uses path length as an evaluation function and is widely used and effective in path planning [28; 29; 30].  
Through the above analysis, the application of the genetic algorithm and A* algorithm in the MRTA has shown good results [31; 32; 33]. However, the performance of these algorithms largely depends on the quality of the heuristic algorithm of the fitness function. Therefore, an algorithm model construction of the energy penalty strategy for the optimal and balanced control of energy consumption in multirobot cooperative operations is proposed. The proposed model combines GA and A* algorithm to optimize the MRTA and task sequence in stages, and verifies the algorithm performance through multiple experiments. Compared to the algorithm [34], the total energy consumption is reduced by 0.3%, the standard deviation is reduced by 29.6%, and the optimization time reduced by about 2 s.  
The paper is organized as follows. The next section provides the problem statement and algorithm description. The description of the algorithm model is addressed in Section 3, including the computing methods of constraint conditions, objective functions, robot energy consumption, and other related parameters. The algorithm implementation for solving the MRTA is presented in Section 4, including coding methods, genetic operations, and algorithm steps. In Section 5, experimental and simulation results are given. Finally, the conclusion of this paper is drawn in Section 6.