## 1 Introduction  
Mobile robots have received widespread attention because of their great potential and research value in industrial applications, manufacturing, search and rescue, medical service, and intelligent transportation system [1]. Navigation is a key technology of mobile robot researches because it defines how mobile robots perceive, locate, and plan paths in an environment [2]. Path planning is an important part of robot navigation research. The main purpose is to find a collision-free optimal path from a starting point to final point for the mobile robot in a known environment [3]. The path planning of mobile service robots generally considers both static and dynamic environments [4]. The static environment refers to the location of a starting and ending point is known, and obstacles are also stationary. However, the location of obstacles changes with time in a dynamic environment. A mobile robots need to make corresponding decisions based on sensor information. According to the robot's perception of the environment, path planning can be divided into two types. One is the robot plans route offline with the known map information, which is called global path planning [5]. In another type, the robot does not input environmental information in advance. It is necessary to use the sensor to establish an environmental map in real time, avoid obstacles, and find a suitable path. This kind of path planning is called local path planning [6]. The global path planning method is applied to a static environment in the paper. In recent years, many researchers have carried out significant research on the path planning of mobile service robots and proposed relevant control methods. The methods include artificial potential field method [7], fuzzy algorithm [8], A-Star algorithm [9],DWA algorithm [10], genetic algorithm [11], immune algorithm [12] and neural network algorithm [13]. The genetic algorithm and neural network algorithm are studied in these papers. They are belonging to the metaheuristic algorithm and the same as the ant colony algorithm. [PERSON] et al. [14] fused the artificial potential field algorithm with the genetic algorithm and proposed a hybrid approach for path planning of multiple mobile robots in continuous environments. [PERSON] et al. [15] combined the Dijkstra algorithm with the bioinspired neural network. It reduced the accuracy requirement of the robot path planning on the environment model and saved the time costs. The combination of heuristic algorithms and intelligent control methods to maintain strengths and make up for shortcomings has become a research hotspot in related algorithm research. In 1992, [PERSON] proposed ant colony algorithm [16] from the foraging behavior of real ants in nature, which is a meta-heuristic algorithm. The ant colony algorithm has been gradually applied to the field of mobile service robot path planning [17] because of its parallel processing, distributed computing and strong robustness. Although the ant colony algorithm has shown good performance in the field of path planning, it still cannot solve the shortcomings of long search time, easy stagnation, slow convergence speed and local optimization. In order to improve the performance of the algorithm, many scientists have done relevant research. [PERSON] and [PERSON] [18] proposed a fuzzy ant colony algorithm to minimize the iterative learning error of ant colony algorithm under the fuzzy control. [PERSON] et al. [19] combined advantages of ant colony algorithm and genetic algorithm and proposed a new hybrid GA-ACO algorithm. [PERSON] et al. [20] verified the efficiency of the ant colony algorithm based on the TSP model. [PERSON] et al. [21] improved its performance by applying a rollback strategy to basic ant colony algorithm. [PERSON] and [PERSON] [22] combined a directional motion and a vector motion of mobile robot in a grid map to propose a quick ant colony algorithm. [PERSON] et al. [23] proposed an improved ant colony algorithm based on dynamic parameters and pheromone update mechanism.