###### Abstract
In recent years, the ant colony algorithm has been widely used in transportation, logistics distribution, network analysis, and other fields [26]. Nevertheless, the traditional ant colony algorithm has the defects of a low search efficiency and a slow convergence speed, and it is also easy to fall into local extremes. Researchers have put forward various improved methods to optimize the search ability of the ant colony algorithm. [PERSON] et al. [27] proposed an improved ant colony algorithm with multiple heuristics (MH-ACO), which is better reflected in the global search ability and convergence. However, the parameter setting is complex, which brings randomness to the experiment. [PERSON] et al. [28] used a stimulating probability to help the ants choose the next grid and employed new heuristic information based on the principle of unlimited step length to expand the field of view and improve the visibility accuracy. The improved algorithm speeds up the convergence speed and expands the search space, but the safety of the trajectory cannot be guaranteed. In addition, [PERSON] et al. [29] designed a new pheromone smoothing mechanism to enhance the search performance of the algorithm. When the search process of the ant colony algorithm is close to stagnation, the pheromone matrix is reinitialized to increase the diversity of the connections at the expense of a large time cost. Furthermore, the improved ant colony algorithm is combined with some two-stage trajectory planning methods. [PERSON] et al. [30] proposed a fast two-stage ant colony algorithm based on the odor diffusion principle, including two stages of preprocessing and trajectory planning, which accelerated the convergence speed but did not consider the trajectory optimization. [PERSON] et al. [31] proposed a multi-factor improved ant colony algorithm (MF-ACO) to solve the problem related to the fact that the trajectory planning algorithm of mobile robots cannot cope with the complex actual environment. The maximum and minimum ant strategy was adopted to avoid local optima. Then the dynamic tangent point adjustment method was used to smooth the path to further improve the quality of the trajectory, but the smoothness needed to be further improved. Although the above-mentioned improved algorithm attempts to improve the search performance of ACO and speed up the convergence speed, it does not consider the height information in the environment, which is different from ordinary raster maps, and the convergence performance of ACO can be further improved. For trajectory planning and optimization in complex and uneven environments, this paper proposes a trajectory generation and optimization method based on mutual learning and adaptive ant colony optimization (MuL-ACO), which can make robots safely and quickly plan a short and smooth trajectory in uneven environments. In this method, the global trajectory planning of mobile robots is divided into two consecutive parts: the initial trajectory generation and trajectory optimization. Firstly, the improved adaptive ant colony algorithm further accelerates the convergence of ACO to quickly generate the initial trajectory. The initial planned trajectory may contain redundant points and inflection points, which results in high memory consumption and poor trajectory quality. Then, a trajectory optimization algorithm based on mutual learning is proposed to further optimize the length and smoothness of the initial trajectory. The main contributions of this paper are as follows. 1. The 2D-H raster map is proposed to simulate the uneven outdoor environment. The height information in the three-dimensional environment is stored in the 2D plane;
2. A hybrid scheme using mutual learning and adaptive ant colony optimization is proposed in this paper. The global robot trajectory planning problem is divided into two consecutive parts: the trajectory generation part and the trajectory optimization part;
3. An improved adaptive ant colony algorithm is proposed to generate the initial trajectory.