###### Abstract  
Aiming at the trajectory generation and optimization of mobile robots in complex and uneven environments, a hybrid scheme using mutual learning and adaptive ant colony optimization (MuL-ACO) is proposed in this paper. In order to describe the uneven environment with various obstacles, a 2D-H map is introduced in this paper. Then an adaptive ant colony algorithm based on simulated annealing (SA) is proposed to generate initial trajectories of mobile robots, where based on a de-temperature function of the simulated annealing algorithm, the pheromone volatilization factor is adaptively adjusted to accelerate the convergence of the algorithm. Moreover, the length factor, height factor, and smooth factor are considered in the comprehensive heuristic function of ACO to adapt to uneven environments. Finally, a mutual learning algorithm is designed to further smooth and shorten initial trajectories, in which different trajectory node sequences learn from each other to acquire the shortest trajectory sequence to optimize the trajectory. In order to verify the effectiveness of the proposed scheme, MuL-ACO is compared with several well-known and novel algorithms in terms of running time, trajectory length, height, and smoothness. The experimental results show that MuL-ACO can generate a collision-free trajectory with a high comprehensive quality in uneven environments. when the size of the environment increases. Therefore, scholars have tried to find simpler and more applicable modeling methods. In [10; 11; 12], the authors tried to reduce the cost of 3D radar modeling, using RGB-D (Red Green Blue-Depth) sensors to store the height information and coordinates of the environment in the same grid to obtain a discrete 3D grid map, namely a 2.5D elevation map. This paper proposes a 2D-H grid map based on a 2.5D elevation map, which maps the height information of the environment to a 2D plane. Compared with the 2.5D elevation map, the 2D-H method further reduces the number of calculations and saves memory space, which not only meets the needs of timeliness but is also practical enough. The goal of trajectory planning is to find a trajectory for a robot from a starting point to an ending point without colliding with obstacles and meeting other constraints, such as the trajectory length and smoothness. In recent years, trajectory planning has attracted much attention in the field of robotics. Traditional methods, such as simulated annealing (SA) [13] and the artificial potential field method (APF) [14], are widely used because of their ease of understanding and implementation. However, [15] these methods may easily fall into a local optimal solution and cannot reach the end point when a complex environment is encountered. When dealing with trajectory planning in a complex dynamic environment, intelligent bionic algorithms often play an important role [16], including genetic algorithms (GA) [17], neural networks [18], particle swarm optimization (PSO) [19], and the ant colony algorithm (ACO) [20]. The GA algorithm has strong uncertainty in the planned trajectory due to its large number of parameters and the randomness of the initial population [21]. In the PSO algorithm, [22] the initial particles are randomly selected, which leads to a variety of different planning results. [23]. Neural network algorithms spend a lot of time on pre-training and adjusting parameters. Not only is the number of calculations significant, but also the interpretability is not ideal. In an uneven environment with obstacles, the uncertainty of the environment, such as the distribution of obstacles and the complexity of the environment, brings difficulties to the trajectory planning of mobile robots. Therefore, the required path planning algorithm needs a strong search ability and good stability. ACO is a probabilistic technique to solve computational problems which is robust and easy to combine with other methods [24; 25].