# Path Planning of Obstacle-Crossing Robot Based on Golden Sine Grey Wolf Optimizer
## 1 Introduction  
Mobile robots with obstacle-crossing capabilities can perform wider and more efficient searches, so they are often used in complex work environments [1]. The movement mode of the obstacle-crossing robots is more complex and diverse than those that cannot cross the obstacles, which can open up new paths but also bring new challenges to path-planning technology [2]. Robot path planning refers to the mobile robot independently designing a safe and collision-free path with the shortest distance from the starting point to the end point, taking the least time. Algorithm is the core of robot path planning [3]. The path-planning algorithm can be roughly classified as (1) path-planning algorithms based on map search, such as the A-star algorithm [4; 5; 6], artificial potential field algorithm [7; 8], etc., (2) sampling-based path-planning algorithms, such as the RRT algorithm [9; 10; 11], PRM algorithm [12], etc., and (3) swarm intelligence algorithms based on global optimization, such as the ant colony optimizer [13; 14; 15], artificial bee colony optimizer [16; 17], algorithms based on deep learning [18; 19; 20], etc. The GWO is a kind of swarm intelligence algorithm [21]. Because of its strong convergence performance and relatively simple algorithm structure, it has been applied to parameter optimization [22; 23], fault diagnosis [24; 25], path planning [26; 27; 28] and other fields. However, the GWO also has problems, such as a too singular initial population, slow convergence speed and the ease with which it falls into the local optimum. To solve these problems, [PERSON] [29] proposed an improved grey wolf algorithm driven by mutation,which used the Levy flight model to perform mutation operation on the population and the greedy selection method to update the path. [PERSON] [30] proposed two grey wolf algorithms for position updating based on alpha wolves and all wolves, respectively, and analyzed the advantages and disadvantages of the two algorithms and their usage scenarios. [PERSON] [31] proposed a grey wolf algorithm with an adaptive convergence factor and convergence times, which calculates the next convergence factor and determines whether to end the program using historical optimization data. [PERSON] [32] proposed a multi-strategy integrated improved grey wolf algorithm, which improved the GWO in many aspects and formulated new leader election rules. [PERSON] [33] proposed two different strategies to improve the grey wolf algorithm and applied them to the 3D environmental path planning of agricultural robots. [PERSON] [34] combined BPNN and ALGWO to enhance the unpredictable behavior and exploration ability of the grey wolf algorithm and applied it to the PID control model. Although the performance of the GWO has been significantly improved by the efforts of many scholars, there are still problems such as a single initial population, slow convergence speed in the later stage and the ease with which it falls into the local optimum, and when it is used in the path planning of obstacle-crossing robots, because the path selection of the robot is more diversified, the shortcomings are more prominent. Aiming at this problem, this paper proposes an improved GWO based on the golden sine strategy. Firstly, a piecewise chaotic map is introduced to generate the distribution and initial population. Secondly, the nonlinear convergence factor and dynamic weight index are used to balance the global search and local search ability of the algorithm, so as to avoid falling into the local optimum and find the optimal solution as accurately as possible. Finally, the golden sine strategy is introduced to perform secondary convergence of the population, optimize the optimization method and enhance the search ability of the algorithm. At the same time, the feasibility of the application of the algorithm in the path planning of the obstacle-crossing robot is discussed. The grey obstacle-surmountable area is added to the traditional path-planning map and given a certain traffic cost.