# A Multilevel Adaptive Path-Planning Model in Off-Road Environments
## 1 Introduction  
Existing path-planning algorithms are applicable only to specific scenarios, such as container transport at ports [1, 2], warehouse logistics [3, 4], and obstacle avoidance in robots [5, 6, 7]. When applied to engineering fields such as agricultural machinery, forest fire protection, traffic, and transportation, the algorithm needs to be designed to find the optimal trafficable path by considering the possibility that there might be no road or only rugged roads amid hills and mountains. The environments for these scenarios are more complex and the path length can range from several to hundreds of kilometers. Therefore, it is crucial to find a path-planning model for long-distance off-road environments. The first step of path planning is to process the real-world environment and construct an environmental model. The grid map method, topological method, and Voronoi diagram method are common modeling methods. The grid map method converts the area to be studied into cells, which are termed grids. In recent years, many types of grids have been proposed including diamond grids, fan grids, and honeycomb grids [8, 9, 10], but the most intensively studied is the rectangular grid. The different trafficability properties of the grids indicate whether the regions they represent are trafficable or not. Popular path-planning algorithms include traditional algorithms such as the Dijkstra algorithm and the rapidly exploring random tree (RRT) algorithm, as well as intelligent algorithms such as the genetic algorithm and ant colony algorithm. The traditional algorithms, which were proposed earlier and are based on simple mechanics, have been widely used, especially in path planning for unmanned aerial vehicles (UAVs) [11, 12] and driverless cars [13, 14]. The fundamental algorithms represented by reactive path-planning algorithms [15, 16, 17, 18] such as potential field, velocity obstacle, collision cone, etc., also play a huge role in solving such problems. [PERSON] et al. [15] presented a novel vision-based framework for tracking dynamic objects using guidance laws based on a rendezvous cone approach. Furthermore, by performing a series of simulations to show the efficacy oftheir methods, [PERSON] et al. [16] modelled the shapes of objects using quadric surfaces. A collision/rendezvous cone concept was employed. A computationally efficient approach was presented to compute the collision/rendezvous cone between finite-sized quadric surfaces (which were not necessarily of the same shape). As bionics research advances and interdisciplinary studies develop, intelligent algorithms are seeing wider adoption in path planning. In 1992, [PERSON] et al. [19] put forward the ant colony algorithm (ACA). Inspired by foraging behaviors of ants that often find the shortest path towards food, ACA has gained popularity in path-planning tasks. [PERSON] [20] proposed an algorithm using fuzzy ant clustering, which detected and combined the overlapping nodes to reduce the redundancy and improve the quality of the clusters. To address the intrinsic susceptibility of ACAs to a local optimum, [PERSON] [21] adjusted the initial distribution of pheromones by introducing new heuristic functions and adaptive updating rules of pheromones. Many solutions have been proposed for off-road path planning. To find the optimal path for off-road autonomous driving with static obstacle avoidance, [PERSON] et al. [22] determined the priority of each path by considering the path safety cost, path smoothness, and path consistency. [PERSON] et al. [23] proposed a path-planning method based on fuzzy support vector machine (FSVM) and general regression neural network (GRNN) to provide a solution path for autonomous vehicles navigating in off-road environments and verified through experiments that their method could navigate vehicles on smooth and obstacle-free routes when satisfying the constraint of vehicle kinematics. [PERSON] et al. [24] considered the influence of terrain slope and soil strength on a vehicle's off-road trafficability.