## 4 Discussion  
This paper presents a study of the APF-Dijkstra fusion algorithm based on volume and steering model constraints. Relying on the optimality of the global path Dijkstra algorithm, whose gravity comes from the path points of the optimized global path, the main improvements of the fusion algorithm are as follows:  
1. The map preprocessing of the raster map of the algorithm's operating environment was carried out, known obstacles were inflated with an expansion width of 1 raster distance, and the search direction of the global path Dijkstra algorithm was optimized by removing 45\({}^{\circ}\) of the search direction when obstacles appeared near the search neighborhood. Simulation experiments show that the distance between the path that can be planned and the obstacle is increased by at least 1 m.
2. Aiming at the problem that the path planned by the traditional APF algorithm cannot fit the global path well and the combined potential energy cannot converge to 0 when reaching the target point, the path inflection point in the optimized global path is used as the temporary target point of the APF algorithm, and the potential energy function of the APF algorithm is improved by introducing a Gaussian function and distance factor. Simulation experiments show that through the distance factor and Gaussian decay term, a nonlinear and adaptive potential field is realized, and the minimum value of the combined potential energy point is 0.0006, which almost converges to 0.
3. Aiming at the local oscillation phenomenon of the APF algorithm caused by static U-shaped obstacles, by ellipsing the U-shaped obstacles and selecting the point with the lowest resultant potential energy as the virtual target point to provide attraction, the U-shaped obstacles can be avoided in time, and the algorithm step size is optimized based on the obstacle density.
4. As the traditional APF algorithm suffers from uneven combined force when avoiding obstacles, it is prone to problems such as path cusps and unrestricted steering angle. Based on the vehicle steering model, using the three-point arc method to smooth the path in real time is more reasonable than post-processing the path. Simulation experiments show that the average steering angle is 12.57\({}^{\circ}\), 7.98\({}^{\circ}\), and 8.28\({}^{\circ}\); the maximum turning angle does not exceed the set 40\({}^{\circ}\), while the average curvature rate of change is 0.248, 0.162, and 0.169, which can show that the planned path smoothness is better.
5. Traditional fusion algorithms usually consider the carrier as a material point; the planned path seems to avoid obstacles, but in fact, if the volume is considered, it will still collide with the obstacles. Therefore, in this paper, we instantiate the algorithm carrier as a rectangle with a length of 4.5 m and a width of 2.5 m and use three rows of 14 envelope circles to wrap the body to further expand the radius of the collision detection, which combines with the map preprocessing in (1) and adopts a temporary target point bias strategy to further expand the distance between the vehicle and the obstacles. This method is combined with the map preprocessing in (1), and a temporary target point bias strategy is used to further expand the distance between the vehicle and the obstacle. Simulation experiments show that the minimum distance between the obstacle and the center of the rear axle of the vehicle is 1.79 m, 1.82 m, and 1.66 m, respectively, which are higher than the minimum distance of 1.60 m set in this paper.