A Path Planning Algorithm Based on Tangent Point Search and Constrained B-Spline

Abstract

The traditional Tangent Point Search (TPS) algorithm, as a path planning algorithm suitable for large-scale maps, performs well in the presence of large rectangular obstacles. However, it has two disadvantages: 1. it requires that the obstacles be rectangular so that the shape of obstacles is limited to the fixed form. 2. its resulting path does not meet the curvature constraints of vehicles so that it makes vehicles difficult to be tracked smoothly. To expand its scope of application, this paper categorizes obstacles into three types: polygonal obstacles, linear obstacles, and point obstacles. Based on this classification, a TPS+B algorithm is proposed to improve its ability to determine the tangent point cells in the TPS algorithm by convexifying the obstacles. To solve the problem of limited obstacle shapes, the cell coordinates of obstacle vertices are extended to the coordinates of convex hull vertices when the obstacles are arbitrary shapes. When using the B-spline algorithm for trajectory smoothing, the situation where the curved trajectory intersects with obstacles may occur. To avoid such a situation, the locally optimized path planning is designed by incorporating obstacle avoidance constraints and curvature constraints. The aim of such a design is to shift the path points of the TPS algorithm, thereby obtaining a collision-free trajectory that satisfies the vehicle's curvature constraints. Without considering the constraint of path curvature, a comparison of the A*, Dijkstra, Rapidly-exploring Random Tree (RRT), Jump Point Search (JPS), and the improved TPS algorithms reveals that the improved TPS algorithm achieves optimal performance in both algorithm time and path length. Specifically, in the large-scale map, the algorithm time is reduced by 69.16% compared to JPS, and the path length is shortened by 3.47% compared to Dijkstra. In the small-scale map, the algorithm time is reduced by 39.16%, and the path length is shortened by 1.27%. When considering the constraint of path curvature, a comparison between the Dynamic Window Approach (DWA) and Hybrid A* algorithms further demonstrates that the TPS+B algorithm remains optimal in both algorithm time and path length. In this scenario, in the large-scale map, the algorithm time is decreased by 97.56% compared to DWA, and the path length is reduced by 2.02% compared to Hybrid A*. In the small-scale map, the algorithm time is decreased by 61.9%, and the path length is reduced by 3.68%. The experimental results confirm the superiority of the TPS+B algorithm in path planning for different scale maps with various obstacles.