基于混合A*和可变半径RS曲线的自动泊车路径优化方法

路径规划是自动泊车系统的重要组成部分，是确保泊车运动安全、缩短行车距离、提高乘坐舒适性的关键。而当前自动泊车规划系统往往面临行驶空间狭小、障碍物多、路径搜索难度大等技术挑战，同时搜索曲线半径固定容易导致路径接点处曲率不连续，增大了路径跟随控制难度和轮胎磨损程度，这些都提升了泊车路径规划的研究难度。针对以上问题，设计可变半径的Reeds-Shepp曲线，提出基于混合A^*和该曲线的自动泊车路径规划方法，通过调整曲线半径，提升其在复杂场景下路径的搜索能力和灵活性。随后，设计基于分段贝塞尔曲线和梯度下降的路径优化方法，利用其多阶导数连续的优势优化已搜索的路径曲率，并采用梯度下降来保证路径曲率大小和对障碍的规避，解决直线与圆弧相接等位置曲率变化不连续的难题。结合路径搜索与路径优化的泊车规划方法能够切实满足复杂场景下的泊车需要。最后，基于团队自主研发的PanoSim虚拟系统与MATLAB搭建联合仿真环境，针对多种自动泊车工况测试验证提出的方法。研究结果表明：调整Reeds-Shepp曲线的搜索半径进行全局路径搜索，可获得更短和更易跟随的路径，具有良好的灵活性；基于贝塞尔曲线和梯度下降法的路径优化可有效消除曲率突变点、约束路径曲率并保证对障碍的无碰撞要求。

Path Optimization Algorithm for Automatic Parking Based on Hybrid A* and Reeds-Shepp Curve with Variable Radius

Path planning is an important part of automatic parking systems. It is the key to ensuring parking safety, shortening driving distance, and improving ride comfort. However, current automatic parking planning systems face certain technical challenges, such as narrow driving space, the presence of several obstacles, and difficulty in path search. Furthermore, the fixed radius of the search curve easily leads to discontinuous curvature at the path joints, increasing the difficulty of path-following control and the degree of tire wear. Accordingly, these factors complicate parking-path planning. Thus, in this study, a path optimization algorithm for automatic parking was developed based on hybrid A^* and the Reeds-Shepp curve with variable radius. Adjusting the curve radius can improve path-search ability and flexibility in complex scenarios. Moreover, a path optimization method based on the segmented Bezier curve and gradient descent was developed. Continuous multi-order derivatives were used to optimize the curvature of the searched path, and gradient descent was used to ensure path safety and avoid obstacles. Thus, discontinuous curvature changes at the point where a straight line meets an arc can be handled. The proposed parking planning method, which combines path search and path optimization, can effectively meet parking needs in complex scenarios. Finally, based on MATLAB and PanoSim virtual system, which was independently developed by Vehicle Controls and Intelligence Lab (VCI Lab), a joint simulation environment was developed to test and verify the proposed method under a variety of automatic parking conditions. The results demonstrate that the variable curve radius for global path search yields a shorter path that is easier to follow, and achieves considerable flexibility. The path optimization method based on the segmented Bezier curve and gradient descent can effectively eliminate sudden curvature changes, constrain path curvature, and ensure safe driving.