This paper proposes a local path planning method with a reachable set for Automated vertical Parking Systems (APS). First, given a parking lot layout with a goal position, we define an intermediate pose for the APS to accomplish reverse parking with a single maneuver, i.e., without changing the gear shift. Then, we introduce a reachable set which is a set of points consisting of the grid points of all possible intermediate poses. Once the APS approaches the goal position, it must select an intermediate pose in the reachable set. A minimization problem was formulated and solved to choose the intermediate pose. We performed various scenarios with different parking lot conditions. We used the Hybrid-A* algorithm for the global path planning to move the vehicle from the starting pose to the intermediate pose and utilized clothoid-based local path planning to move from the intermediate pose to the goal pose. Additionally, we designed a controller to follow the generated path and validated its tracking performance. It was confirmed that the tracking error in the mean root square for the lateral position was bounded within 0.06m and for orientation within 0.01rad.

翻译：本文提出了一种基于可达集的局部路径规划方法，用于自动垂直泊车系统(APS)。首先，针对给定包含目标位置的停车场布局，我们为APS定义了一个中间位姿，使其能够通过单次操作（即无需换挡）完成倒车入库。接着引入可达集概念，该集合由所有可能中间位姿的网格点构成。当APS接近目标位置时，必须从可达集中选择一个中间位姿。通过建立并求解最小化问题来确定最优中间位姿。我们针对不同停车场条件设计了多种场景测试。全局路径规划采用Hybrid-A*算法实现车辆从起始位姿到中间位姿的运动，局部路径规划则使用回旋曲线方法完成从中间位姿到目标位姿的移动。此外，我们设计了路径跟踪控制器并验证其跟踪性能。结果表明，横向位置的均方根跟踪误差控制在0.06m以内，航向角误差控制在0.01rad以内。