Time-optimal path planning in high winds for a turning-rate constrained UAV is a challenging problem to solve and is important for deployment and field operations. Previous works have used trochoidal path segments comprising straight and maximum-rate turn segments, as optimal extremal paths in uniform wind conditions. Current methods iterate over all candidate trochoidal trajectory types and select the one that is time-optimal; however, this exhaustive search can be computationally slow. In this paper, we introduce a method to decrease the computation time. This is achieved by reducing the number of candidate trochoidal trajectory types by framing the problem in the air-relative frame and bounding the solution within a subset of candidate trajectories. Our method reduces overall computation by 37.4% compared to pre-existing methods in Bang-Straight-Bang trajectories, freeing up computation for other onboard processes and can lead to significant total computational reductions when solving many trochoidal paths. When used within the framework of a global path planner, faster state expansions help find solutions faster or compute higher-quality paths. We also release our open-source codebase as a C++ package. The website and demo can be bound at https://bradymoon.com/trochoids, codebase at https://github.com/castacks/trochoids, and video at https://youtu.be/qOU5gI7JshI .

翻译：高风速环境下考虑转弯速率约束的无人机时间最优路径规划是一个具有挑战性的问题，对实际部署与野外作业至关重要。已有研究采用包含直线段与最大速率转弯段的次摆线段作为均匀风场中的最优极值路径。现有方法需遍历所有候选次摆线轨迹类型并选取时间最优解，然而这种穷举搜索会导致计算效率低下。本文提出一种降低计算时间的方法：通过将问题转换至空气相对坐标系，并将解限定在候选轨迹子集内，从而减少候选次摆线轨迹类型的数量。在Bang-Straight-Bang轨迹中，本方法相较现有方法整体计算量降低37.4%，释放出的计算资源可用于其他机载进程，并在求解多条次摆线路径时实现显著的总计算量缩减。当该方法集成至全局路径规划框架时，更快的状态扩展有助于加速解算或生成更高质量的路径。我们同时以C++软件包形式开源了代码库。相关网站与演示可在https://bradymoon.com/trochoids获取，代码库地址为https://github.com/castacks/trochoids，视频演示见https://youtu.be/qOU5gI7JshI。