Time-Optimal Path Planning in a Constant Wind for Uncrewed Aerial Vehicles using Dubins Set Classification

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, which consist of straight and maximum-rate turn segments, as optimal extremal paths in uniform wind conditions. Current methods iterate over all candidate trochoidal trajectory types and choose the time-optimal one; however, this exhaustive search can be computationally slow. In this paper we present a method to decrease the computation time. We achieve this via a geometric approach to reduce the candidate trochoidal trajectory types by framing the problem in the air-relative frame and bounding the solution within a subset of candidate trajectories. This 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.