In long-range Earth surface planning scenarios, the curvature of the spherical surface significantly influences trajectory planning. Addressing the problem of long-range spherical trajectory planning with initial and end-state constraints, a DCS-Anya trajectory planning method is presented in this paper. Firstly, the S-Anya method is employed to define path-finding nodes into binary groups. A heuristic function is constructed based on the great circle line distance, enabling trajectory searches at any angle and facilitating the determination of optimal waypoints. Then, multiple great-circle trajectories are constructed based on the waypoints, and geometric curves are applied for trajectory smoothing of multiple great-circle trajectory segments, leading to the formulation of the CS-Anya method, which effectively addresses the issue of trajectory segment discontinuity. Furthermore, based on the Dubins method, the concepts of the critical cut-in/cut-out points are proposed to obtain the shortest velocity-adjusted trajectories, and the resulting DCS-Anya method is developed to specifically address constraints on the initial and final states within the context of great-circle trajectories. Finally, comparative simulation experiments are conducted between the proposed method and the A* algorithm to validate the rationality and effectiveness of the proposed approach.
A 2025 study studied this question.