Aerocapture Trajectory Planning Using Hierarchical Differential Dynamic Programming

Aerocapture is a flight maneuver that achieves orbit insertion around a planet by using the aerodynamic drag generated by the atmosphere of the planet to decelerate. Trajectory planning, which provides a feasible or optimal trajectory, plays an important role in aerocapture. This study develops a differential dynamic programming (DDP)-based trajectory planning algorithm that can solve the optimized aerocapture maneuver efficiently and reliably. Firstly, the aerocapture trajectory planning is formulated into an optimal control problem, where the objective of minimizing the post-aerocapture periapsis raise maneuver impulse is considered. Then, the original problem is reformulated into a new optimization problem, which satisfies the standard DDP form only with the discrete dynamics. Next, a simplified problem, in which the dynamics and the objectives are approximated using the previous DDP iteration solution, is constructed to reduce the derivative calculation in the DDP process. Finally, a hierarchical DDP (H-DDP) method, where a solution with lower accuracy is used as the initial control profile of the solution with higher accuracy, is designed to improve the DDP convergence. Compared with existing methods, sequential convex programming and GPOPS, numerical examples verify that the H-DDP method is feasible and computationally efficient, which has potential for real-time application. In addition, the analysis for two important inputs of the H-DDP method, the initial control profile and the time of flight, shows that the optimality of the H-DDP method may depend on the initial control profile. Appropriately increasing the time of flight can reduce the aerocapture maneuver impulse, and the reduction is about 13% in the case of this paper.