Onboard optimization of multi-arc trajectories with constraints on duration of arcs

Autonomous operation of rocket-powered vehicles is a promising technique that could significantly improve the adaptiveness of rocket-powered vehicles. However, to remedy in-flight engine failures and allow mission changes, the autonomous operation requires an onboard method to optimize the powered trajectories. While onboard methods to optimize the powered trajectories have been proposed before, none of them considered the constraints on duration of arcs in multi-arc trajectory optimization problems. The constraints on the duration of burn arcs and coast arcs often arise from the safe operating conditions of rocket engines, and violating these constraints will likely result in physically-infeasible trajectories. Determining the optimal duration of each arc while satisfying the constraints is a challenging problem for onboard trajectory optimization methods. In this paper, an onboard method to optimize multi-arc trajectories is proposed that is capable of enforcing the constraints on the duration of burn arcs and coast arcs. The proposed method employs a hybrid regularization approach to facilitate the convergence of the duration of arcs. Quadratic penalty terms and fixed-radius trust-region terms are simultaneously used to limit the change of duration of arcs between iterations. The two terms complement each other, contributing to the efficiency of the hybrid regularization approach. Moreover, we propose an optimality-based stopping criterion that certifies the optimality of optimized duration of arcs and helps reduce unnecessary iterations. Numerical results on an onboard computational platform are provided to validate the efficiency of the proposed method.