标题： 基于多项式的约束求解器用于燃料最优低推力轨迹优化 显示英文标题

标题： A polynomial-based constrained solver for fuel-optimal low-thrust trajectory optimization

摘要： 微分动态规划（DDP）是一种轨迹优化方法，对不良的初始猜测特别具有鲁棒性。 然而，与其它方法相比，其较长的运行时间使其不太适合嵌入式系统。 在本工作中，我们引入了基于多项式的DDP方法，在优化燃料效率的同时能够强制约束。 此外，实现了一个基于多项式的牛顿求解器，以高精度强制约束。 所提出的求解器，基于微分代数的微分动态规划（DADDy），在各种天体力学场景中进行了验证和测试。 结果表明，DADDy实现了与最先进的DDP方法相同的结果，但运行时间显著减少。 具体而言，对于本工作中研究的场景，最稳定的方法能够实现100%的收敛，并在日心二体问题中实现了70%的运行时间减少，在地月CR3BP中实现了23%到94%的运行时间减少，在地心二体问题中实现了46%到59%的运行时间减少。 显示英文摘要

摘要： Differential Dynamic Programming (DDP) is a trajectory optimization method, particularly resilient to poor initial guesses. However, its long run times compared to other methods make it less suitable for embedded systems. In this work, we introduce polynomial-based DDP methods capable of enforcing constraints while optimizing for fuel efficiency. Additionally, a polynomial-based Newton solver is implemented to enforce constraints with high precision. The proposed solver, Differential Algebra-based Differential Dynamic programming (DADDy), is validated and tested on various astrodynamics scenarios. Results demonstrate that DADDy achieves the same solutions as state-of-the-art DDP methods but with significantly reduced run times. Specifically, for the scenarios investigated in this work, the most stable method was able to achieve 100% convergence and achieved runtime reductions of 70% in the Sun-centered two-body problem, 23% to 94% in the Earth-Moon CR3BP, and 46\% to 59% in the Earth-centered two-body problem.