AI 中文总结
研究机载应用目标问题，利用微分代数将轨迹优化转为多项式优化问题，用矩和平方和优化求解，与传统方法比较，该方法在保证精度同时能收敛到全局最优，还扩展到低推力轨道保持场景，适用于机载自主应用。
AI 中文摘要
本文围绕精度、计算效率和可靠性解决目标问题。首先利用微分代数将轨迹优化问题重铸为多项式优化问题（POP），通过计算非线性动力学和约束的高阶泰勒展开式。然后利用矩和平方和（SOS）优化来解决此POP，还提出了基于动力学二阶展开的凸公式。对于脉冲目标，将矩-SOS和凸方法与传统非线性规划（NLP）求解器和地图反演技术进行比较。结果表明，矩-SOS方法提供的解与传统NLP一样准确，且在温和假设下保证收敛到全局最优。该方法在处理大机动和长传播时间方面表现出色。还将该方法扩展到地月圆受限三体问题中的连续低推力轨道保持（SK）场景，并在存在显著状态误差的情况下评估算法性能。矩-SOS方法能够直接处理非凸约束并将复杂非线性动力学重铸为具有可靠收敛特性的公式，适用于机载自主应用。
英文摘要
This paper solves the targeting problem focusing on accuracy, computational efficiency, and reliability. The trajectory optimization problem is first recast as a polynomial optimization problem (POP) by leveraging differential algebra to compute high-order Taylor expansions of the nonlinear dynamics and constraints. Moment-sum-of-squares (SOS) optimization is then utilized to solve this POP. A convex formulation based on a second-order expansion of the dynamics is also proposed. For impulsive targeting, the moment-SOS and convex approaches are compared against traditional nonlinear programming (NLP) solvers and map inversion techniques. Results indicate that the moment-SOS approach provides solutions as accurate as traditional NLP, but with the critical advantage of guaranteeing convergence to the global optimum under mild assumptions. Furthermore, the method excels at handling large maneuvers and long propagation times, conditions in which standard linear approximations rapidly degrade. To demonstrate its versatility, the methodology is extended to a continuous low-thrust station keeping (SK) scenario in the Earth-Moon Circular Restricted Three-Body Problem. The algorithm's performance is then evaluated in the presence of significant state errors. The ability to directly handle non-convex constraints and recast complex, nonlinear dynamics into formulations with reliable convergence properties makes the moment-SOS approach suitable for autonomous onboard applications.
