用于低推力行星际交会的 B 样条形状设计
B-spline shaping for low-thrust interplanetary rendezvous
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中文总结 AI 辅助
研究低推力行星际交会轨迹设计，提出用夹紧 B 样条对坐标参数化的方法，利用微分平坦性恢复控制加速度，简化问题为非线性规划，无需运动方程数值传播。通过数值计算与比较，得出 B 样条配置优势及特定样条为质量与效率的良好折衷。
中文摘要 AI 辅助
低推力行星际交会轨迹的快速初步设计需要结合计算效率、灵活性和足够解质量的参数化方法。本文提出一种基于形状的方法，使用夹紧 B 样条对日心圆柱坐标进行参数化。利用低推力圆柱动力学的微分平坦性从成形轨迹及其导数代数地恢复控制加速度。夹紧 B 样条参数化解析地满足端点位置和速度条件，将原始的固定时间、最小 delta-v 问题简化为自由内部 B 样条控制点的有限维非线性规划。该公式不需要运动方程的数值传播，仅用数值积分来评估目标函数。对从地球到火星、水星、近地小行星 1989 ML 和彗星坦普尔 1 的低推力交会转移进行了数值计算，并将结果与高阶速矢端迹形状设计进行比较。在所有测试的细网格计算和保留的有限解中，所有 B 样条配置相对于速矢端迹基准都降低了平均、中位数和最小累积速度增量。特别是，一个十个控制点的五次 B 样条被确定为解质量和计算效率之间的良好折衷，而高维参数化对于优化选定的转移机会是有效的。
英文摘要
Rapid preliminary design of low-thrust interplanetary rendezvous trajectories requires parameterizations that combine computational efficiency, flexibility, and sufficient solution quality. This work presents a shape-based method in which the heliocentric cylindrical coordinates are parameterized using clamped B-splines. The differential flatness of the low-thrust cylindrical dynamics is exploited to recover the control acceleration algebraically from the shaped trajectory and its derivatives. The clamped B-spline parameterization satisfies the endpoint position and velocity conditions analytically, reducing the original fixed-time, minimum delta-v problem to a finite-dimensional nonlinear program in the free interior B-spline control points. The formulation therefore requires no numerical propagation of the equations of motion; numerical quadrature is used only to evaluate the objective function. Numerical campaigns are conducted for low-thrust rendezvous transfers from Earth to Mars, Mercury, the near-Earth asteroid 1989 ML, and comet Tempel 1, and the results are compared with high-order hodographic shaping. Across the tested fine-grid campaigns and among the finite solutions retained, all B-spline configurations reduce the mean, median, and minimum accumulated velocity increment relative to the hodographic benchmark. In particular, a ten control-point quintic B-spline is identified as a favorable compromise between solution quality and computational efficiency, while higher-dimensional parameterizations are effective for refining selected transfer opportunities.
