Direct optimization of many-revolution spacecraft trajectories is performed using an unconstrained formulation with many short-arc, embedded Lambert problems. Each Lambert problem shares its terminal positions with neighboring segments to implicitly enforce position continuity. Use of embedded boundary value problems (EBVPs) is not new to spacecraft trajectory optimization, including extensive use in primer vector theory, flyby tour design, and direct impulsive maneuver optimization. Several obstacles have prevented their use on problems with more than a few dozen segments, including computationally expensive solvers, lack of fast and accurate partial derivatives, unguaranteed convergence, and a non-smooth solution space. Here, these problems are overcome through the use of short-arc segments and a recently developed Lambert solver, complete with the necessary fast and accurate partial derivatives. These short arcs guarantee existence and uniqueness for the Lambert solutions when transfer angles are limited to less than a half revolution. Furthermore, the use of many short segments simultaneously approximates low-thrust and eliminates the need to specify impulsive maneuver quantity or location. For preliminary trajectory optimization, the EBVP technique is simple to implement, benefiting from an unconstrained formulation, the well-known Broyden–Fletcher–Goldfarb–Shanno line search direction, and Cartesian coordinates. Moreover, the technique is naturally parallelizable via the independence of each segment’s EBVP. This new, many-rev EBVP technique is scalable and reliable for trajectories with thousands of segments. Several minimum fuel and energy examples are demonstrated, including a problem with 6143 segments for 256 revolutions, found within 5.5 h on a single processor. Smaller problems with only hundreds of segments take minutes.

多转航天器轨迹的直接优化是使用具有许多短弧嵌入兰伯特问题的无约束公式来执行的。每个 Lambert 问题与相邻段共享其终端位置，以隐式地强制执行位置连续性。使用嵌入式边界值问题 (EBVP) 对航天器轨迹优化并不陌生，包括广泛用于引物矢量理论、飞越之旅设计和直接脉冲机动优化。一些障碍阻止了它们在包含几十个部分的问题上的使用，包括计算成本高的求解器、缺乏快速准确的偏导数、无法保证的收敛性以及非平滑的解空间。在这里，通过使用短弧段和最近开发的朗伯求解器克服了这些问题，完成必要的快速和准确的偏导数。当传递角被限制在小于半圈时，这些短弧保证了朗伯解的存在性和唯一性。此外，使用许多短段同时近似于低推力并消除了指定脉冲机动数量或位置的需要。对于初步轨迹优化，EBVP 技术易于实施，受益于无约束公式、众所周知的 Broyden-Fletcher-Goldfarb-Shanno 线搜索方向和笛卡尔坐标。此外，该技术通过每个段的 EBVP 的独立性自然地可并行化。这种新的多转 EBVP 技术对于具有数千个段的轨迹具有可扩展性和可靠性。展示了几个最低燃料和能源的例子，包括在 5.5 小时内在单个处理器上发现的 256 转 6143 段的问题。只有数百个段的较小问题需要几分钟。