发表机构
Sejong University（世宗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于逐次凸化的燃油最优助推-返回制导算法，通过终端瞬时撞击点约束和解析滑行段处理，在降低计算成本的同时实现接近最优的推进剂消耗，并基于Falcon 9任务验证了其有效性。
AI 中文摘要
本文针对可重复使用运载火箭，提出了一种基于逐次凸化（SCvx）的燃油最优助推-返回制导算法。制导问题被建模为一个具有终端瞬时撞击点（IIP）约束的自由终端时间最优控制问题。该约束仅依赖于关机点位置和速度，并确保在球形地球、中心引力模型下，预测的弹道撞击点与目标重合。通过解析处理滑行段，该公式将轨迹离散化限制在动力段内，减小了问题规模，并显式表示了熄火-滑行（bang-off）结构。它还避免了在长滑行段上离散化缺陷的累积，以及需要在单相网格上求解燃烧-滑行转换的问题。考虑了两种终端约束公式：闭式开普勒IIP和基于偏近点角的F&G解。它们的雅可比矩阵通过复步进微分计算。该算法在基于Falcon 9 CRS-10任务的返回发射场案例研究中得到验证。与单相全轨迹公式、包含飞行路径角速率的闭式制导律以及离线轨迹优化基准的比较，评估了计算成本与最优性之间的权衡。结果表明，在降低计算成本的同时，推进剂消耗接近最优。
英文摘要
This paper proposes a fuel-optimal boost-back guidance algorithm for reusable launch vehicles using successive convexification (SCvx). The guidance problem is formulated as a free-final-time optimal control problem with a terminal instantaneous impact point (IIP) constraint. This constraint depends only on the burnout position and velocity and enforces that the predicted ballistic impact point coincides with the target under a spherical-Earth, central-gravity model. By handling the coast analytically, the formulation confines trajectory discretization to the powered phase, reduces the problem size, and explicitly represents the bang-off structure. It also avoids the accumulation of discretization defects over the long coast and the need to resolve the burn-coast transition on a single-phase grid. Two terminal constraint formulations are considered: the closed-form Keplerian IIP and the eccentric-anomaly-based F&G solution. Their Jacobians are evaluated using complex-step differentiation. The algorithm is validated in a return-to-launch-site case study based on the Falcon 9 CRS-10 mission. Comparisons with a single-phase full-trajectory formulation, a closed-form guidance law incorporating the flight path angle rate, and an offline trajectory optimization benchmark assess the trade-off between computational cost and optimality. The results demonstrate near-optimal propellant consumption with reduced computational cost.
