通过到时间-到-到等时线的法向收缩实现撞击时间制导

中文摘要 AI 辅助

我们提出了一种基于收缩理论的撞击时间制导视角，该视角在基线寻的指令上附加一个时间偏差。所提出的视角将规定的时间表视为移动的时间-到-到等时线，并通过速度法向侧向加速度调节相对于该集合的法向运动，同时保持拦截器速度恒定。我们推导了一个输运方程来表征与寻的兼容的时间-到-到坐标，并定义了一个预测器缺陷，用于量化近似映射的失配。我们证明标量时间通道在法向商空间上诱导出一个坐标不变的秩一度量。为考虑有界侧向加速度，我们制定了一个鲁棒标量滤波器，并推导了点态可行性的充要条件。随后我们证明，在所述假设下，终端校准和漏斗不变性确保了在规定时间的首次拦截。我们还开发了一种终端前对齐和寻的手交接策略，以避免在接近碰撞航线对齐时侧向时间权限消失导致的奇异反演。所提出的视角适用于满足所需校准和正则性条件的解析、数值和学习型时间-到-到映射。

英文摘要

We develop a contraction-based perspective on impact-time guidance that augments a baseline homing command with a timing bias. The proposed perspective treats the prescribed schedule as a moving time-to-go isochron and regulates motion normal to that set through velocity-normal lateral acceleration while the interceptor's speed remains constant. We derive a transport equation that characterizes homing-compatible time-to-go coordinates and define a predictor defect that quantifies the mismatch of approximate maps. We show that the scalar timing channel induces a coordinate-invariant rank-one metric on the normal quotient. To account for bounded lateral acceleration, we formulate a robust scalar filter and derive a necessary and sufficient condition for pointwise feasibility. We then show that terminal calibration and funnel invariance establish first interception at the prescribed time under the stated assumptions. We also develop a preterminal alignment and homing handover that avoids singular inversion as lateral timing authority vanishes near collision-course alignment. The proposed perspective accommodates analytic, numerical, and learned time-to-go maps that satisfy the required calibration and regularity conditions.

发表机构

• University of Cincinnati（辛辛那提大学）

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