Impact-Time Guidance via Normal Contraction to a Time-to-Go Isochron

2026-09-22

AI Summary

本文提出了一种基于归约的视角来解决拦截时间控制问题，通过调整横向加速度使飞行器按照预定的时间到达目标。

Abstract

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.

Problem

• Impact-Time Guidance
• Time-to-Go Isochron
• Lateral Acceleration

Innovation

• Impact-Time Guidance
• Normal Contraction
• Time-to-Go Isochron
• Robust Scalar Filter
• Preterminal Alignment