[论文解读] Trajectory Stability and Signature Diagnostics for Comet-Based Interstellar Navigation

Bo Pieter Johannes Andrée|arXiv (Cornell University)|Mar 17, 2026

Spacecraft Dynamics and Control被引用 0

一句话总结

该论文为基于喷射驱动的彗星式星际导航建立多层稳定性框架，并推导残差诊断以区分主动稳定与自然动力学。

ABSTRACT

Interstellar objects (ISOs) motivate a coupled mission-design and inference question relevant to spacecraft dynamics and control in extreme environments: if volatile-rich, rotating comet-like bodies were used for sustained deep-space navigation by exploiting pre-existing hyperbolic motion and in-situ propellant, what stability requirements arise under non-gravitational forcing, and what astrometric signatures might distinguish active stabilization from uncontrolled natural dynamics? We develop a stability-theoretic framework for trajectory tracking with jet-actuated correction, and show that high-speed transit geometry -- including debris-belt avoidance and encounter phasing -- tightly constrains feasible trajectories, making long-horizon tracking stability mission-critical. We model tracking residuals as the balance of disturbances and corrective action, and derive stability conditions across four levels: disturbance-energy stability, outer-loop contraction, actuator-memory stability, and rotation-mediated (Floquet) stability. The analysis implies residual diagnostics that can motivate empirical tests: under comparable forcing, effective stabilization is expected to strengthen short-horizon error correction, reduce event-conditioned persistence and variance clustering, regularize standardized innovations, and yield bounded post-shock recovery. More broadly, the framework provides a reference for deep-space guidance and control under nonlinear, multi-field disturbances and for planetary-defense concepts involving attitude shaping or impulsive kinetic impact.

研究动机与目标

• 在非引力扰动下，将星际物体（ISOs）的导航视为耦合的任务设计与推断问题以实现实现动机
• 为喷射驱动矫正下的高速度轨迹跟踪建立稳定性理论，面对持续的随机扰动
• 识别几何约束（碎片规避、节点布置）对可行轨迹的严格约束
• 提出基于残差的诊断，用以区分被动动力学与主动稳定，并指导经验测试

提出的方法

• 将一个以地心引力为参照的高速度ISO样轨迹的随机跟踪问题形式化
• 提出一个四条件的多层稳定性框架：扰动能量稳定性、外环收缩性、执行器记忆稳定性以及旋转介导的Floquet稳定性
• 将残差建模为非引力驱动与矫正动作在统一的x_t = x^grav_t + x^plan_t + s_t − o_t分解中的平衡
• 用移动平均（MA）持续性与GARCH风格能量聚合来表征扰动通道，将执行器通道建模为对控制输入的VARMA过程
• 将喷射驱动与矫正偏移o_t联系起来并推导围绕参考轨迹的线性化误差动力学
• 提供残差诊断并将稳定性理论与可观测的天体测量与执行器特征信号联系起来

Figure 1 : Schematic geometry linking debris-belt avoidance, node placement, and inner-system vertical offset. (a) Inner-system side view ( $x$ – $z$ , $|x|\leq 6\,\mathrm{AU}$ ). Solid lines compare two slope choices ( $7^{\circ}$ and $5^{\circ}$ ) with the node placed near $1.25\,\mathrm{AU}$ —a h

实验结果

研究问题

• RQ1 在非引力扰动下，长期跟踪彗星样ISO轨迹需要哪些稳定性条件？
• RQ2 碎片规避几何和侦察约束如何形塑可行轨迹轮廓及其稳定性要求？
• RQ3 残差动力学如何在深空导航中区分被动非线性动力学与主动稳定？
• RQ4 残差中有哪些可观测信号表明有效稳定性与被动扰动之间的差异？

主要发现

• 高速通行几何性由于规避碎片带与遇合相位而对可行轨迹形成严格约束
• 稳定性需要对扰动能量进行界限化并实现收缩，共有四个层级：扰动能量稳定性、外环收缩、执行器记忆稳定性、以及旋转介导的Floquet稳定性
• 在持续残差扰动下，有限均方跟踪误差的充要条件是收缩范数界限，且当残差持续性增强（AR–MA权衡）时界限收紧
• 主动稳定应降低残差持续性与方差聚类、正则化创新项，并在冲击后实现有界恢复，相较于被动动力学表现出改进
• 该框架支持在非线性、多场扰动下的深空制导，并为涉及姿态塑性或冲击影响的行星防御概念提供信息

Figure 2 : Stability signatures under identical stochastic forcing. Trajectory context: (a) 3D view and (b) ecliptic projection for gravity-only baseline (gray dotted), planned reference (black dashed), passive realization (red; $\mathbf{o}_{t}\equiv\mathbf{0}$ ), and active realization (blue; offse