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Adversarial Pursuits in Cislunar Space

Filippos Fotiadis, Quentin Rommel, Gregory Falco, Ufuk Topcu

TL;DR

The paper addresses adversarial pursuits in cislunar space by formulating a nonlinear zero-sum differential game on CR3BP dynamics. It introduces dynamic reference orbit phasing and manifold-aware cost shaping to enable fuel-efficient, robust evasion while remaining near the nominal orbit. The solution uses continuous-time differential dynamic programming to compute saddle-point policies, and numerical experiments on a near-rectilinear halo orbit demonstrate rapid, sustained separation under realistic thrust constraints. The findings offer a framework for defending cislunar missions against cyber-physical threats such as co-located jamming and pursuit, with implications for secure relays and operator autonomy in deep-space environments.

Abstract

Cislunar space is becoming a critical domain for future lunar and interplanetary missions, yet its remoteness, sparse infrastructure, and unstable dynamics create single points of failure. Adversaries in cislunar orbits can exploit these vulnerabilities to pursue and jam co-located communication relays, potentially severing communications between lunar missions and the Earth. We study a pursuit-evasion scenario between two spacecraft in a cislunar orbit, where the evader must avoid a pursuer-jammer while remaining close to its nominal trajectory. We model the evader-pursuer interaction as a zero-sum adversarial differential game cast in the circular restricted three-body problem. This formulation incorporates critical aspects of cislunar orbital dynamics, including autonomous adjustment of the reference orbit phasing to enable aggressive evading maneuvers, and shaping of the evader's cost with the orbit's stable and unstable manifolds. We solve the resulting nonlinear game locally using a continuous-time differential dynamic programming variant, which iteratively applies linear-quadratic approximations to the Hamilton-Jacobi-Isaacs equation. We simulate the evader's behavior against both a worst-case and a linear-quadratic pursuer. Our results pave the way for securing future missions in cislunar space against emerging cyber threats.

Adversarial Pursuits in Cislunar Space

TL;DR

The paper addresses adversarial pursuits in cislunar space by formulating a nonlinear zero-sum differential game on CR3BP dynamics. It introduces dynamic reference orbit phasing and manifold-aware cost shaping to enable fuel-efficient, robust evasion while remaining near the nominal orbit. The solution uses continuous-time differential dynamic programming to compute saddle-point policies, and numerical experiments on a near-rectilinear halo orbit demonstrate rapid, sustained separation under realistic thrust constraints. The findings offer a framework for defending cislunar missions against cyber-physical threats such as co-located jamming and pursuit, with implications for secure relays and operator autonomy in deep-space environments.

Abstract

Cislunar space is becoming a critical domain for future lunar and interplanetary missions, yet its remoteness, sparse infrastructure, and unstable dynamics create single points of failure. Adversaries in cislunar orbits can exploit these vulnerabilities to pursue and jam co-located communication relays, potentially severing communications between lunar missions and the Earth. We study a pursuit-evasion scenario between two spacecraft in a cislunar orbit, where the evader must avoid a pursuer-jammer while remaining close to its nominal trajectory. We model the evader-pursuer interaction as a zero-sum adversarial differential game cast in the circular restricted three-body problem. This formulation incorporates critical aspects of cislunar orbital dynamics, including autonomous adjustment of the reference orbit phasing to enable aggressive evading maneuvers, and shaping of the evader's cost with the orbit's stable and unstable manifolds. We solve the resulting nonlinear game locally using a continuous-time differential dynamic programming variant, which iteratively applies linear-quadratic approximations to the Hamilton-Jacobi-Isaacs equation. We simulate the evader's behavior against both a worst-case and a linear-quadratic pursuer. Our results pave the way for securing future missions in cislunar space against emerging cyber threats.

Paper Structure

This paper contains 18 sections, 2 theorems, 41 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Nomenclature
  2. Introduction
  3. Problem Formulation
  4. Spacecraft Dynamics in Cislunar Space
  5. Adversarial Pursuits in Cislunar Space
  6. Zero-Sum Dynamic Game for Cislunar Adversarial Pursuits
  7. Reference Orbit Phasing Adjustment
  8. Nonlinear Dynamic Game Formulation
  9. Game-Theoretic Differential Dynamic Programming
  10. Regularization of Continuous-Time DDP
  11. Cost Function Shaping using Stable and Unstable Manifolds
  12. Numerical Experiments
  13. Simulation of Saddle-Point Pursuit-Evasion Policies
  14. Effect of Reference Phasing Control and Cost-Function Shaping
  15. Evasion Against a Linear-Quadratic Baseline Pursuer
  16. ...and 3 more sections

Key Result

Theorem 1

Consider the backward differential equations eq:backward, with $\bar{\mathrm{Q}}_{\mathbf{w}_\mathrm{e}\mathbf{w}_\mathrm{e}}$ and $\bar{\mathrm{Q}}_{\mathbf{w}_\mathrm{p}\mathbf{w}_\mathrm{p}}$ substituted with $\bar{\mathrm{Q}}_{\mathbf{w}_\mathrm{e}\mathbf{w}_\mathrm{e}}+\lambda I_{4}$ and $\bar{

Figures (9)

  • Figure 1: Close-proximity jamming in a periodic orbit around $L_1$. Because of the vast distances involved, the Earth-satellite communication link is relatively weak, making it especially susceptible to jamming. To mitigate the jamming effect, the satellite must maneuver away from the jammer.
  • Figure 2: The simulated near-rectilinear halo orbit.
  • Figure 3: The evolution of the position tracking errors $\mathbf{p}_\mathrm{i}-\mathbf{p}_{\mathrm{di}}$, $\mathrm{i}\in\{\mathrm{e},\mathrm{p}\}$, of the evader and the pursuer.
  • Figure 4: The evolution of the thrust profiles $\mathbf{u}_\mathrm{i}$, $\mathrm{i}\in\{\mathrm{e},\mathrm{p}\}$, of the evader and the pursuer.
  • Figure 5: The evolution of the phasing controls $\tau_\mathrm{i}$, $\mathrm{i}\in\{\mathrm{e},\mathrm{p}\}$, of the evader and the pursuer.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Theorem 1
  • Theorem 2