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Scalable Satellite Swarm Deployment via Distance-based Orbital Transition Under $J_2$ Perturbation

Yuta Takahashi, Shin-ichiro Sakai

TL;DR

Problem: enabling scalable deployment of satellite swarms to form coplanar, equidistant, large-scale structures under $J_2$ perturbation with fuel-free actuation. Approach: derive averaged $J_2$ relative orbital parameters to separate drift from periodic motion, and implement a distance-based orbital stabilizer operating in a normalized swarm frame, with centralized grouping for manageability. Contributions: closed-form averaged relative orbital dynamics under $J_2$, a Lyapunov-based distance controller with convergence guarantees, outage-tolerant deployment via drift/distance management, and centralized multi-leader grouping. Findings: numerical experiments with $N=50$ and $N=100$ satellites show convergence to a coplanar equidistant formation in user-defined planes and robustness to outages. Significance: enables scalable, autonomous distributed space structures with fuel-free actuation for large-scale science, communication, and power beaming applications.

Abstract

This paper presents an autonomous guidance and control strategy for a satellite swarm that enables scalable distributed space structures for innovative science and business opportunities. The averaged $J_2$ orbital parameters that describe the drift and periodic orbital motion were derived along with their target values to achieve a distributed space structure in a decentralized manner. This enabled the design of a distance-based orbital stabilizer to ensure autonomous deployment into a monolithic formation of a coplanar equidistant configuration on a user-defined orbital plane. Continuous formation control was assumed to be achieved through fuel-free actuation, such as satellite magnetic field interaction and differential aerodynamic forces, thereby maintaining long-term formation stability without thruster usage. A major challenge for such actuation systems is the potential loss of control capability due to increasing inter-satellite distances resulting from unstable orbital dynamics, particularly for autonomous satellite swarms. To mitigate this risk, our decentralized deployment controller minimized drift distance during unexpected communication outages. As a case study, we consider the deployment of palm-sized satellites into a coplanar equidistant formation in a $J_2$-perturbed orbit. Moreover, centralized grouping strategies are presented.

Scalable Satellite Swarm Deployment via Distance-based Orbital Transition Under $J_2$ Perturbation

TL;DR

Problem: enabling scalable deployment of satellite swarms to form coplanar, equidistant, large-scale structures under perturbation with fuel-free actuation. Approach: derive averaged relative orbital parameters to separate drift from periodic motion, and implement a distance-based orbital stabilizer operating in a normalized swarm frame, with centralized grouping for manageability. Contributions: closed-form averaged relative orbital dynamics under , a Lyapunov-based distance controller with convergence guarantees, outage-tolerant deployment via drift/distance management, and centralized multi-leader grouping. Findings: numerical experiments with and satellites show convergence to a coplanar equidistant formation in user-defined planes and robustness to outages. Significance: enables scalable, autonomous distributed space structures with fuel-free actuation for large-scale science, communication, and power beaming applications.

Abstract

This paper presents an autonomous guidance and control strategy for a satellite swarm that enables scalable distributed space structures for innovative science and business opportunities. The averaged orbital parameters that describe the drift and periodic orbital motion were derived along with their target values to achieve a distributed space structure in a decentralized manner. This enabled the design of a distance-based orbital stabilizer to ensure autonomous deployment into a monolithic formation of a coplanar equidistant configuration on a user-defined orbital plane. Continuous formation control was assumed to be achieved through fuel-free actuation, such as satellite magnetic field interaction and differential aerodynamic forces, thereby maintaining long-term formation stability without thruster usage. A major challenge for such actuation systems is the potential loss of control capability due to increasing inter-satellite distances resulting from unstable orbital dynamics, particularly for autonomous satellite swarms. To mitigate this risk, our decentralized deployment controller minimized drift distance during unexpected communication outages. As a case study, we consider the deployment of palm-sized satellites into a coplanar equidistant formation in a -perturbed orbit. Moreover, centralized grouping strategies are presented.

Paper Structure

This paper contains 20 sections, 2 theorems, 64 equations, 14 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement and Related Works
  3. Contributions and Paper Organization
  4. Preliminaries
  5. Algebraic Graph Theory mesbahi2010graph
  6. Relative Orbital Dynamics of Spacecraft Formation Flying Under $J_2$ Gravity Effects fehse2003automatedschweighart2002highmorgan2012swarm
  7. Baseline Stabilizer for a Satellite Swarm in a Coplanar Equidistant Plane
  8. Averaged $J_2$ Relative Orbital Parameters
  9. Target Relative Orbit Description for a Satellite Swarm with Equal Spacing in a Single Orbital Plane
  10. Drift Elimination in Swarms with Identical Inclinations
  11. Relative Orbit Plane Control
  12. Distance Adjustment on Normalized Swarm Frame
  13. Distance-based Orbital Stabilizer
  14. Performance Analysis: Satellite Swarm Array Deployment in $J_2$-Perturbed Orbit
  15. Connectable Period Maximization Results
  16. ...and 5 more sections

Key Result

Theorem III.1

For $N=|\mathcal{V}|$ satellites, we assume that their connected graph $\mathcal{G}(\mathcal{V},\mathcal{E})$ and its incidence matrix $E\in\mathbb{R}^{N\times |\mathcal{E}|}$ are given and the controllable region is sufficiently large, i.e., $r_s\gg 1$. Then, ${u}^{\mathrm{main}}_j$ in Eq. (network acheives $E^\top [C_4]\rightarrow 0$ and $E^\top U_x\rightarrow 0$ as $t\rightarrow \infty$ if the

Figures (14)

  • Figure 1: Typical relative orbital motion and time definitions.
  • Figure 2: Relaxed connectable period $\hat{T}_{\mathrm{conn}}(C_{1,4})$ in Eq. (\ref{['T_conn']}).
  • Figure 4: One desired example of the distributed space structure on the grid.
  • Figure 5: Large $C_1$ conditions: Connectable period transition.
  • Figure 6: Small $C_1$ conditions: Connectable period transition.
  • ...and 9 more figures

Theorems & Definitions (11)

  • Definition 1: Connectable Time
  • Theorem III.1: Distance-based Orbital Stabilizer
  • proof
  • Remark 1
  • Definition 2: Multi-Leader Grouping and Graph
  • Definition 3
  • Definition 4
  • Lemma V.1
  • proof
  • Definition 5: Multi-Leader Digraph
  • ...and 1 more