NODA-MMH: Certified Learning-Aided Nonlinear Control for Magnetically-Actuated Swarm Experiment Toward On-Orbit Proof

TL;DR

The paper addresses the challenge of maintaining large-scale satellite swarms using magnetically actuated, learning-aided control under nonholonomic and underactuated dynamics. It combines time-integrated AC magnetic control with a learned, model-based dipole allocation (NODA-MMH) to achieve power-optimal, stable swarm behavior, and provides a rigorous safety-stability analysis with an input-to-state stability framework. The authors validate the approach experimentally on a ground testbed with coil-based magnetorquers, including proximity docking and multi-satellite formations, and demonstrate that the learned magnetic model improves tracking accuracy and convergence, especially in near-range operations. The work advances practical swarm control by enabling decentralized, scalable, and computationally tractable control of magnetically actuated satellites toward orbit proof, with the potential to reduce propulsion needs and extend formation maintenance capabilities in space missions.

Abstract

This study experimentally validates the principle of large-scale satellite swarm control through learning-aided magnetic field interactions generated by satellite-mounted magnetorquers. This actuation presents a promising solution for the long-term formation maintenance of multiple satellites and has primarily been demonstrated in ground-based testbeds for two-satellite position control. However, as the number of satellites increases beyond three, fundamental challenges coupled with the high nonlinearity arise: 1) nonholonomic constraints, 2) underactuation, 3) scalability, and 4) computational cost. Previous studies have shown that time-integrated current control theoretically solves these problems, where the average actuator outputs align with the desired command, and a learning-based technique further enhances their performance. Through multiple experiments, we validate critical aspects of learning-aided time-integrated current control: (1) enhanced controllability of the averaged system dynamics, with a theoretically guaranteed error bound, and (2) decentralized current management. We design two-axis coils and a ground-based experimental setup utilizing an air-bearing platform, enabling a mathematical replication of orbital dynamics. Based on the effectiveness of the learned interaction model, we introduce NODA-MMH (Neural power-Optimal Dipole Allocation for certified learned Model-based Magnetically swarm control Harness) for model-based power-optimal swarm control. This study complements our tutorial paper on magnetically actuated swarms for the long-term formation maintenance problem.

Figures (8)

• Figure 1: Distributed space antenna concept takahashi2025distanceshim2025feasibilitytakahashi2025anticipatory and two-axis magnetorquer testbed on a linear air track. The satellite swarm is decentralized to a small group by the time-integrated control, as shall be introduced in subsection \ref{['Time_Integrated_Control_of_Alternating_Current']}.
• Figure 2: Testbeds and gravity compensation results.
• Figure 3: Experimental results for two far target positions.
• Figure 4: Experimental results of proximity position control.
• Figure 5: Experimental results for position and attitude control.

Theorems & Definitions (19)

• Theorem III.1: Kinematics control takahashi2022kinematics
• Lemma IV.1
• proof
• Lemma IV.2: Exact/far-magnetic model mapping
• proof
• Theorem IV.3: Input-to-State Stability Analysis
• proof
• Remark 1
• Theorem IV.4: NODA-MMH
• proof