Decentralized Power-Optimal Coordination for Spacecraft Swarms Using Time-Varying Magnetorquer Actuation

Yuta Takahashi; Shin-ichiro Sakai

eess.SYOct 1, 2026

Decentralized Power-Optimal Coordination for Spacecraft Swarms Using Time-Varying Magnetorquer Actuation

Authors: Yuta Takahashi, Shin-ichiro Sakai

Organizations: Department of Mechanical Engineering, Institute of Science Tokyo, Tokyo, Japan · Department of Spacecraft Engineering, Japan Aerospace Exploration Agency, Kanagawa, Japan

Abstract

This paper presents a decentralized power-optimal coordination framework for magnetically actuated spacecraft swarms. Swarms that form large space structures overcome the aperture limit set by the launch vehicle and hold their shape on solar-generated power alone. Magnetic actuation is propellant-free and generated by a magnetorquer, which is commonly used for attitude control. However, every spacecraft interacts with every other within range, and its effect depends on the actuation power and a carrier frequency. We therefore design a decentralized power-optimal framework to jointly derive the interaction graph, frequency grouping, and controller gains. Our decentralized controller preserves angular momentum, which is a nonholonomic constraint. Then, this framework for connected groups whose memberships overlap across carriers guarantees that the relative position errors, the absolute attitude errors, and the imbalance of the reaction-wheel momenta converge to the desired states under the decentralized power-optimal allocation. A closed-loop simulation of a thousand spacecraft with the complete alternating-current interaction confirms the framework. A fast approximate integration with a proven error bound extends the framework to a long-horizon orbital reconfiguration held with high precision.

Figures & tables

Fig. 1 : Magnetically actuated swarm reconfiguration and system diagram of grouping and controller design.

Panel of Figure 2 — Fig. 2 : Mission energy over the neighbor distance, finite-coil correction with a minimum ratio of $0.80$ in force and $0.67$ in torque, and delay margin.

Algorithm 1 Agglomerative grouping.

Panel of Figure 4 — Fig. 3 : Grouping mechanisms: (a) routing and the alignment penalty; (b) $\rho_{g}$ per group size.

Panel of Figure 5 — Fig. 4 : (a) Power ratio over the alignment weight $w_{\mathrm{a}}$ . (b) Mission ratio $W(n{=}2)/W(\mathrm{Method})$ .

Clique	Med.	Max	Mission	Med.	Max
3-clique	$1.75$	$2.9$	Inv. $K{=}10^{2}$	$0.79$	$0.94$
4-clique	$2.42$	$5.1$	Inv. $K{=}10^{5}$	$0.93$	$0.94$
5-clique	$4.02$	$9.0$	ODA $n{=}2$	$1.00$	$1.00$
Octahedron	$3.19$	$6.3$	Grp. $n{=}4$	$1.39$	$15.9$

TABLE I : Power ratios

J(Z(2))/J(Z(n))

on isolated cliques and

W(Z(2))/W(\mathrm{method})

Panel of Figure 7 — Fig. 5 : The terminal formation representing the Tokyo Tower (Tokyo Digital Twin Project, CC-BY).

	$n{=}2$	$n{=}3$	$n{=}4$
Power gain (median)	$1.15\times$	$1.34\times$	$1.58\times$
Power gain (range)	$1.05$ – $1.94\times$	$1.23$ – $2.29\times$	$1.39$ – $2.78\times$
Error gain (median)	$1.04\times$	$1.28\times$	$1.54\times$
Error gain (10–90%)	$0.40$ – $2.50\times$	$0.58$ – $2.94\times$	$0.76$ – $3.67\times$
Lower error	$54\%$	$73\%$	$83\%$

TABLE II : Gain over the best-of-

K

inverse allocation (

K{=}1000

) in the closed-loop sweep, total power per frame and time-averaging error per spacecraft.

	$n{=}2$	$n{=}3$	$n{=}4$	$n{=}5$	$n{=}6$	$n{=}7$
Count	$130598$	$97483$	$60378$	$37857$	$22966$	$13291$
Mean	$1.000$	$1.110$	$1.218$	$1.315$	$1.382$	$1.431$
Std	$0.000$	$0.128$	$0.190$	$0.228$	$0.237$	$0.239$
Max	$1.000$	$1.533$	$1.812$	$2.006$	$2.087$	$2.133$

TABLE III : Empirical certificate

\gamma_{W}=W_{\mathrm{ODA}}/J_{\mathrm{dual}}

Panel of Figure 11 — Fig. 8 : Orbital reconfiguration of $64$ spacecraft ( $y$ along-track, $z$ normal, viewed from the radial direction).

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