Kinematics Control of Electromagnetic Formation Flight Using Angular-Momentum Conservation Constraint

TL;DR

This work addresses the challenge of propellant-free satellite formation control by enabling simultaneous electromagnetic force and torque outputs while preventing nonuniform and accumulating angular momentum in reaction wheels. It introduces a kinematics framework grounded in angular-momentum conservation, uses AC-based dipole modulation to realize arbitrary force/torque, and demonstrates a controller that requires only one RW set for all satellites. Through analytical results (Theorems 1 and 2) and three numerical case studies, the approach shows elimination of RW saturation, feasibility of formation maintenance and reconfiguration, and mitigation of angular-momentum buildup via simple unloading on a chief satellite. The methods have practical significance for scalable, fuel-free space missions and flexible formation configurations.

Abstract

Electromagnetic formation flight (EMFF) uses the electromagnetic force to control the relative positions of multiple satellites without using conventional fuel-based propulsion. To compensate for the electromagnetic torque generated alongside the electromagnetic force, in most previous studies, all satellites were assumed to have reaction wheels (RWs) besides electromagnetic coils. However, the RW-loaded angular momentum becomes non-uniformly distributed among the satellites, because the electromagnetic torque usually differs between satellites. Without a proper control scheme, this deviation increases over time, and the RWs become saturated quickly, preventing the attitudes of the satellites from being controlled. In this study, a new controller is proposed that enables the electromagnetic force and torque to be controlled simultaneously. The EMFF kinematics derived from the conservation of angular momentum are used for the controller design. This controller can control $n$ satellites without saturating the RWs, and only one set of RWs is required among all satellites. The combination of the proposed controller with a simple unloading control exclusive to the chief satellite results in the elimination of the accumulation of angular momentum in the entire system. The effectiveness of the proposed controller is demonstrated through numerical simulations of the formation maintenance and formation reconfiguration of a five-satellite system.

Figures (70)

• Figure 1: Coordinate systems mainly used in this paper.
• Figure 2: Conventional system diagram.
• Figure 3: Proposed system diagram.
• Figure 5: Conceptual diagram of numerical calculation imitating situation of space interferometer project.
• Figure 6: The entire system.