Experimental Demonstration of a Decentralized Electromagnetic Formation Flying Control Using Alternating Magnetic Field Forces
Electromagnetic formation flying (EMFF) is challenging due to the complex coupling between the electromagnetic fields generated by each satellite in the formation. To address this challenge, this article uses alternating magnetic field forces (AMFF) to decouple the electromagnetic forces between each pair of satellites. The key idea of AMFF is that a pair of alternating (e.g., sinusoidal) magnetic moments results in a nonzero time-averaged interaction force if and only if those alternating magnetic moments have the same frequency. Hence, the approach in this article is to drive each satellite's electromagnetic actuation system with a sum of sinusoids, where each frequency is common to only a pair of satellites. Then, the amplitudes of each sinusoid are modulated (i.e., controlled) to achieve the desired forces between each pair of satellites. The main contribution of this article is an experimental demonstration of 3-satellite decentralized closed-loop EMFF using AMFF. To the authors' knowledge, this is the first demonstration of AMFF with at least 3 satellites in open or closed loop. This is noteworthy because the coupling challenges of EMFF are only present with more than 2 satellites, and thus, a formation of at least 3 is necessary to evaluate the effectiveness of AMFF. The experiments are conducted on a ground-based testbed consisting of 3 electromagnetically actuated satellites on linear air tracks. The closed-loop experiments demonstrate decentralized EMFF with AMFF where the maximum steady-state formation error is less than $\pm $0.01 m and the settling time is less than 30 s. These experiments validate the decoupling of intersatellite forces through frequency-multiplexed AMFF. The closed-loop experimental results are compared with the behavior of numerical simulations.