Relative-Position Formation Control of Satellites using Electromagnetic Actuation with Piecewise-Sinusoidal Controls

We present a decentralized relative-position formation control algorithm for satellites with electromagnetic actuation. Each satellite's actuation system is driven by a sum of sinusoidal signals, each having different frequencies and piecewise constant amplitudes, which are considered as the controls. The piecewise-sinusoidal controls are designed to interact with neighbor satellites while decoupling interactions with non-neighbor satellites. Each satellite has relative-position and relative-velocity feedback of neighboring satellites, and the communication structure is a connected undirected graph. An ideal controller is designed based on an average dynamic model, and an optimal allocation scheme is used to compute the amplitude controls. The algorithm is demonstrated with a numerical example and a single-degree-of-freedom experiment.