Cyclic Pursuit for Spacecraft Formation Control

In this paper we present decentralized control policies for spacecraft formation, based on the simple idea of cyclic pursuit. First, we extend the existing cyclic-pursuit control laws devised for a single integrator to a double integrator. Such dynamically extended control laws only require relative measurements of position and velocity of two leading neighbors, and allow spacecraft to converge, globally in three dimensions, to a single point, a circle or a logarithmic spiral pattern, depending on the value of a control parameter. Second, we modify the aforementioned control laws to allow convergence to elliptical trajectories in three dimensions, that represent natural trajectories of the relative motion between spacecraft in a rotating frame around the earth. Finally, we discuss the applicability of the devised control laws to the problem of spacecraft coordination for interferometric imaging, and their implementation on a 4DOF testbed.