Closed-Loop Control of Satellite Formations Using a Quasi-Rigid Body Formulation

Satellites in formation work together to fulfill the role of a larger satellite. The purpose of this article is to develop a quasi-rigid body formulation for modeling and controlling such a formation as a single entity. In this article, a definition of a quasi-rigid body coordinate frame is presented, which, when attached to a formation, conveniently describes its orientation in space. Using this formulation, the equations of motion for a satellite formation are recast, and natural circular formations are expressed more succinctly. When the J(2) perturbation is considered, a correction factor on the formation's spin rate is introduced. The control of a satellite formation can effectively be separated into (I) a control torque to maintain the attitude and (2) control forces that maintain the rigidity of the formation. With this in mind, a nonlinear Lyapunov controller is derived using the formulation, which acts on the formation as a whole. Simulations validate this controller and illustrate its utility for maintaining circular formations, in particular, in the presence of gravitational perturbations.