Attitude coordination strategies in satellite constellations and formation flying

The coordination of the attitude among different spacecraft belonging to a multiple platform system (formation or constellation) is a basic requirement in several missions, mainly the ones involving sensors like radars or optical interferometers. It is also an open topic in research, above all as it matches the characteristics of the current trend towards interoperability and federated systems. Different approaches are possible to define and chase such a coordinated attitude. The classic control strategy is the so-called leader-follower architecture, where all spacecraft depend on ("follow") the behavior of a single master. Alternatively, the behavioral approach involves a continuous re-selection of the desired target configuration which is computed on the basis of the behavior of all the platforms. A third possibility is to define a "virtual" architecture, especially suitable with respect to the mission requirements, which is not dependent on the current kinematic state of the platforms. The paper proposes a unified treatment of these concepts by using some fundamental definitions of the consensus dynamics and cooperative control. The convergence to the targeted configuration is addressed both analytically, by using Lyapunov stability criteria, and numerically, by means of numerical simulations. The attitude requirements and constraints are highlighted and a solution for the control algorithm - involving continuous actuators on each platform - is developed. A comparative analysis of different optimal control strategies, the Linear Quadratic Regulation (LQR) and the State Dependent Riccati Equation (SDRE) - suitably modified to address the needs of coordination - is presented. The results show the general value of the proposed approach with respect to either linear or nonlinear models of the dynamics.