A model of relative translation and rotation in leader-follower spacecraft formations

In this paper, a model of a leader-follower spacecraft formation in six degrees of freedom is derived and presented. The nonlinear model describes the relative translational and rotationalmotion of the spacecraft, and extends previous work by providing a more complete factorization, together with detailed information about the matrices in the model. The resulting model shows many similarities with models for systems such as robot manipulators and marine vehicles. In addition, mathematical models of orbital perturbations due to gravitational variations, atmospheric drag, solar radiation and third-body effects are presented for completeness. Results from simulations are presented to visualize the properties of the model and to show the impact of the different orbital perturbations on the flight path.