Formation Modelling and 6DOF Spacecraft Coordination Control

In this paper we present a 6DOF Euler-Lagrange model formulation of relative translation and rotation in a leader-follower spacecraft formation. To show the applicability of the model, we also present a solution to the problem of relative translational and rotational tracking, using the concept of vectorial integrator backstepping. The controller solution utilizes the quaternion representation to achieve a shorter rotation path on commanded attitude changes, and the equilibrium points in the closed-loop system are proved to be uniformly asymptotically stable. Finally, simulation results are presented to show the performance of the derived control law, together with the impact of orbital perturbations when these are left uncompensated.