Nonlinear dynamics, trajectory generation, and adaptive control of multiple spacecraft in periodic relative orbits

This paper considers the problem of relative position control for multiple spacecraft formation flying. Specifically, nonlinear dynamics describing the motion of a follower spacecraft relative to a leader spacecraft are developed for the case where the leader spacecraft is in an elliptical orbit. Next, a Lyapunov-based nonlinear, adaptive control law is designed which guarantees global asymptotic convergence of the position tracking error in the presence of unknown, constant or slow-varying spacecraft masses and exogenous disturbance forces. In addition, a formation initialization constraint is developed for the ideal, unperturbed, periodic relative motion of the spacecraft formation which serves as a desired, relative motion trajectory. Simulation results are provided to illustrate the efficacy of the formation initialization methodology and the adaptive controller performance.