Credits: 9

Learning objectives
Introduction (current and future missions involving formation flying). Linear circular keplerian case (Hill-Clohessy-Wiltshire equations, curvilinear vs Cartesian coordinates; periodicity). Linear elliptic keplerian case (Tschauner-Hempel, Melton, Yamanaka equations; periodicity). Mission to a comet with highly elliptic orbit and residual gravitational field. Linear circular perturbed case (J2 effect and special inclinations, drag effect, advanced linear models). Nonlinear dynamics (Newton approach, Lagrange approach, energy matching). Relative motions in terms of differential orbital elements. Relative attitude dynamics. Formation flying control (LQR, discrete LQR, PWM, impulsive, artificial potential). Formation  flying navigation (RF, GPS, laser ranging, visual navigation). A case of formation flying: remote sensing missions. Orbital configuration. Lazy and tight formations. Rendezvous. The phases of a rendezvous mission. Approach safety and collision avoidance. The drivers for the approach strategy (location and direction of target capture, range of sensors, Sun illumination, communication windows). Docking. Mating systems. Special features of the GNC system for rendezvous and docking (mode sequencing and equipment engagement, fault identification and recovery concepts, remote interaction with the automatic system, automatic GNC system with man-in-the-loop). Special cases of formation flying. Tethered formations and space webs. Swarms of spacecraft.