In-plane motion control of Hill-Clohessy-Wiltshire equations by single input

The in-plane motion of the Hill-Clohessy-Wiltshire (HCW) equations is controllable with along-track input but not controllable with crosstrack input. However, in the controllable subspace of the latter, the drift velocity is zero and the free motion is periodic. Thus, formation reconfiguration for the in-plane motion is possible by cross-track input. In the case of the continuous-time feedback controllers, the total velocity change of the along-track controller is larger than that of the two-input controller, but the difference is less than 8% for the settling time larger than five periods. In the case of pulse feedback controllers, the sampling time used for discretization is one-half of the period for the two-input controller and one-quarter of the period for all other single-input controller. The two-input and along-track feedback controllers are robust and effective for the nonlinear relative dynamics.