Feasibility Analysis and Synchronization Control for Underactuated Spacecraft Formation Hovering

Abstract

This paper develops a synchronization control scheme for underactuated spacecraft formation hovering in the case without along-track thrust. The feasible sets of initial positions for this underactuated case are derived based on the nonlinear and linear relative orbital dynamics. Then, a nonpreset parameter underactuated controller is designed to deal with the unmatched disturbances caused by the loss of alongtrack control. Moreover, a synchronization item is added to the above controller to synchronize the hovering motion between the follower spacecraft. The Lyapunov-based analysis indicates that the minimum nonzero eigenvalue of the Laplace matrix corresponding to the synchronization item determines the stable hovering accuracy of the system states. Numerical simulations also demonstrate the validity of the presented underactuated synchronization controller.

Feasibility analysis and saturation control for underactuated spacecraft formation reconfiguration in elliptic orbits

“…Meanwhile, the linearization error ΔF(X) is less than 0.03% while kρ i k ≤ 100 km, which is smaller than the order of the J 2 disturbance differential. 22,23 Thus, D could be regarded as a bounded disturbance. Given that the system is controllable for the case without radial thrust and the order of the error dynamics is six.…”

“…In other words, the fully actuated error dynamics should not be given here. As the controllability for this case is the same as that in circular orbits, 22,23 the error dynamics in circular orbits can be referred to present the fifth-order underactuated dynamics in elliptic orbits…”

“…After that, a variety of underactuated control schemes were developed for formation reconfiguration and hovering in circular reference orbits. [20][21][22][23] Since adjusting the relative motion by changing the attitude takes more control time and affects the continuity of the observation mission, the underactuated relative orbital control without changing the spacecraft attitude is more suitable for formation flying to perform Earth observation, deep space exploration, etc. 14,15,[20][21][22][23] It is noteworthy that the previous underactuated feasibility analysis and control schemes for circular reference orbits cannot be directly applied to elliptic ones.…”

“…[20][21][22][23] Since adjusting the relative motion by changing the attitude takes more control time and affects the continuity of the observation mission, the underactuated relative orbital control without changing the spacecraft attitude is more suitable for formation flying to perform Earth observation, deep space exploration, etc. 14,15,[20][21][22][23] It is noteworthy that the previous underactuated feasibility analysis and control schemes for circular reference orbits cannot be directly applied to elliptic ones. As the linearized Tschauner-Hempel (TH) equation is a linear time-varying one, 24,25 the controllability analysis based on the rank criterion method can only give a sufficient condition rather than a necessary and sufficient one.…”

“…20–23 Since adjusting the relative motion by changing the attitude takes more control time and affects the continuity of the observation mission, the underactuated relative orbital control without changing the spacecraft attitude is more suitable for formation flying to perform Earth observation, deep space exploration, etc. 14,15,20–23…”