Finite-time synchronization control scheme for underactuated satellite formation reconfiguration

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.…”

“…Here, the designed USC (22) calculates only the bounded value δ 1m of the disturbance δ 1 but does not estimate the real value. This completes the design of the saturation controller, which is applied to drive the follower to fly from the initial configuration I to the desired configuration II in the presence of radial thrust loss and input saturation constraint.…”

“…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.…”