A robust guaranteed cost tracking control problem for thrust-limited spacecraft rendezvous in near-circular orbits is investigated in one of my research papers: Robust Tracking Control for Rendezvous in Near-Circular Orbits, which was published in 2013.

A novel relative motion mode, which represents the noncircularity of the reference orbit a parameter uncertainty, is raised in this article. A guaranteed cost tracking controller with input saturation is designed via a linear matrix inequality method, which is more concise and less conservative compared with the previous works. Sufficient conditions for the existence of this robust tracking controller are given, and the numerical examples are provided for both time-invariant and time-variant reference signals to illustrate the effectiveness of the proposed control scheme when applied to the terminal rendezvous and other astronautic missions with scheduled states signal.

The following video is a demonstration for the tracking controller when applied to track a Epitrochoid-shpae reference orbit ^[1], the tracking position and velocity signals are given below:

      and     .

The video shows the relative motion trajectory on the reference orbit as well as the chaser’s control output of the thrusters along the x- and y- axis of the relative coordinate system.

Youtube Video:

[1] Lawrence, J. Dennis. A catalog of special plane curves. Courier Corporation, 2013.