Finite-time coordination control for formation flying spacecraft without unwinding

This paper investigates three distributed coordination control laws by using sliding mode control for formation flying spacecraft based on the rotation matrix. The first and second robust finite-time controllers can compensate external disturbances with known and unknown bounds, respectively, while the third one could compensate both external disturbances with unknown bounds and the uncertainty of the model parameters by using an adaptive control method. Through introducing two novel sliding modes, exchange of control signals between neighboring spacecraft becomes unnecessary in all three controllers, and it is able to reduce the communication burden. Because the controllers are designed based on the rotation matrix which represents the set of attitudes both globally and uniquely, the system can overcome the drawback of unwinding which results in extra fuel consumption. Theoretical analysis shows that the coordinated controllers can guarantee the finite-time stability of the overall closed-loop system through local information exchange and numerical simulations also demonstrate their effectiveness.