Attitude control of spacecraft using two wheels via hierarchical input-output linearization

In this paper, we propose the nonlinear controller which stabilizes the attitude of underactuated spacecraft equipped with two reaction wheels in the case of the non-zero initial angular momentum. The attitude of spacecraft is expressed by Rodrigues parameters, and Rodrigues parameters has the property that the attitude converges to specific one when the magnitude of Rodrigues parameters goes to infinity with keeping their ratio to the specified value. To raise the magnitude and keep the ratio, we decoupled two inputs, and design controllers for kinematics model [11][12]. However, in the case of dynamics model, we cannot decouple the inputs for the reason that the decoupling matrix becomes singular. Thus, we use the hierarchical technique which changes geometric nature by designing inputs in step by step. Using the hierarchical technique, the attitude control of underactuated spacecraft can be achieved since the linearization of the system between input and output is possible. As an advantage of our proposed method, the hierarchical technique can linearize the system up to five out of six dimensions whereas the conventional input-output linearization can do up to four dimension. Therefore, we can easily analyze the stability of system including unobservable zero dynamics. Finally, the numerical simulation shows effectiveness of proposed method.