Deployment and attitude control of a tethered subsatellite with controllable arm

The paper presents an investigation on the position and attitude control problem concerning the in-plane motions of a tethered sub-satellite, the attitude of which is controlled by using a controllable arm instead of momentum-wheel actuation in the phase of tether deployment. There are two main steps in the design of the controller. Firstly, a study accounting for the state-control constraints is presented on the nonlinear optimal control problems of the position and attitude of the sub-satellite, the open-loop solution of which is determined by using the Legendre pseudo-spectral algorithm in the second-order form. Secondly, a feedback control law is derived to track the reference trajectory prescribed by the open-loop control law, and the gains of online feedback control are determined by interpolating a sequence of gain data pre-computed via the algorithm of open-loop optimal control. The case studies in the paper well demonstrate the performance of the proposed strategy.