Orbit-transfer control for TSS using direct collocation method

An orbit-transfer scheme of a tethered satellite system (TSS) without the retrieval of the sub-satellite is discussed. It is assumed that the mass center of the TSS moves along a classical trajectory of Hohmann orbit-transfer. The unstrained length acceleration of the tether is selected as the control input for the TSS motion between the two impulses. The control minimization is discretized into a problem of large scale nonlinear programming by means of Hermite-Simpson discretization, which is one of the direct collocation methods. Then it is solved using MATLAB software package SNOPT. As the initial states might have large errors due to practical constraints, a feedback control law using direct collocation and receding horizon control is introduced. Numerical simulation results prove that the optimal orbit-transfer of a TSS has smooth trajectory and the control consumption is very limited. The closed-loop feedback control works well, too, so that initial errors can be eliminated after a certain period.