Deployment of Tethered Satellites in Low-Eccentricity Orbits Using Adaptive Sliding Mode Control

Tethered satellites system has a great potential in completing various space missions. However, existing researches mainly focus on the deployment of satellites in circular orbit, while the deployment in elliptical orbit, especially with disturbances, is rarely studied. Herein, this paper develops a new control strategy to deploy tethered satellites in a low-eccentricity elliptical orbit, meanwhile considering the system uncertainties and external disturbances. First, the periodical solution of the librational motion of a tethered satellite system in elliptic orbit is calculated. Since there is no fixed equilibrium point for deployment in elliptical orbit, the periodical solution is set as the end condition for deployment. After that, the controllability of the system is verified and an open-loop tension control law is optimized by the particle swarm optimization (PSO) and Nelder-Mead method. To eliminate the effects from uncertainties in initial states and the errors from the deployment mechanism, an adaptive sliding mode controller is designed to achieve high-precision trajectory-tracking. The performance of the proposed controller is compared quantitatively with the proportion-derivative (PD) controller and normal sliding mode controller. Furthermore, the Monte Carlo simulation is conducted to demonstrate the effectiveness and robustness of the proposed controller when subjecting to uncertain initial states. The simulation results indicate that the proposed control strategy enables the stable deployment of tethered satellites system despite the uncertainties and perturbations.