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

Tethered-satellite systems have great potential in completing various space missions. However, existing researches mainly focus on the deployment of satellites in a circular orbit, whereas deployment in an elliptical orbit, especially with disturbances, is rarely studied. This study develops a new control strategy to deploy tethered satellites in a low-eccentricity elliptical orbit that also considers system uncertainties and external disturbances. First, the periodical solution of the librational motion of a tethered-satellite system in an elliptic orbit is calculated. Because there is no fixed equilibrium point for deployment in elliptical orbits, 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 particle swarm optimization (PSO) and the Nelder-Mead method. To eliminate effects from uncertainties in initial states and 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 a proportion-derivative (PD) controller and normal sliding mode controller. Furthermore, Monte Carlo simulations are conducted to demonstrate the effectiveness and robustness of the proposed controller when subjected to uncertain initial states. The simulation results indicate that the proposed control strategy enables the stable deployment of tethered-satellite systems despite the uncertainties and perturbations.