Propulsionless Station Keeping of a Platform Tethered to a Sailcraft in the Sun–Earth Elliptical Restricted Three-Body System

To perform station keeping of a platform connected by a massless extra-long tethered sailcraft with respect to (w.r.t.) the Earth in the Sun–Earth system enables envisaged space missions. The position of the platform could be balanced and controlled exploiting the nature of the dumbbell tethered system in the three-body dynamical environment by placing the platform and sailcraft with modulatable lightness number within and beyond the Sun–Earth L1 point respectively. This propulsionless scheme merely utilizing surrounding gravitational environment and modulatable solar pressure for station keeping is worth exploring. In this work, nonlinear dynamics considering positions of the platform and sailcraft along the Sun–Earth line is established in the Sun–Earth elliptical restricted three-body system (SEER3BS). Equilibria of the tethered system are analyzed parametrically as a reference for parameter selection for performing closed-loop dynamic analysis. Sliding mode control scheme is applied to station keeping of the platform. The tether’s tension is a force directly applied to the platform, and is determined by the platform-sail distance, which is adjustable by varying the sailcraft’s lightness number. Transient and steady-state dynamic responses of closed-loop system are investigated respectively. Specific time histories of physical variables such as the Earth-platform and Earth-sail distances, the elastic elongation, tension and strain of the tether, and the sailcraft’s lightness number, are presented to verify the effectiveness of the controller. Moreover, influences of the system’s dimensionless circular frequency on transient dynamic responses are studied as an example to show the existence of feasible/infeasible parameter ranges. Furtherly, envelopes of elastic tensions and strains, the Earth-sail distance, and the required lightness number are given in steady-state closed-loop dynamic responses. Influences of parameters such as the platform’s mass, the dimensionless circular frequency, the natural length of the tether, and the Earth-platform distance on the envelopes of the preceding physical variables are explored to give the feasible parameter ranges in a comprehensive manner. The corresponding discussion and suggestions on parameter selection are also given.