Adaptive fast nonsingular terminal sliding mode control of Lorentz-augmented spacecraft relative motion

An electrostatically charged spacecraft is subject to Lorentz force as it moves through the planetary magnetic field. The induced Lorentz force could be used as propellantless electromagnetic propulsion for orbital maneuvers. Such vehicle is referred to as Lorentz spacecraft. By modeling the Earth’s magnetic field as a tilted dipole that corotates with Earth, a nonlinear dynamical model is developed to characterize the orbital motion of a Lorentz spacecraft relative to an arbitrary Earth orbit. A fast nonsingular terminal sliding mode control law is then proposed, based on which an adaptive controller is designed for Lorentz-augmented spacecraft relative motion to deal with the uncertain parameters and perturbations. Due to the constraint that the direction of Lorentz force is naturally perpendicular to the local magnetic field and the vehicle’s velocity relative to the magnetic field, which does not necessarily coincide with the direction of the required control force, thus, the Lorentz force works as auxiliary propulsion to reduce the fuel consumption in most cases. Then, a fuel-optimal distribution law of Lorentz force and traditional chemical propulsion is proposed. Furthermore, the stability of the closed-loop control system is proved via a Lyapunov-based approach. Numerical simulations substantiate the feasibility and validity of the proposed controller for Lorentz-augmented relative orbital control.