Dynamics and control of spacecraft hovering using the geomagnetic Lorentz force

To achieve hovering, a spacecraft thrusts continuously to induce an equilibrium state at a desired position. Due to the constraints on the quantity of propellant onboard, long-time hovering around low-Earth orbits (LEO) is hardly achievable using traditional chemical propulsion. The Lorentz force, acting on an electrostatically charged spacecraft as it moves through a planetary magnetic field, provides a new propellantless method for orbital maneuvers. This paper investigates the feasibility of using the induced Lorentz force as an auxiliary means of propulsion for spacecraft hovering. Assuming that the Earth’s magnetic field is a dipole that rotates with the Earth, a dynamical model that characterizes the relative motion of Lorentz spacecraft is derived to analyze the required open-loop control acceleration for hovering. Based on this dynamical model, we first present the hovering configurations that could achieve propellantless hovering and the corresponding required specific charge of a Lorentz spacecraft. For other configurations, optimal open-loop control laws that minimize the control energy consumption are designed. Likewise, the optimal trajectories of required specific charge and control acceleration are both presented. The effect of orbital inclination on the expenditure of control energy is also analyzed. Further, we also develop a closed-loop control approach for propellantless hovering. Numerical results prove the validity of proposed control methods for hovering and show that hovering around low-Earth orbits would be achievable if the required specific charge of a Lorentz spacecraft becomes feasible in the future. Typically, hovering radially several kilometers above a target in LEO requires specific charges on the order of 0.1 C/kg.