Resonant Control of Many-Revolution Low-Thrust Transfer between Circular Orbit and Elliptical Orbit

Electric propulsion is widely used in space missions, such as constellation deployments and geostationary orbit transfers, due to its ability to reduce fuel consumption compared to chemical propulsion systems. The low thrust-to-mass ratio characteristic of spacecraft equipped with electric thrusters results in tens or hundreds of transfer revolutions. How to parameterize and design the many-revolution low-thrust transfer trajectories has been a research focus. Resonant control is a methodology for solving many-revolution low-thrust transfer trajectories based on a predefined control law. An artificial resonance between orbital period and thrust control is established by parameterizing the control as a truncated Fourier series expansion. The efficacy of this resonance lies in its potential to enhance thrust efficiency and maintain a low fuel consumption during the transfer process. Resonant control has been previously used in many-revolution transfers between non-coplanar circular orbits. For the elliptical orbit, existing resonant control methods can modify eccentricity independently, but not the argument of perigee. This is due to the fact that the resonant control dynamics of argument of perigee is highly coupled to those of the other elements. In this paper, a resonant control approach for many-revolution low-thrust transfer between circular orbit and elliptical orbit is developed. This method applies the resonant control approach to elliptical orbit transfer for the first time and derives an analytical solution for the velocity increment during the transfer. First, a general resonant control law and dynamic are derived based on the Fourier expansion of Gauss variational equations. Subsequently, a propulsive efficiency metric is introduced to analyse the fuel efficiency and construct a joint resonant control law for the semimajor axis and eccentricity. Furthermore, well-designed control parameters are introduced to make the joint control law automatically satisfy the maximum acceleration constraint. Finally, a resonant control approach for transfer between circular orbit and elliptical orbit is constructed based on the elliptical orbit resonant control law, and an analytical solution for the velocity increment required for the transfer is derived. Two simulation scenarios, specifically geosynchronous transfer orbit (GTO) to the geostationary orbit (GEO) transfer and lunar low-thrust capture, are employed to verify the efficiency of the resonant control approach developed in this paper. The numerical results demonstrate the capability of the resonant control approach to perform many-revolution low-thrust transfer between circular orbit and elliptical orbit with low velocity increments. Furthermore, the analytical solution can evaluate the velocity increment quickly and accurately.