Optimization of Satellite Orbits with Resonant Cross-Track Control

This paper is dedicated to developing a new approach for solving the low-thrust trajectory optimization problem of spacecraft in low Earth orbits. The unknown control function is parameterized by its Fourier coefficients up to a given order, thus transforming the optimal control problem into a nonlinear parameter optimization problem. An adequate choice of the period and the maximum degree of the truncated Fourier expansion leads to the creation of a resonance between the natural frequency of the orbital dynamics and the control function. Resonance is a well-known phenomenon; however, the novelty of the presented approach is to create the resonance artificially, in order to increase the effect of the control acceleration on the satellite trajectory evolution. This artificial resonance contributes to creating a rapid change of the cross-track orbital elements, using the low-thrust control acceleration. The proposed technique is applied to low Earth orbits constellation optimization, involving the minimization of the geometric dilution of precision of an Earth coverage problem.