An Approach to Near-Optimal Continuous-Thrust Solution for Plane Constellation Deployment

Abstract

Paving the way in satellite constellation deployment, this article presents the Comprehensive Program (GCP) for planning constellation deployment missions by introducing a near-optimal solution for continuous-thrust maneuvers. The GCP establishes time constraints, enabling appropriate time scheduling and eliminating reconfiguration phases. It considers various cases of satellite departure and arrival sequences, collision avoidance constraints, and time limitations. A near-optimal solution for the continuous-thrust trajectory of each satellite is introduced, relying on the Fourier series approximation of the thrust pointing angle. The Fourier series with constant coefficients replaces the thrust angle in the satellite’s orbital motion equations in polar coordinates. The primary advantage of this near-optimal approach lies in its simplicity in accommodating space perturbations, posing no challenges in problem-solving. Additionally, the approach is beneficial due to its straightforward implementation and simple mathematical computations. This approach does not require pre-determining the revolution number of the transfer trajectory, unlike shape-based methods. The proposed method’s flexibility allows it to adapt and optimize the trajectory without prior assumptions about the number of revolutions required for the mission. Analyses demonstrate the proposed algorithm’s versatility and precision across various scenarios involving different orbital eccentricities, thrust forces, and thrust pointing angles. The constant coefficients of the Fourier series are determined by defining a set of objective functions and minimizing them using the Multi-Objective Particle Swarm Optimization algorithm (MOPSO). The first and second objective functions ensure that the transfer orbit reaches the desired deployment point, while the third and fourth ones guarantee the tangential conditions between the transfer orbit and the final orbit. An additional objective function minimizes the trajectory time. As a perturbation of interest, the effect of Earth’s oblateness is considered.