Homotopy-based optimal trajectory design to transfer from Earth orbit to halo orbits

Abstract

Halo orbits are of importance for observation and study of the space due to their specific characteristics including the orbital position and the periodic motion. In this regards, present paper has focused on optimal trajectory planning to transfer to halo orbits. To this aim, homotopy approach has been adopted for optimal trajectory design. This approach has improved the convergence rate and insensitivity of the problem to initial guess. The designed trajectory transfers a spacecraft orbiting the Earth to a Halo orbit around Lagrangian point L1 of the Earth-moon restricted three-body system. The propulsion system has been assumed to be low thrust with constant specific impulse. Homotopy approach has a broad domain of applicability and methods in which continuation method has been employed here among them. The optimal designed trajectory minimizes the fuel consumption via transforming solution of the minimum energy problem utilizing the homotopy approach. This approach simplifies solution of the complex problem of minimum fuel indeed.

Keywords

• halo orbit
• homotopy approach
• homotopy continuation method
• shooting method
• optimal trajectory design
• orbit transfer