Parametric Analysis of Minimum-Energy Trajectories between Coplanar Circular Orbits

The minimum-energy solution is often used in low-thrust trajectory optimization problems due to its good numerical properties. At the same time, the analytical form of this solution is known only in a number of special cases (e.g., the averaged problem and the problem of optimal transfer between close near-circular orbits), while in general it is found numerically by solving the two-point boundary value problem resulted from the maximum principle. To the authors’ knowledge, an exhaustive parametric analysis of minimum-energy low-thrust trajectories has not been done yet, even for the case of coplanar circular orbits in the central gravitational field. Such an analysis is attempted in this research. It is shown that the optimal rendezvous solutions in the adjoint vector space form a single manifold. The submanifold of globally optimal solutions is identified and accurately approximated with the use of symbolic regression tools. The results provide a good initial guess for numerical optimization in more complex dynamical models.