Optimal Low-Thrust Earth Orbit Transfers with Eclipses Using Indirect Heuristic Approaches

Low-thrust propulsion allows substantial propellant saving if compared to high-thrust systems. However, multirevolution orbit transfers are affected by the unavailability of electrical power along eclipse arcs. This research addresses the identification of minimum-time low-thrust Earth orbit transfers with spacecraft eclipsing. Two different indirect heuristic approaches, based on the use of the analytical conditions for optimality, in conjunction with stochastic fractal search, are applied: 1) regularization through the hyperbolic tangent function and 2) multi-arc formulation of the problem. Both of them require no averaging, and the respective advantages and shortcomings are identified. Approach 2 leads to an extended set of multipoint conditions for optimality, which are shown to be solvable sequentially in the numerical solution process. Implicit costate transformation is proven to be a key ingredient for the purpose of obtaining closed-form solutions of the jump relations that hold for the adjoint variables at light/eclipse transitions. Some illustrative examples prove effectiveness of the two indirect heuristic approaches 1 and 2 in finding minimum-time low-thrust orbit transfers between either two coplanar or two noncoplanar Earth orbits. Approach 2 proves to be superior in terms of both computational efficiency and accuracy of the numerical results.