Low-Thrust Trajectory Optimization with Averaged Dynamics Using Analytical Switching Detection

This paper presents an efficient indirect optimization method for the time- and fuel-optimal low-thrust many-revolution transfers with averaged dynamics. Compared with the previous indirect method, the proposed method involves a new set of variables and several near-optimal control laws to formulate the two-point boundary value problem based on three practical assumptions. Then, the costate transformations between two reference frames are first derived with respect to the the corresponding Eulerian angles, such that the switching function can be expressed with a six-degree polynomial function and the number of parameters used to determine the energy-optimal solutions is reduced to 6. Finally, a neural network is trained to generated the initial guesses, and the solution algorithms for solving the time- and fuel-optimal problem are formulated. Numerical simulations demonstrate that the convergence ratio of initial guesses is higher than 98%, the proposed assumptions are reasonable for guaranteeing the near optimality, and the presented method can obtain convergent solutions within tenths of a second for the Earth- and moon-centered external/interior transfers considering the shadow J2 and third-body perturbations.