Systematic Direct Approach for Optimizing Continuous-thrust Earth-orbit Transfers

This article presents a systematic direct approach to carry out effective optimization of a wide range of continuous-thrust Earth-orbit transfers with intermediate-level thrust acceleration, including minimum-time (with a single burn arc) and minimum-fuel (with multiple burn arcs) transfers. With direct control parameterization, in which the control steering programs of burn arcs are interpolated through a finite number of nodes, the optimal control problem is converted into the parameter optimization problem to be solved by nonlinear programming. An inertial coordinate transformation strategy is proposed to produce general simple terminal constraints for transfers to inclined and eccentric orbits. This strategy eliminates possible singularities when the spacecraft transfers to the retrograde equatorial orbit and also results in better convergence of optimization iterations. Multiple shooting is used in order to further improve the convergence robustness, and strategies to allocate multiple-shooting variables for certain types of transfers are presented. Numerical examples include single-burn minimum-time transfers, multiple-burn minimum-fuel transfers with up to 12 burn arcs as well as fixed-time transfers with variable specific impulses. All the converged solutions are obtained from simply defined initial guesses. The proposed direct approach is briefly compared with other methods. Finally, we discussed the potential onboard guidance scheme using model predictive control.