Inter-orbital spacecraft transfer: trajectory design by iterating parameter values within a data grid

This paper considers the problem of designing an optimal inter-orbital spacecraft transfer. We present a computational algorithm and modeling results of the optimal transfer trajectory between near-Earth elliptical orbits for spacecraft with a chemical booster and fixed thrust. The trajectory design procedure includes four stages as follows: a) formation of the primary ranges of initial approximations for typical optimization problems; b) iterative integration to find the domains of convergence for a typical variational problem; c) determination of the optimal position for each problem statement within the accepted ranges and its implementation by calculating the terminal conditions residuals; d) analysis of the results obtained. We use numerical methods of mathematical analysis and mathematical programming. The risk of “overstepping” the potentially optimal result is minimized by varying the accuracy at different stages of calculations. Based on the results, we improve the primary solution of the reference problem statement, identify the domains of convergence of solutions, and obtain the sets of initial approximation vectors ensuring convergence of the considered problems for further analysis. The results of this study can be used to develop further and refine an algorithm for selecting optimal initial approximations for different optimization problems (including spacecraft trajectory optimization as a typical one).