The trajectory optimization of a spacecraft subject to the gravitational effects of the moon, Earth, and sun are considered. The problem is how to achieve Earth-interface conditions from a low lunar orbit. Practical constraints of maximum thrust, fuel budget, and flight time generates a constrained, nonautonomous, nonlinear optimal control problem. Severe constraints on the fuel budget combined with high-accuracy demands on the endpoint conditions necessitate a high-accuracy solution to the trajectory optimization problem. The problem is first solved using the standard Legendre pseudospectral method. The optimality of the solution is verified by an application of the covector mapping principle. It is shown that the thrust structure consists of three finite burns with nearly linear steering-angle time histories. A singular arc is detected and is interpreted as a singular plane change maneuver. The Bellman pseudospectral method is then employed for mesh refinement to improve the accuracy of the solution.
Bibliographical noteFunding Information:
We gratefully acknowledge funding for this research provided in part by U.S. Naval Postgraduate School under Grant N00244-10-1-0049. We would like to thank one of the anonymous reviewers for independently validating our results.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics