An interval programming method of earth-moon trajectory for manned lunar exploration mission under interval uncertainty

There are always uncertainties in practical engineering, and the design of the optimal Earth-Moon trajectory under uncertainties significantly reduces flight risk for the manned lunar exploration mission (MLEM). This paper proposes an interval programming method to optimize the trans-lunar trajectory under interval uncertainties. Firstly, the influence of the trans-lunar injection uncertainties (TLI) is investigated, finding that the reached orbit at the perilune is very sensitive to the impulse errors at TLI. Then, the design methods of the Earth-Moon trajectory and the trajectory correction maneuver (TCM) are presented. Based on the mathematical tool of the interval possibility degree, the interval programming model is built to transform the uncertain optimization problem into a deterministic one, and then a multi-layer optimization scheme is proposed to solve it. The uncertain objectives and constraints’ interval bounds are calculated in the inner loop, and the design variables are searched and optimized in the outer loop. The proposed method is used to design the Earth-Moon trajectories of both manned and unmanned spacecraft. The designed trajectories are insensitive to the uncertainties and are validated by the Monte Carlo simulations.