Global 4D Trajectory Optimization Design for Lunar Vertical Soft Landing

A combinatorial algorithm, including dynamic programming and conjugate gradient, was proposed for 4D trajectory global optimization of the lunar probe vertical soft landing. By employing the suboptimum control variable calculated from dynamic programming as the initial control variable of conjugate gradient algorithm, the more precise optimum control variable and flight trajectories were obtained. The lunar probe vertical soft landing trajectory consists of two segments, i.e., the brake and landing segments. The performance index is to minimize fuel consumption of the lunar detector. The 4D trajectory of lunar vertical soft landing is optimized by this combinatorial optimization algorithm. Simulation results showed good accuracy, rapid convergence, and robustness with initial values for this combinatorial algorithm, which promise it to on-line generate a feasible vertical soft landing trajectory on the onboard computer. Meanwhile, the combinatorial algorithm could be extended to other two-point boundary value problems of terminal time uncontrolled type.