An optimal trajectory design for the lunar vertical landing

A research for designing the optimal lunar vertical landing trajectory to reduce the total energy or mass of propellant is addressed in this paper. Most of these problems can be divided into two phases: breaking and approach phase. The optimal landing trajectory in general does not consider the pitch-up motion so that the landing problem has been only solved in the breaking phase. For this reason, there are some attempts to find the optimal trajectory including the final vertical landing phase by including the equations of angular motion of the vehicle. However, the optimal solution using this approach depends on the scale factor of a cost function because the cost function consists of two different mechanical parameters such as the final mass and total control torque. The final control constraints are augmented for vertical lunar landing instead of the equations of angular motion. The obtained optimal trajectory has an additional positive effect of the image acquisition as well as the final vertical landing.