An optimal trajectory design for the lunar vertical landing

Abstract

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.

Performance-improved vertical GaN-based light-emitting diodes on Si substrates through designing the epitaxial structure

“…To deploy the lunar lander onto the lunar surface, soft landing of the lunar lander is one of the most fundamental technologies. The soft landing typically involves two phases: de-orbit burn phase and powered descent phase [1]. The powered descent phase aims to use the retropropulsion determined by the guidance command to meet the required final condition [2].…”

“…Since the thrust engine is usually fixed with the lunar lander's body, the vertical landing introduces a final attitude constraint, which can be represented by the final steering angle [8]. Consequently, there were some attempts to generate the optimal trajectory ending with a vertical landing [1], [2], [15]- [17]. For instance, in [1], the lunar landing trajectory was divided into two parts, with the final steering angle constraint augmented into the cost functional.…”

“…Consequently, there were some attempts to generate the optimal trajectory ending with a vertical landing [1], [2], [15]- [17]. For instance, in [1], the lunar landing trajectory was divided into two parts, with the final steering angle constraint augmented into the cost functional. As a result, the original TPBVP became a Multi-PBVP.…”

“…Consequently, the altitude of the lunar lander above the lunar surface can be expressed as h = r − R 0 . The lunar lander is propelled by an engine with a constant thrust magnitude T [1], [18]. The thrust steering angle, denoted by β ∈ [0, 2π], represents the angle between the local horizontal line of the lunar lander and the thrust vector.…”