Analytical optimal guidance algorithm for lunar soft landing with terminal control constraints

In this paper it is proposed to augment an existing optimal analytical guidance algorithm for the purpose of achieving terminal angle constraint during the terminal powered descent phase of a lunar soft landing mission. Basic algorithm formulation caters to minimizing the acceleration due to onboard engines to minimize the fuel spend and reach the desired position with desired velocity. However, in order to cope up with terminal angle constraint, an augmentation is proposed in the objective function wherein the aim is not only to minimize the energy but also to minimize the terminal error in acceleration achieved and the desired acceleration specified by the designer. This inadvertently leads to the desired terminal angle. Simulations done for the fine braking phase of lunar soft landing mission prove that terminal attitude constraints are met with the modification in objective function.