Inverse polynomial based explicit guidance for lunar soft landing during powered braking

In this paper an explicit guidance law for the powered descent phase of the soft lunar landing is presented. The descent trajectory, expressed in polynomial form is fixed based on the boundary conditions imposed by the precise soft landing mission. Adapting an inverse model based approach, the guidance command is computed from the known spacecraft trajectory. The guidance formulation ensures the vertical orientation of the spacecraft during touchdown. Also a closed form relation for the final flight time is proposed. The final time is expressed as a function of initial position and velocity of the spacecraft (at the start of descent) and also depends on the desired landing site. To ensure the fuel minimum descent the proposed explicit method is extended to optimal guidance formulation. The effectiveness of the proposed guidance laws are demonstrated with simulation results.