Polynomial guidance law for lunar soft landing

With the assumption that vertical optimal landing trajectory can be represented as three-order polynomial, explicit guidance law is designed for lunar soft landing according to open-loop optimization criterion. The explicit expression of thruster directional angle, that is control variable, is obtained by analyzing the geometrical relation of acceleration vectors. The guidance law proposed in this paper is function of local time that is relative to lander's state variable and landing final constraint only. The guidance law needs no iteration, which is easy to be implemented by suboptimum closed-loop real-time control.