Accuracy Analysis of the Analytical Solution for the Lunar Lander Terminal Guidance Problem

Abstract

An analysis of the accuracy and reliability of the proposed analytical solution for the lunar lander terminal guidance problem was carried out. The analytical solution for 3D terminal guidance problem was obtained for a constant acceleration trajectory and thrust vector orientation programs, which are essentially linear with time. In order to achieve 6 terminal conditions (position and velocity terminal vector components) 6 guidance law parameters were used: time-to-go, braking deceleration, initial pitch angle and pitch rate, initial yaw angle and yaw rate. The simulation results of the lunar lander terminal guidance using the proposed analytical solution were presented. The analysis of the proposed terminal guidance scheme and some similar schemes were carried out by mathematical modeling of the landing maneuver from a certain initial state to the desired spot near the lunar surface. By varying the initial position and the velocity parameters, when the terminal point was fixed, the statistic characteristics of the terminal guidance solution errors in the terminal position and velocity were estimated. An analysis of the simulation results validates the basic performance of the proposed terminal guidance scheme for the lunar pinpoint landing. Estimates of the terminal guidance accuracy for the proposed scheme exceed the corresponding estimates for the alternative considered schemes. The next phase of this research will be intended for studying the influence of variations in the initial prelanding orbit parameters (obliquity, ascending node longitude, argument of periapsis, periapsis height, apoapsis height) on the terminal guidance accuracy.