Minimum-jerk guidance for lunar lander

An optimal guidance law derived by solving the minimum-acceleration problem has been reported for control of a lunar lander. In our past work, the guidance law was proved to enable vertical/soft landing. However, it was not robust against disturbance because there was a constraint condition relative to initial conditions in order to satisfy optimality. Therefore, if the constraint is not satisfied, the lunar lander must be controlled to track the reference trajectory generated by the optimal guidance law in order to be robust against disturbance. The control system makes the landing system complex and fuel consumption is increased in comparison to a guidance law without tracking control. Consequently, this study restructures the optimal control problem as a minimum-jerk problem to solve it. Jerk is a physical quantity defined as the time derivative of acceleration. The new optimal guidance law obtained has no constraints on the initial conditions. The results of computer simulation confirm the usefulness of the proposed guidance law.