Optimal Linear Quadratic Powered Descent With An Optimally Selected Intermediate Point

In the current paper, we present an optimal-control-based power descent guidance law, which enables soft landing while passing through an optimally selected intermediate point. The optimal intermediate point is selected such that it minimizes the cost function, shapes the trajectory to avoid a ground collision, and controllers the lander’s terminal approach direction. We employed 3D point mass dynamics with a constant gravitational field, and a closed-form solution was derived for a quadratic cost function on the terminal miss, intermediate point miss, terminal velocity error, and control effort. The derived analytical solution allows performance prediction (i.e., control effort, propellant consumption, miss distance, and terminal velocity) and permits an efficient parametric investigation. The derived guidance law was evaluated in a realistic simulation, and demonstrated excellent terminal performance (i.e., position and velocity), low control effort, ground collision avoidance, and terminal approach direction control.