Linear Quadratic Powered Descent With Bounded Thrust and Ground-Collision Avoidance

The paper proposes a new approach to address bounded-thrust powered-descent problem while ensuring ground-collision avoidance. A time-dependent polynomial approximation of the mass consumption is employed to introduce a new bounded linear-quadratic formulation of the optimal control problem that minimizes the thrust-acceleration control effort, the terminal miss, and the terminal velocity error. The approximated mass consumption is used to "hardly" constrain the horizontal thrust profile, while keeping the vertical thrust unbounded. This hierarchical separation of the thrust allocation enables ground-collision avoidance while accounting for the bounded thrust. The guidance law predicts ground collision and the entry and exit times from the saturation regions and shapes the thrust-acceleration profile to achieve a soft landing, even when the controller is saturated for long periods of the flight. It is computationally efficient due to its analytical-based nature, and its thrust-acceleration profile is continuous, facilitating implementation in real-world applications. The derived guidance law was evaluated in a realistic simulation and demonstrated excellent performance with ground-collision avoidance.