Linear Quadratic Powered Descent with Approach Angle Control and Thrust Bounds

Space exploration has expanded significantly in recent years. The powered descent maneuver used in planetary landing uses the lander’s rocket engines to guide it to a soft landing at the designated landing site (i.e., zero velocity at the target coordinates). The primary challenges in designing guidance laws for a soft landing stem from real-world mission constraints, like avoiding ground collisions, controlling approach angles, and accounting for thrust saturation, while minimizing fuel consumption.

The research proposes two different formulations of the problem to address these challenges. The first formulation addresses the approach angle problem and proposes a linear-quadratic optimal guidance law with an optimally selected intermediate point. This allows for trajectory shaping and control of the terminal approach direction. The second formulation uses a time-dependent polynomial approximation of the mass consumption to formulate a bounded linear-quadratic optimal control problem. The guidance law predicts the entry and exit times from the saturation regions and shapes the thrust acceleration profile to achieve a soft landing while avoiding ground collision. The two guidance laws are computationally efficient, and their thrust acceleration profiles are continuous, facilitating implementation in real-world applications.

The performance of the two guidance laws is evaluated in simulations. It will be shown that both guidance laws achieve a soft landing with excellent performance while maintaining their intended design objectives and constraints.