Biased-Proportional-Navigation-Based Predictor–Corrector Landing Guidance for Reusable Launch Vehicles

This paper introduces an innovative approach to landing guidance for reusable launch vehicles. With the consideration of aerodynamic forces, it is very challenging to solve the Earth landing guidance problem. Although predictor–corrector methods have demonstrated remarkable efficiency and reliability in various guidance problems considering aerodynamic forces, the complexity arises in the launch vehicle landing scenario because three control variables are involved: thrust magnitude, angle of attack, and sideslip angle. To mitigate this complexity, this paper employs the biased proportional navigation law to transform the angle of attack and sideslip angle into functions of the states, thereby reducing the control variables to a singular one-thrust magnitude. Subsequently, the theoretical analysis establishes fuel-optimal ignition time (the initiation of the powered descent phase) and thrust magnitude profile, allowing parameterization of the remaining one control variable with a single adjustable parameter. This results in a low-complexity algorithm that only involves one-parameter root-finding problems, conducive to real-time implementation in embedded computers. Numerical examples are provided to demonstrate the high performance of the proposed landing guidance algorithm.