Linear Pseudospectral Entry Guidance Algorithm Using Differential Flat Output for High Lift-to-Drag Ratio Entry Vehicle

This paper aims at proposing an entry guidance algorithm for high lift-to-drag ratio entry vehicle, which is based on linear pseudospectral model predictive control and differential flatness theory. The algorithm consists of two phases: descent phase and glide phase. First, the longitudinal plane of the entry process is differentially flat, and the nonlinear system in the longitudinal plane can be transformed into a linear system using the properties of the differential flat system. Then, considering quadratic performance index, the entry longitudinal plane guidance problem is transformed into a linear optimal control problem with terminal constraints. Collocation with Legendre–Gaussian points is used to translate them into a set of algebraic equations. And then, the guidance commands of longitudinal plane, which reduce terminal errors, can be derived in an analytical manner in the form of polynomials. Finally, the heading angle error corridor is used to control the lateral plane motion to obtain the final guidance commands. To evaluate the guidance performance and robustness of the proposed algorithm, nominal trajectory simulation and Monte Carlo simulation were carried out for different target positions. The results show that this method has high computational efficiency, high numerical accuracy, strong adaptability, and robustness, which is applicable for many entry scenarios.