High-Accuracy Entry Guidance with Analytical Trajectory Prediction for Large-Maneuver Gliding

In hypersonic vehicle entry guidance, trajectory prediction is widely used, and its accuracy directly affects the performance of the flight mission. To fast predict the trajectory, existing methods mainly focus on deriving analytical solutions of dynamics. However, the dynamics nonlinearity significantly increases when the vehicle performs large maneuvers due to the coupling between the motions of the lateral and longitudinal channels, making it difficult to derive the analytical form. To deal with this nonlinearity, this paper introduces a systematic approach. First, a foundational solution is derived based on simplified dynamics that neglects Earth's rotation and nonlinear terms related to lateral motion; Then, this paper creatively derives error compensation terms to bridge the gap between the simplified and exact dynamics. Thus, the trajectory prediction analytical solution is constructed as the sum of the foundational solution and the error compensation solution. In this approach, the error compensation solution is derived using the homotopy analysis method framework, where nonlinear terms are expanded into a series of high-order linear components. This expansion allows for the straightforward derivation of analytical solutions for each component. Finally, the proposed analytical solution is used in the entry guidance application, and a predictor-corrector guidance law is obtained. Simulation results showed that this method has a millisecond calculation time and superior guidance accuracy under large-lateral-maneuver conditions.