Design of analytical prediction-correction skip entry guidance law based on matched asymptotic expansions

In order to adapt to the demand of the long range for the entry return of low lift-drag ratio aircraft, and considering the difficulty of obtaining the analytical solution directly due to the complex flying environment of the atmospheric skip entry, an analytical prediction-correction skip entry guidance law based on the matched asymptotic expansion method is designed. The flight profile and guidance section method of low lift-drag ratio aircraft atmospheric skip entry flight are given at first. Then the outer expansions for the gravitational-dominated region and the inner expansions for the aerodynamic-dominated region are derivated respectively, and the closed-form analytical composite expansions of the governing equations are obtained by matching the asymptotic expansions. Based on the analytical expansions, the range-to-go to the target is computed in real time, and the vertical-lift-drag ratio component is adjusted using a secant iteration method until the predicted downrange error is satisfied. Finally, different guidance strategies are designed for different stages of skip entry flight to obtain the terminal command of bank angle. The simulation results show that the range of Apollo command module can be 8348 km with technology of skip entry return, while the landing error of the analytical prediction-correction guidance law is 0.338 km, which prove the effectiveness of the method.