Analytical time-coordinated entry guidance for multi-hypersonic vehicles within three-dimensional corridor

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A coordinated entry mission requires multiple hypersonic vehicles to arrive at the designated area simultaneously from different times and locations. To satisfy the coordinated entry mission, this paper investigates the coordinated entry guidance problem for multi-hypersonic vehicles. An analytical time-coordinated entry guidance method is proposed based on the algorithms of analytical prediction, profile correction, and coordination time determination. Firstly, considering the altitude variations of the trajectory, high-precision analytical solutions for the remaining flight time and range are derived based on quasi-equilibrium glide conditions. Compared to the traditional numerical integration prediction methods, this analytical prediction method achieves superior computational efficiency while ensuring high-precision prediction. Subsequently, a flight corridor based on longitudinal lift-to-drag ratio is constructed, extending from the traditional two-dimensional corridor to a three-dimensional one. Within the corridor, the analytical lift-to-drag ratio profile is corrected by minimizing the prediction errors, and the guidance commands for both angle of attack and bank angle can be generated directly without tracking law. With the above analytical solutions and algorithms, the coordinated entry guidance method enables rapid generation of guidance commands for each hypersonic vehicle. Finally, numerical simulations under dispersed launching time and launching location conditions are performed, and the simulation results verify the effectiveness and robustness of the proposed time-coordination entry guidance algorithm.