Analytical entry guidance for coordinated flight with multiple no-fly-zone constraints

This paper addresses the problem of coordinating a group of Hypersonic Glide Vehicles (HGVs) for the goal of simultaneous arrival in the presence of multiple No-Fly Zones (NFZs). Firstly, a high-precision analytical solution of flight time is derived from the nonlinear entry dynamics model built over a spherical and rotating Earth. Next, an entry guidance considering multi-NFZs and flight-time constraints is designed based on the new analytical flight-time formula as well as the existing 3-D analytical gliding-trajectory formulae. In the longitudinal part of the guidance, the flight-time and downrange formulae are used jointly to plan the longitudinal reference profile by considering both energy-management and flight-time requirements. In the lateral part, the downrange and crossrange formulae are used to plan the bank-reversal sequence according to the NFZ constraints. Additionally, in order to improve the accuracy of terminal time, speed, and altitude, a multi-objective iterative planning scheme employing onboard trajectory simulation is put forward and enabled at a time between the last two bank reversals to fine-tune the remaining short trajectory. In this scheme, the quasi-Newton method is improved by the use of directional derivatives such that the number of the trajectory simulations required to calculate the Jacobian matrix is reduced from 3 to 2 in each iteration, which greatly reduced the amount of calculation. Finally, a flight-time coordination scheme is developed for multiple HGVs to determine the starting times of entry flight, which can further determine the launch times once the boost guidance is specified. The superior performance of the guidance is demonstrated by Monte-Carlo simulations in stochastic disturbed circumstances.