Time-coordination entry trajectory planning for multihypersonic vehicles

In recent years, the research on high-speed vehicles has become a hot spot, among which the research on hypersonic vehicles is particularly important. Multihypersonic vehicles will inevitably work cooperatively in the future under the weaponization and armament acquisition processes of hypersonic vehicles. However, the characteristics of hypersonic vehicles, such as without thrust and with strong nonlinearity, strong coupling, and multiple constraints, have led to considerable difficulties and challenges in the cooperative formation control problem of multihypersonic vehicles. This paper proposes a time-coordination entry trajectory planning method for multihypersonic vehicles for scenarios where multihypersonic vehicles arrive at a designated area with cooperative time constraints. First, the coupling problem between the re-entry flight time and lateral maneuvering of a vehicle is solved by reasonably simplifying the motion equation of the vehicle in the longitudinal plane, and a longitudinal trajectory planning method considering arrival time and range constraints is designed based on the binary Newton iteration method. Then, the inverse logic of the bank angle is designed based on the heading angle deviation corridor; thus, the terminal flight range constraint and heading angle deviation constraint can be satisfied, and the three-dimensional trajectory of the vehicle is obtained. However, the impact of the lateral motion will inevitably result in a certain deviation between the final and expected flight times. Therefore, a strategy for compensation and renewal is designed and the entry trajectory is planned iteratively until meeting the flight range and arrival time constraints. Simultaneously, the impact of different bank angle profiles on the flight range, flight time, and terminal height in trajectory planning of vehicles is investigated, and on this basis, a method for determining the collaborative flight time, terminal altitude, and flight range of the vehicles is introduced. Finally, the numerical simulation is conducted to verify the trajectory planning problem of multiple vehicles with time coordination, and the simulation results show that multihypersonic vehicles can simultaneously arrive at the terminal area using the method proposed in this study, which can satisfy the flight range, arrival time, and terminal height constraints and has good calculation accuracy. Meanwhile, varying degrees of uncertainty can be detected in the initial altitude, speed, longitude, latitude, flight path angle, heading angle, and other initial conditions and various disturbances, such as atmospheric density and aircraft mass, during the actual flight of the hypersonic vehicle. Moreover, the Monte Carlo simulation verified that the trajectory planning method with time coordination has strong robustness to various disturbances and remarkable application prospects.