Rapid reentry trajectory planning of multi-gliding vehicles for coordinated formation

Multi-gliding vehicles' coordinated formation can enhance their multi-task execution and anti-interference capabilities. However, the complex near-space environment, high-speed underactuated flight characteristics, and communication difficulties in the blackout zone make it challenging to achieve strict coordinated formation flight. The introduction of complex constraints such as rendezvous point spatiotemporal states and formation configurations further complicates the reentry trajectory planning problem for underactuated gliding vehicles, with a minimal feasible region and significant difficulty in rapid solution. Thus, it is crucial to develop a fast reentry trajectory planning method for coordinated formation to meet the requirements of practical missions.

This paper proposed a dual-phase coordinated formation reentry trajectory planning method based on the CAFM (coordinated assembly and formation maintenance) strategy. In the coordinated assembly segment, a trajectory planning method with a dual-layer coordination-execution framework was designed. The coordination layer includes modules for spatiotemporal capability boundary forecasting, rendezvous point information calculation and distribution, and adaptive correction of rendezvous point information, which can quickly determine rendezvous point information considering the vehicles' control capabilities. The execution layer used a trajectory planning method considering spatiotemporal full-state constraints to achieve high-precision assembly of multiple vehicles. In the formation maintenance segment, a trajectory planning method based on fixed-time consistency was developed, using virtual altitude and heading angle as coordination information to maintain the formation over long ranges.

The simulation results, using the CAV-H coordinated formation as a case study, show that in the horizontal plane formation simulation, the deviation of each vehicle at the rendezvous point is small, and the average trajectory planning computational time is less than 0.01s/100km/vehicle, indicating high planning accuracy and real-time capability. In the vertical plane formation simulation, the method can also achieve high-precision assembly and maintain the formation configuration, demonstrating good adaptability. The Monte Carlo simulation verifies that the method still has good multi-task adaptability in the presence of initial reentry position deviations.

The proposed CAFM flight scheme and algorithm framework can achieve the consistent convergence of the spatiotemporal full states of each vehicle at the rendezvous point, establishing a favorable initial condition for formation maintenance. The adaptive iterative method for computing, distributing, and correcting rendezvous point information improves the success rate and safety of coordinated formation flight. Using virtual altitude and heading angle as coordination information based on the fixed-time consistency theory can maintain the formation configuration in different altitude planes, but it may cause certain formation configuration deviations in long-distance and different altitude plane missions due to the irreversible energy characteristics of gliding vehicles. Overall, this method effectively addresses the coordinated formation problem of reentry gliding vehicles and has certain advantages in terms of adaptability and safety.