This paper introduces an innovative approach to optimizing flight corridors under complex constraints, particularly focusing on the Terminal Area Energy Management (TAEM) phases of reusable vehicles, where nominal trajectories may be inadequate due to initial condition and aerodynamic deviations. Leveraging the elegant principles of symmetry, the proposed optimal flight corridor design method, based on the Lagrange multiplier technique, offers a harmonious balance between trajectory accuracy and adaptability. By describing the TAEM flight corridor through a range–altitude profile and utilizing iterative optimization to uphold physical constraints such as dynamic pressure, overload, and roll angle, this method ensures symmetrical alignment of the design parameters. Through a comprehensive analysis of aerodynamic and initial position uncertainties, this method showcases exceptional symmetry in adapting to trajectory design uncertainties. The simulation results demonstrate the resilient nature of the designed flight corridor, capable of seamlessly accommodating initial state deviations and aerodynamic uncertainties. This symmetrical optimization of flight corridors not only enhances trajectory planning and control capabilities during the terminal energy management phase, but also showcases a paradigm shift towards precision and balance in aerospace engineering. Our simulation findings underscore the efficiency of this approach by reducing the flight corridor range by 50% compared to the nominal state while maintaining robustness across deviation conditions, embodying the symmetrical resilience needed for optimal trajectory design.

Aiming at the characteristics of air-breathing combined power vehicles with many constraints in the ascent stage and high precision requirements of terminal windows, a flight corridor design method based on the velocity-altitude profile is proposed. The velocity-altitude profile is used to describe the flight corridor, the relationship between constraints and velocity and altitude is analyzed, and the constraints contained in the upper and lower boundaries of the corridor are determined. Based on the analysis of the constraints, the angle of attack that satisfies the constraints and maximizes or minimizes the altitude at the current velocity is solved. A sample vehicle is used as an example to design and analyze the flight corridor in the ascent stage, and the calculation result shows that the method can be used for flight corridor design under multiple constraints in the ascent stage of the combined power vehicle.