关键词: 高超声速滑翔, 快速轨迹优化, 同伦分析法, 半解析灵敏度, 原对偶内点法

Abstract: To address the challenges of strong nonlinearity, multiple constraints, and stringent real-time requirements in the reentry trajectory optimization of Hypersonic Glide Vehicles (HGVs), an efficient trajectory optimization method based on Homotopy Analytical Propagation (HAP) is proposed. First, a homotopy analysis method based on a linearized dynamics operator is introduced. By constructing an auxiliary linear operator that incorporates the system Jacobian matrix, a set of explicit analytical recursive formulas for state variables is derived, achieving high-precision and rapid prediction of flight trajectories. Second, leveraging the explicit structure of the analytical solution, a semi-analytical gradient computation strategy is proposed. This strategy utilizes the computational efficiency of the analytical predictor to acquire gradient information through a combination of the chain rule and forward sensitivity propagation. This approach avoids the cumbersome numerical integration of variational equations, thereby significantly reducing the computational burden while maintaining gradient accuracy. Finally, a trajectory optimization framework based on the Primal-Dual Interior Point Method is established. By utilizing the aforementioned efficient gradient information to guide the search, this framework effectively handles highly nonlinear path and terminal constraints—such as heat flux and load factor—while ensuring algorithmic convergence. Simulation results demonstrate that the proposed analytical propagation algorithm achieves millisecond-level computational time for a single trajectory prediction while maintaining high accuracy. Compared with traditional pseudospectral methods or numerical shooting methods, the proposed method significantly improves computational speed and generates smooth trajectories that strictly satisfy all flight constraints, demonstrating significant potential for online applications.

Key words: Hypersonic Gliding, Efficient Trajectory Optimization, Homotopy Analysis Method, Semi-analytical Sensitivity, Interior Point Method