Glide Trajectory Optimization of Guided Projectiles Using an Improved Grey Wolf Optimizer and hp-Adaptive Radau Pseudospectral Method

This study proposes an NSL-GWO-hpRPM framework for constrained glide trajectory optimization of guided projectiles. The method combines an improved Grey Wolf Optimizer with the hp-adaptive Radau pseudospectral method to reduce the dependence of hpRPM on initial guesses and improve global search performance. In the improved GWO, Sobol low-discrepancy sequence initialization is used to enhance population diversity, a nonlinear convergence strategy is introduced to balance exploration and exploitation, and Levy flight is adopted to improve the ability to escape local optima. The optimized solution obtained by NSL-GWO is then used as the initial guess for hpRPM to achieve high-precision local refinement. Simulation results show that the proposed NSL-GWO-hpRPM achieves a feasible range of 71,211.514 m, improving the range by 4.53% over hpRPM and 1.48% over GWO-hpRPM. Statistical results from 35 independent runs further demonstrate that the proposed method obtains the best mean range, Friedman mean rank, and significant Wilcoxon test results with p<0.001. The optimized trajectory reaches a maximum range of approximately 71.2 km with an optimal launch angle of 62.4∘ while satisfying all flight constraints, indicating that the proposed framework is effective for complex constrained glide trajectory optimization.