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| Glide Trajectory Optimization for Hypersonic Vehicles Based on Adaptive Chebyshev Pseudo-Spectral Method |
| MIAO Yuheng1， LI Rufei2， E Bin1， WANG Xiaogang1， CUI Naigang1 |
| 1. School of Astronautics， Harbin Institute of Technology， Harbin 150001， Heilongjiang， China；
2. Shanghai Electro-Mechanical Engineering Institute， Shanghai 201109， China |
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Abstract The trajectory of hypersonic vehicles during unpowered high-speed gliding flight within the atmosphere is a complex nonlinear multi-constraint optimisation problem. To address trajectory optimisation under different objective functions for the unpowered gliding phase of hypersonic vehicles, the dynamics equations for the gliding phase were established, simplified, and improved in this study. A trajectory optimisation method based on the hp-adaptive Chebyshev pseudo-spectral method was employed, and the analytical gradients of the objective functions in numerical form were derived. The trajectory optimisation problems for minimum flight time and minminm heat generation under specified conditions were solved. The results demonstrate that this method can solve trajectory optimisation problems for hypersonic vehicles with high computational accuracy. Besides, the correctness of the provided gradient calculation formulas was verified in this study, which could improve the computational efficiency of the algorithm to a certain extent.
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Received: 05 March 2025
Published: 15 July 2025
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2025, Vol. 8 
