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在同时存在路径约束和边界条件时确定助推-滑翔飞行器的最优运动轨迹是近年来的热点问题。本文讨论了助推-滑翔飞行器的具有最大纵向航程和横向航程的两种最优轨迹。Gauss伪谱法是由Benson和Huntington提出的,在求解复杂的最优控制问题时有较快的收敛速度并能提供高精度的解。文中介绍了该方法并利用其将轨迹优化问题变换为可由NLP求解器进行数值求解的非线性规划问题。文中还介绍了其它相关的技术,例如端点控制的计算方法、处理包含奇异弧段的多阶段问题的处理方法、获得初始猜测值的方法和验证结果的方法等。仿真结果可以说明在给定的热流、过载和动压约束下最优轨迹的若干关键特性。通过优化和仿真计算,同时证明了此方法的实用性和有效性。
It is a hot issue in recent years to determine the optimal trajectory of the booster-glide aircraft when there are both path constraints and boundary conditions. This article discusses the two optimal trajectories of a booster-glide aircraft with maximum longitudinal and lateral range. Gauss pseudospectral method is proposed by Benson and Huntington. It has faster convergence speed and can provide high-precision solution for solving complex optimal control problems. This paper introduces the method and uses it to transform the trajectory optimization problem into a nonlinear programming problem that can be numerically solved by the NLP solver. The paper also introduces other related technologies, such as the calculation of endpoint control, the processing of multi-stage problems with singular arcs, the method of obtaining the initial guess and the method of verifying the results. The simulation results illustrate some of the key features of the optimal trajectory for a given heat flow, overload and dynamic pressure constraints. Through the optimization and simulation calculation, at the same time proved the practicality and effectiveness of this method.