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作为直接法的典型代表,高斯伪谱方法在处理复杂约束条件(含路径点或禁飞区约束)下再入高超声速滑翔飞行器轨迹优化问题时,仅能保证所得轨迹在各高斯节点处严格满足各项约束,而节点之间轨迹的可行性无法保证,为解决这一问题,文章提出改进多阶段高斯伪谱方法。该方法首先使用新定义的两类节点(固定节点和虚拟节点)将轨迹分段,其中固定节点是用来保证路径点与高斯节点重合,虚拟节点则是用来保证禁飞区附近分布更多的高斯节点,此分段方式能保证所得轨迹在任意位置可行;然后,向各分段轨迹插入指定数目的高斯节点;最后,使用序列二次规划方法对此多阶段轨迹优化模型进行求解。仿真结果表明,改进多阶段高斯伪谱方法在处理复杂约束条件下再入高超声速滑翔飞行器轨迹优化问题时快速有效。
As a typical representative of the direct method, the Gaussian pseudospectral method can only ensure that the resulting trajectory strictly meets at each Gaussian node when dealing with the trajectory optimization problem of the hypersonic gliding vehicle under complex constraints (including the path point or the no-fly zone constraint) However, the feasibility of trajectories between nodes can not be guaranteed. To solve this problem, the paper proposes an improved multi-stage Gaussian pseudospectral method. In this method, two kinds of newly defined nodes (fixed node and virtual node) are used to segment the trajectory. The fixed node is used to ensure that the path point coincides with the Gaussian node and the virtual node is used to ensure more distribution near the no-fly zone The Gaussian nodes of this method can ensure that the resulting trajectory is feasible at any position. Then, a specified number of Gaussian nodes are inserted into each segment trajectory. Finally, the quadratic programming method is used to solve this multi-stage trajectory optimization model. The simulation results show that the improved multi-stage Gaussian pseudospectral method is fast and effective when re-entering the trajectory optimization problem of hypersonic gliding aircraft under the condition of dealing with complex constraints.