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A Novel Approach to the 2D Differential Geometric Guidance Problem

机译：二维微分几何制导问题的新方法

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摘要

This paper presents a detailed study of the two-dimensional (2D) differential geometric (DG) guidance problem, as well as its iterative solution and initial conditions. The DG guidance curvature command is transformed from an arc length system to the time domain using the classical DG theory. Subsequently, an algorithm for commanded angle-of-attack is developed to formulate the DG guidance system, whose iterative solution is established based on Newton's iterative algorithm. Moreover, a flight control system is presented using the classical PID controller so as to form the DG guidance and control system. Finally, a new necessary initial condition is deduced to guarantee the capture of a high-speed target. Simulation results demonstrate that Newton's iterative algorithm works well and accurately in DG guidance problems and the proposed DG guidance law exhibits similar performance to the proportional navigation guidance (PNG) law in the case of intercepting a non-maneuvering target. However, the proposed method performs better than PNG in the case of intercepting a maneuvering target.
机译：本文介绍了二维（2D）微分几何（DG）制导问题的详细研究，以及其迭代解和初始条件。 DG引导曲率命令使用经典DG理论从弧长系统转换到时域。随后，提出了一种用于指令攻角的算法来制定DG制导系统，该算法基于牛顿迭代算法建立了迭代解。此外，提出了一种使用经典PID控制器的飞行控制系统，以形成DG制导和控制系统。最后，推导出新的必要初始条件以确保捕获高速目标。仿真结果表明，牛顿迭代算法在DG制导问题上运行良好且准确，在截获非机动目标的情况下，拟议的DG制导律表现出与比例导航制导（PNG）律相似的性能。但是，在拦截机动目标的情况下，提出的方法比PNG的性能更好。

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