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基于固定时间收敛误差动力学的微分几何制导律设计

白显宗1,黎克波2,李昊键3,董伟4   

  1. 1. 军事科学院国防科技创新研究院
    2. 国防科技大学
    3. 国防科技大学,空天科学学院
    4. 北京理工大学
  • 收稿日期:2023-10-12 修回日期:2024-02-01 出版日期:2024-02-02 发布日期:2024-02-02
  • 通讯作者: 黎克波
  • 基金资助:
    国家自然科学基金

Differential Geometric Guidance Law Design based on Fixed-Time Con-vergent Error Dynamic Method

  • Received:2023-10-12 Revised:2024-02-01 Online:2024-02-02 Published:2024-02-02
  • Contact: Ke-Bo LI
  • Supported by:
    National Natural Science Foundation of China

摘要: 提出了一种具有固定时间收敛特性的微分几何制导律设计方法。首先,提出一种新的固定时间收敛误差动力学方法的控制参数选择机制,将控制参数从4个缩减为3个,并给出更为准确的误差收敛时间上界。其次,针对固定目标打击制导问题,基于古典微分几何曲线原理,将固定时间收敛误差动力学方法拓展至弧长域,提出固定路程收敛微分几何制导律设计方法。然后,分别针对碰撞角控制制导和飞行路程控制制导问题,设计了相应的固定路程收敛微分几何制导律。最后通过数值仿真,对所提方法的有效性进行了验证。

关键词: 误差动力学, 古典微分几何曲线原理, 固定时间收敛, 固定路程收敛, 微分几何制导律

Abstract: A differential geometric guidance law design method is proposed, which is with a fixed-time-convergent characteristic. Firstly, a new control parameter selection mechanism is presented, for the recently proposed fixed-time convergent error dynamics (FxTED) method. The number of control parameters are reduced from four to three, and a more accu-rate upper-bound of the error settling time is obtained. Secondly, for the guidance law design problem against station-ary targets, based on the classical differential geometric curve theory, the FxTED method is extended to the arc-length domain, and the differential geometry guidance law design method with the property of fixed-range convergence is pro-posed. After that, aiming at the impact-angle-control guidance and flight-range-control guidance problems, two differen-tial geometry guidance laws are respectively designed. Finally, the effectiveness of the proposed method is verified through numerical simulation examples.

Key words: Error dynamics, Classical differential geometric curve theory, Fixed-time convergence, Fixed-range conver-gence, Differential geometric guidance law