基于微分几何的拦截弹制导律研究∗

摘要

针对战术导弹的拦截问题，根据质点微分几何运动学在弧长系下及在时域内的关系，将弧长系下的微分几何制导律应用到实际的TBM拦截过程中，得到了空间中时域内的微分几何制导律以及相应的过载指令。根据拦截过程中目标的不同机动方式，采用微分几何制导与比例导引进行了仿真对比与分析，得到了两种导引律下的脱靶量与拦截时间。仿真结果表明，微分几何制导律能够在拦截过程中降低视线角速度并使其趋于稳定，在拦截开始其过载需求较大并逐渐降低至接近0，脱靶量及拦截时间都小于比例导引律，采用微分几何制导律能够在更短时的时间内进行精确拦截。%In this paper, the endo⁃atmosphere tactical ballistic missile interceptor is studied, especially on the terminal guidance law. According to the relationship between arc system and time domain, differential geometry guidance law will be applied to the process of TBM interception. Differential geometric guidance law and the relative overload command in the time domain of 3D space is derived. When it is compared with the classic proportion navigation law in the simulation toward a high speed maneuvering target, the designed differential geometry guidance law demonstrates its superiority by an obviously lower miss distance and lower line of sight rate.