基于零化曲率变化率的微分几何制导律研究

摘要

Based on the idea of zeroing the curvature rate ,a new differential geometirc guidance law was proposed in order to intercept the maneuver target. Firstly, the triangle geometric relation of the missile and the target was analyzed, the shape invariability criterion of the triangle was used to design the guidance law in the Ferent coordinate based on the idea of zeroing the curvature rate,also the definite iteration algorithm was given. Secondly,the plane geometry theory was used to construct the function of Lya-punov in order to prove the stability of the derived differential geometric guidance law. Simulation results show that, compared with the proportional guidance law and integrated guidance and control method, the differential geometric guidance law has high precision, the intercept time is shorter,and the rate of the trajectory curve converges to zero in the end. Also it overcomes the load increasing sharply caused by the sight line rate divergence.%基于零化拦截器弹道曲率变化率的思想设计了一种微分几何制导律.论文首先分析了弹目拦截的几何三角形,以三角形形状的不变性为基本思想确定拦截器的飞行方向,在伏雷内(Frenet)标架内得到拦截器的制导指令,并给出每个时刻拦截器飞行方向确定的迭代算法.其次结合平面几何知识,通过构造李亚普诺夫(Liapunov)函数对设计的制导律稳定性进行理论证明推导.仿真结果表明,相对于比例导引,基于零化曲率的微分几何制导律具有较高的制导精度,弹道较为平直,末端弹道曲率变化率趋近于零,克服了比例导引末端视线角速率发散的情况,降低了执行机构的要求.