Differential Geometry Guidance Law For Intercepting Maneuvering Target

This dissertation took the terminal guidance law for intercepting maneuvering targets as the research objective. The application of differential geometric guidance law in terminal guidance was mainly investigated in this paper. A new idea was advanced which devided the rotation of line of sight (LOS) into two kinds: the rotation in the instantaneous rotation plain and the rotation of this instantaneuous plain. According to the association of this new rotation idea of LOS and the formula of Frenet-Serret, the relative dynamic equation between interceptor and target was established, on the basis of which the terminal guidance law for intercepting maneuvering targets was researched.Firstly, the rotation of LOS was studied based on classical differential geometry, the concept of curvature and torsion of LOS were brought forward and their expressions were gained. The relative dynamic equation between interceptor and target was gained and used in the research of proportional navigation guidance law (PN), comparing with the traditional PN in the LOS coordinate system. At the same time, PN with the derivative of LOS rate was analyzed and compared with PN.Secondly, the differential geometric guidance law (DG) in the arc domain (advanced by Chiou and Kuo) and in time domain (researched by Chaoyong Li) was deeply studied in this paper. The characteristics of DG were researched by using the dynamic equation given in chapterâ…¡, and the differential geometric guidance law in the instantaneuous rotation plain was advanced. It was proved that there were two modalities of this newly advanced guidance law: the TPN modality and the differential geometric modality (like PPN modality in some degree). It was proved that the differential geometric modality of DG in the instantaneuous rotation plain had the same characteristics of DG in time domain. The initial capture condition of the differential geometric modality was analyzed theoretically.Thirdly, using the relative dynamic equation between interceptor and target and with the research method of capture region advanced by Feng Tyan, the capture regions of three guidance laws in the instantaneuous plain were analyzed. This paper found that the relative eqation used by Feng Tyan had some shortcomings, such as: having plenty of variables, expression was complex and difficult for comprehension. These shortcomings could be solved by using the relative dynamic equation advanced in this dissertation.At last, the realization of the guidance laws advanced in this paper was researched and the computer simulation to validate the theories in this dissertation is implemented. By LOS angle sequences, the LOS rates for TPN, whether of maneuvering target or not, are obtained by the spline filter. The influence on the guidance laws cased by response delay of the control system was investigated. In succession, the realization of DG in the instantaneuous rotation plain was researched, and the augmented differential geometric guidance law (ADG) was advanced. Through the analysis of simulation, this paper found that ADG could efficiently compensate for the maneuvering acceleration of target, and the performance of ADG was closely approximated to the performance of DG in the instantaneuous rotation plain which directly used the maneuvering acceleration of target in the guidance process.The relative dynamic equation proposed in this dissertation which was based on the curvature and torsion of LOS had simpler form and more explicit physics meaning comparing with the counterpart in LOS coordinate system. The instantaneuous rotation plain advanced in this paper to study the terminal guidance laws simplified the 3-dimensional guidance problem to 2-dimensional problem, which minished the difficulty of analysis. Traditional differential geometric guidance law had some limitations on the velocities of interceptor and target (the acceleration was vertical to the velocity, and so the magnitude of velocity didn't change.), the differential geometric guidance law in the instantaneuous plain proposed in this dissertation didn't have such limitations on the velocity of interceptor and target, the guidance acceleration of interceptor could adopt the direction vertical to LOS or to the velocity, so the guidance law could be used in the atmosphere or out of the atmosphere. The augmented differential geometric guidance law advanced in this paper could compensate for the maneuvering acceleration of target by just importing the derivative of LOS rate into the guidance law itself, and the guidance law could greatly decreased the overload of the interceptor, so this guidance law could be utilized efficiently in practical scene of interception.