【作者】 张鹏宇；

【导师】 王子才；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与工程， 2009， 博士

【摘要】 空间技术对一个国家的政治、经济、军事越来越重要,是综合国力的根本保障。空间拦截是一种保障空间安全和战略优势的关键性空间技术。天基拦截尽管技术复杂,但是可以拦截低、中、高轨道目标,比地基拦截更具有战略价值。天基异面直接上升拦截与共轨拦截和共面拦截相比,作战意图更隐蔽,具有拦截异面目标的能力等优点,此外利用一个搭载多颗拦截器的天基平台拦截既可以彻底破坏由分布在多个轨道面上的多个目标组成的星座的功能,又可以降低成本。异面拦截需要初始轨道面外变轨,必然导致燃料损耗较大,因此燃料约束对转移轨道设计具有决定性作用,考虑燃料约束的最优轨道设计是异面拦截的核心问题。提出了一种考虑拦截器初始速度的转移角的求解方法,根据Lambert定理建立了圆锥曲线轨道转移时间与半长轴的对应关系,利用几何学分析了椭圆转移轨道的虚焦点位置对椭圆转移轨道形态的影响,以及转移角对转移时间和偏心率的影响。给出了由轨道半长轴确定空间两点间圆锥曲线转移轨道的方法,随后给出了一种固定发射时刻和转移时间的情况下利用半长轴迭代的圆锥曲线转移轨道求解算法。并仿真验证了该算法对椭圆和双曲线转移轨道均适用。分析了单脉冲多圈飞行拦截的特征速度与转移轨道半长轴之间的关系,指出其最优解实际上为2N+1条满足时间约束的转移轨道中燃料较省的,而不是最省燃料轨道。推导了单脉冲拦截的特征速度与半长轴的导数关系,随后给出了求解最省燃料轨道的计算方法。提出一种脉冲分解多圈飞行拦截,将单脉冲分解成方向相同的两次脉冲,使得拦截器在某特定的椭圆轨道上多圈飞行以消耗掉多余的转移时间,利用剩余转移时间沿最省燃料轨道拦截目标。几何上证明了这种拦截的特征速度与最省燃料轨道的特征速度相同,并且给出了该方法的解的存在性条件。通过两个实例验证了利用该方法设计的转移轨道比单脉冲多圈飞行拦截更节省燃料,同时解的存在性对转移时间的长度要求更低。给出了一种固定发射点到目标轨道的最小特征速度曲线求解方法,通过对共面拦截和异面拦截的最小特征速度曲线的比较,证明了共面拦截中转移角180°最优解的Hohmann变轨在异面拦截中导致极大的燃料损耗,并且分析了拦截器初始轨道根数对最小特征速度曲线的影响。提出一种基于最小特征速度曲线的异面拦截区求解方法,并且分别给出了一圈内飞行拦截、单脉冲多圈飞行拦截和脉冲分解多圈飞行拦截的防区求解算法。通过仿真研究了单脉冲多圈飞行拦截和脉冲分解多圈飞行拦截可以通过增加飞行圈数将目标纳入防区,可以即时发射拦截目标,而一圈内飞行拦截常常需要改变发射点才能拦截目标。一圈内飞行拦截特征速度等高线图可以直接利用圆锥曲线Lambert算法求解。但是由于单脉冲多圈飞行拦截和脉冲分解多圈飞行拦截在转移时间不够长的情况下其解并不存在,采用同样的步骤求解特征速度等高线图会产生奇异值。利用一圈内飞行拦截的解替换奇异值,提出一种求解单脉冲多圈飞行拦截和脉冲分解多圈飞行拦截的特征速度等高线图的方法。通过对发射条件的比较,单脉冲多圈飞行拦截和脉冲分解多圈飞行拦截都能充分利用了拦截区,但后者更节省燃料。最后通过实例验证了利用脉冲分解多圈飞行拦截特征速度等高线图设计的拦截轨道可以对分布在异面轨道的星座上的目标进行拦截。更多还原

【Abstract】 Space technology becomes more and more important to politics, economy and military, as an ultimate guarantee of nation’s power. Space interception is the key of space technology to protect space security and strategic dominance. Although it is complicated in technology, space-based interception, which can intercept a target in any low, middle and high orbit, has more strategic value than ground-based interception. Compare with same orbit interception and coplanar interception, space-based noncoplanar direct ascend interception has some advantages, such as covert purpose, the capability of intercepting targets in noncoplanar orbits. Moreover, a space-based platform with multiple interceptors can not only completely destroy the function of constellation, made up of targets in multiple orbit planes, but also save cost. Since noncoplanar interception will transfer out of initial plane, it consumes lots of fuel consequentially. Because fuel constraint is a crucial fact to design the transfer trajectory, optimal trajectory considering fuel constraint is a primary problem for noncoplanar interception.A calculated method of transfer angle considering interceptor initial velocity was presented. The relationship between transfer time of conic trajectory and semi-major axis was set up based on Lambert theorem. The effect of vacant focus location to shape of elliptical transfer trajectory and transfer angle to transfer time and eccentricity was analyzed using geometry. A method determining conic transfer trajectory between two points in space by a fixed semi-major axis was given. An arithmetic solving conic transfer trajectory by iterating semi-major axis with a specified launch time and transfer time was given. Some simulation proved that this arithmetic was valid to elliptic and hyperbolic transfer trajectory.For single impulse multiple-revolution interception, the relationship between characteristic velocity (?v) and semi-major axis of transfer trajectory was considered, It was proposed that the optimal solution actually is the less fuel trajectory among 2N+1 trajectories satisfying time constraint, but not the minimum fuel trajectory (MFT). A derivate formula between ?v of single impulse interception and semi-major axis was derived. As the single impulse was dissembled into two impulses with the same direction, a interceptor could consume the redundant transfer time by costing multiple-revolution on some specified elliptic orbit, and intercept a target on MFT in the rest transfer time. It was proved that ?v of this interception coincide with that of minimum fuel transfer in geometry. The existence of solutions was studied. Some simulations show that this intercept can save fuel and the existence of solutions is more loosely restrictive on the length of transfer time than single impulse multiple-revolution interception.A calculating method of minimum characteristic velocity curve for a fixed launch point to a target orbit was interpreted. Camparing the two minimum characteristic velocity curves of coplanar and noncoplanar interception study, it was proved that Hohmann transfer, which was the optimal solution of coplanar interception with transfer angle 180°, cost large mount of fuel in noncoplanar interception. The effect of the initial orbital elements of interceptor to minimum characteristic velocity curve is analyzed. A method of computing noncoplanar intercept range based on minimum characteristic velocity curve was proposed. Furthermore, arithmetics of calculating the defence range for lacking-one-revolution interception, single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception were given, respectively. Some simulations prove that single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception can cover the target into the defence range by more revolutions and launch interceptor immediately, but lacking-one-revolution interception often has to change the launch point to intercept the target.Contour of characteristic velocity for lacking-one-revolution interception can be calculated directly by using conic Lambert arithmetic. On the other hand, using the same process to draw contour of characteristic velocity, there will create singularities for single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception, whose solutions are not existed when transfer time is not long enough. Two methods calculating contour of characteristic velocity for single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception was presented, by using the solutions of lacking-one-revolution interception to replace the singularities. Comparing the launch conditions, although both single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception can utilize intercept range well, the latter saves fuel. Finally, an example proves that the intercept trajectory, designed by contour of characteristic velocity for impulse dissembled multiple-revolution interception, can intercept targets of a constellation distributing on noncoplanar orbits.更多还原