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刘超越 , 张成 . 基于高斯伪谱法的二级助推战术火箭多阶段轨迹优化 [J ] . 兵工学报 , 2019 , 40 ( 2 ): 292 - 302 . DOI: 10.3969/j.issn.1000-1093.2019.02.009 http://doi.org/10.3969/j.issn.1000-1093.2019.02.009 针对二级助推战术火箭在多种约束下的高精度轨迹优化问题，提出了一种基于高斯伪谱法（GPM）的多阶段轨迹优化方法。针对二级发动机的工作特点，将全弹道划分为发射段、爬升段、续航段和制导攻击段4个阶段。为了提高禁飞区或敌方火力覆盖区附近的优化轨迹精确度，引入准接触点概念，将全弹道进一步进行阶段细分，并以连接点确保相邻阶段的顺利连接。利用GPM将轨迹规划问题转化为非线性规划问题进行求解。为了进一步提高计算效率、降低初值设置的难度，设计了基于初值生成器的迭代策略，实现了二级助推战术火箭多阶段轨迹优化。充分考虑飞行器各阶段飞行特点和约束，通过数值算例表明了该方法的优点。仿真结果表明，所提优化方法求解效率高，能够得到可行的最佳轨迹。

LIU C Y , ZHANG C . Multi-stage trajectory optimization of tactical two-stage booster rocket based on Gauss pseudospectral method [J ] . Acta Armamentarii , 2019 , 40 ( 2 ): 292 - 302 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.02.009 http://doi.org/10.3969/j.issn.1000-1093.2019.02.009 A multi-stage trajectory optimization method based on Gauss pseudospectral method (GPM) is proposed for optimizing the high-precision trajectory of tactical two-stage booster rockets under multiple constraints. According to the operating characteristic of the two-stage engine, the entire trajectory is divided into four flight phases, such as launching, climb, endurance and attack. In order to improve the accuracy of optimization trajectory near the no-fly zone and enemy fire coverage, the conception of quasi-contact point is introduced, and the trajectory is further subdivided. The connection points are used to ensure the smooth connection between adjacent phases. GPM is used to transform the trajectory optimization problem into a nonlinear programming problem. In order to further improve the computational efficiency and reduce the difficulty of setting the initial value, an iterative strategy based on the initial value generator is designed to achieve the optimization of multi-stage trajectory. Full consideration is given to the various flight characteristics and constraints of rocket in each phase, and the numerical examples are used to demonstrate the merits of the proposed algorithm. The simulated results show that the proposed algorithm has high effectiveness and can get the feasible optimal trajectory. Key

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