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考虑具有终端约束和过程约束的探月返回飞行器再入轨迹设计问题,通过将性能指标泛函定义为再入终端位置误差的平方和,再入轨迹设计问题转化为具有过程约束和状态方程约束的优化问题.首先仅考虑状态方程约束,利用最大值原理,得到该优化问题的必要条件,选取间接法中的共轭梯度算法求解最优控制量.进而针对轨迹约束问题,研究了再入过载和轨道飞行段飞行距离与航迹角以及倾侧角的关系,在此基础上,提出了采用调整初始倾侧角序列的方法实现过程约束.该算法克服了罚函数方法中需要调节参数较多的问题,并且物理意义明确,实现简单.最后,给出了Apollo再入轨迹优化的数值仿真算例,验证了所给出算法的有效性.
Considering the design of trajectory reentry trajectory of lunar return spacecraft with terminal constraints and process constraints, the recursive trajectory design problem is transformed into a constraint with state constraints and constraint equations by defining functional index functionalities as the sum of squares of reentry terminal position errors Firstly, only the state equation constraints are considered and the necessary conditions of the optimization problem are obtained by using the maximum principle, and the conjugate gradient algorithm in the indirect method is chosen to solve the optimal control variables. Then, the trajectory constraints, The relationship between the flight distance and the track angle and the roll angle of the orbit flight section, and based on this, the method of adjusting the initial roll angle sequence is proposed to realize the process constraint.The algorithm overcomes the problem that the penalty function method needs more adjustment parameters, And has a clear physical meaning and a simple realization.Finally, a numerical example of Apollo reentry trajectory optimization is given, and the validity of the proposed algorithm is verified.