基于Radau伪谱方法的轨迹优化

Trajectory Optimization Based on Radau Pseudospectral Method

摘要:

研究了导弹在末制导阶段满足多约束条件下的轨迹优化问题。针对传统方法在处理复杂的非线性运动学、动力学约束上存在的困难,提出了一种基于 Radau伪谱方法(RPM)的求解策略。首先,给出了考虑导弹速度和空气密度变化、终端和过程约束条件以及 2种不同的性能指标函数的最优轨迹优化问题；其次,利用 RPM将轨迹优化问题转化为非线性规划问题,采用序列二次规划算法求得最优解；最后,分 2种初始条件对最大落角和最大终端速度的轨迹优化问题进行了仿真验证,结果表明:本文方法能够在较短的时间内生成一条满足多种约束要求的高精度的最优轨迹。

Abstract:

Trajectory optimization problem of missile which satisfies multi-constraints in the terminal phase was studied inthis paper. In order to deal with the difficulties of traditional method in processing complicated nonlinear kinematic and dy.namic constraints, a strategy which based on Radau pseudospectral method(RPM)was proposed. Firstly, trajectory optimi.zation problem was given which took into consideration missile velocity and air density changing, terminal and process con.straints and two different performance indexes. Secondly, trajectory optimization problem was transformed into a nonlinearprogramming problem using RPM, which could be solved using a sequential quadratic programming algorithm. Finally, nu.merical validation for maximum terminal impact angle and maximum terminal velocity of trajectory optimization problemin two difference initial conditions were used to demonstrate effectiveness of the proposed algorithm. The results showedthat the optimal trajectory which satisfied mult-constraints conditions could be obtained with short time and good preci.sion in this paper.