三维弹道有理Bezier曲线造型与优化方法

为有效克服传统弹道优化方法解的收敛性和最优性受搜索算法、初始猜测等影响大的问题，提出了基于有理Bezier曲线的三维弹道造型与优化计算方法。根据边界条件用光滑且只含少量造型变量的有理Bezier曲线形成待优化三维造型弹道，采用逆动力学方法计算造型弹道倾角、弹道角速度和法向加速度等，结合弹道其它动力学方程和约束计算造型弹道性能指标，通过对弹道造型变量寻优得到最优弹道。这种方法将无限维弹道优化问题转换为对很少造型变量的参数优化问题, 而且得到的最优弹道完全光滑可飞。与间接法相比，无需求解两点边值问题使用方便、鲁棒性强；与直接法相比，不需要对动力学方程离散化、寻优变量少、求解收敛性好,而且解的全局最优性和光滑性更高。仿真结果及与自适应伪谱法的比较校验了方法的实用性和有效性。

3D Trajectory Rational Bezier Curve Based Shaping and Optimization Technique

The convergence and optimality of ordinary trajectory optimization method is influenced by many factors such as initial guess and search algorithm, and so on. In view of this, a novel spatial trajectory shaping and optimization strategy based on the rational Bezier curves is proposed. According to boundary conditions, the unknown spatial trajectory is shaped by using the rational Bezier curves with few shaping variables. And the flight-path angle, the heading angle as well as their rate, the normal acceleration and the performance index are determined by the inverse dynamics technique and dynamics equations of the missile. Consequently, the optimal spatial trajectory can be obtained through optimizing the shaping variables. Finally, the original continuous optimization problem is translated into a simple parameter optimization one in the proposed method, and the resulting optimal trajectory is perfectly smooth and flyable. Compared with the indirect method, the solving for two-point boundary value problem is avoided in this method, thus the accessibility and robustness are guaranteed. In contrast with the direct method, no discretization on the states and controls is involved and few optimizing variables are introduced in this method, thus the solution can be easy to converge to the perfectly smooth and global optimal one. Both validity and practicality of the proposed method are demonstrated by comparison simulation.