中文摘要：

针对制导炸弹对地攻击的垂直打击的弹道特点,研究了多约束条件下的轨迹优化问题,提出了一种基于hp自适应Radau伪谱法（hp-RPM）的迭代求解策略。该方法允许不同区间的插值多项式的阶次不同,并以轨迹曲率作为重新分配配点以提高区间求解精度的依据,当各配点处的计算精度达到设定的误差允许范围时,迭代停止。以某航空制导炸弹为对象进行轨迹快速优化,仿真结果表明,该方法能够在多约束条件下快速生成满足要求的轨迹,且解的Hamilton函数满足最优性条件,与常规方法相比,平均增程效果达到11.45%。

英文摘要：

According to the ballistic characteristics of the vertical attack by an aerial guided bomb,we optimize its trajectory and design the iterative variable-order solution strategy based on the hp-adaptive Radau pseudospectral method（ hp-RPM） to rapidly optimize the glide trajectory under multiple constraints. The strategy allows for different orders of polynomial approximation in different intervals. We enhance the accuracy of the intervals by redistributing allocation points with the trajectory curvature. We iterate the redistribution of allocation points until their computational accuracy is acceptable to an error-tolerant degree. Then we simulate the rapid optimization of the trajectory of a certain aerial guided bomb. The simulation results show that the strategy can rapidly generate satisfactory trajectories under multiple constraints and that the Hamilton function of the solution satisfies optimal performance conditions. Compared with the conventional strategies,the trajectory optimized with our strategy is improved by an average of 11.46%.