基于混合优化的运载器大气层内上升段轨迹快速规划方法

针对运载器大气层内的最优轨迹快速规划问题,提出一种将求解最优控制问题的间接法与直接法相结合的混合优化方法。首先,基于最优控制问题的一阶必要条件,将运载器大气层内的三维最优上升问题转化为Hamiltonian两点边值问题;然后,采用直接法中能以较少的节点获得较高求解精度的Gauss伪谱法进行求解,提高算法的求解效率;最后,采用真空解析解初值及密度同伦技术,解决初值猜测与算法收敛困难的问题。仿真结果表明,混合优化算法能够准确、快速地对运载器大气层内的最优上升轨迹问题进行求解,并在计算精度与效率上均优于间接法,可应用于运载器的轨迹在线规划与闭环制导。

A hybrid optimization approach for rapid endo-atmospheric ascent trajectory planning of launch vehicles

A hybrid optimization approach is proposed for the rapid optimal endo-atmospheric ascent trajectory planning of launch vehicles, combined with the indirect and direct methods for solving optimal control problems. Firstly, based on the first order necessary conditions, the method transforms the three dimensional optimal endo-atmospheric ascent problem into Hamiltonian two point boundary value problem. Then, the Gauss pseudo-spectral method of direct methods is applied to solve the problem, taking advantage of fast convergence rate, with less nodes and higher precision than other traditional methods. Last, vacuum analytical initial solution technology and density homotopy technology are also introduced to overcome the difficulties of initial guesses and convergence. Simulation results show that the hybrid optimization algorithm can accurately and rapidly solve the problem of optimal endo-atmospheric ascent trajectory, with better precision and efficiency than the indirect method. The proposed algorithm also can be applied to on-line trajectory planning and guidance of launch vehicles.