混合法求解考虑路径约束的持续推力快速机动轨道

Path Constrained Trajectory Optimization Using Hybrid Method

近地空间航天器快速机动问题中一个必须考虑的现实约束就是机动轨迹不得低于大气层高度,为此给出考虑路径约束的持续推力快速机动问题的处理方法。通过在性能泛函中加入关于路径约束的惩罚项,使原本不再适用的最优控制理论仍然适用,进而可通过混合法完成问题的求解;同时保证了新问题的最优解为原问题的满足路径约束的近似最优解。最后通过数值仿真的结果验证了方法的有效性。

Minimum-time, continuous thrust solution is obtained for the problem of orbital transfer with interior path constraints. Orbital maneuver in an inverse-square gravitational field was considered, subject to a circular path constraint representing a minimum permissible orbital radius. By reconstructing the performance index J, a new two-point boundaryvalue problem was obtained. Then a near time-optimal solution, which satisfied the path constraint, was obtained by using hybrid trajectory optimization method with single shooting. At the end of the paper, examples were presented to demonstrate this method.