利用虚拟卫星法求解火星探测器近火点制动策略

Mars probe near-center braking strategy using virtual satellite method

针对采用极大值原理求解火星探测器近火点制动最优推力策略时初值不易猜测、迭代不易收敛的问题,介绍并推导了虚拟卫星方法,即通过假想一颗虚拟卫星在目标轨道上运行,探测器利用最优控制算法求解推力策略,使探测器本身与虚拟卫星的终端相对位置和速度为零,从而实现了精确入轨.在利用极大值原理求解最优推力策略的过程中,共轭变量初值的选择问题得到了解决.利用虚拟卫星方法中的相对运动关系,可以将没有实际意义的共轭变量初值转化为具有物理意义或者较易猜测的变量进行初始估计,克服了共轭变量初值猜测的盲目性,使得迭代更容易收敛.仿真结果证明了该方法的有效性.

To deal with the problem that the iteration doesn′t converge well in the maximum principle,a virtual satellite method is proposed to compute a fuel optimal trajectory of Mars probe in the processing of near-center braking.In the virtual satellite method,an optimal trajectory is computed in which the real satellite rendezvous with the virtual satellite so that the real satellite will come into the target orbit.The problem of guessing initial value of co-states is solved by transfer the original co-states,which have no physical meaning,into another one that can be guessed easily and by this way the iteration will converges better.Finally the simulation results prove the efficiency of this method.