一种基于轨道根数约束的最优制导方法

An optimal guidance method based on orbital element constraints

针对航天器空间变轨的制导问题,研究了一种基于轨道根数约束的最优制导方法。在地心惯性坐标系下直接建立航天器的最优控制模型,给出了位置速度表达式和协态变量初值之间的关系;进一步,在不约束真近点角的前提下,推导了5个轨道根数的约束方程,并通过对轨道根数和最优控制理论中协态方程的特性分析,获得了另外两个约束方程。协态变量初值可直接通过求解7个完整约束方程组获得,进而得到最优推力方向。仿真验证了所提制导方法的有效性。

This paper proposes an optimal guidance method based on orbital element constraints,for the guidance problem during orbital transfer of spacecraft.The optimal control model for the spacecraft is established in the earth centered inertial coordinate frame directly.The relationship between expressions for the position and velocity and the initial values of costate variables is then given.Besides,five orbital element constraint equations are derived without constraint on the true anomaly.The other two constraint equations are given based on the analysis of characteristics of orbital elements and costate equations under the optimal control framework,which include the constraint and scale property of the established optimal conditions,respectively.The initial values of costate variables can be obtained by solving the seven complete constraint equations,and the optimal thrust direction can then be given.Simulations demonstrate the effectiveness of the proposed guidance method.