用广义乘子法求解航天器最优平面再入轨迹

Entry Trajectory Optimization Using Generalized Lagrange Multiplier

从纵向平面无量纲航天器质点运动方程出发,引入了能量参数对运动方程进行推导,使得运动方程和优化问题易于处理。通过将优化变量转化为分段连续的线性函数和Runge-Kutta数值计算方法,将轨迹优化问题转化为非线性规划问题,应用广义乘子法对其进行数值分析,给出了不同航程要求下,总加热量最小,满足终端要求以及过载、动压、热流约束的航天器最优轨迹,并分析了其特点。

We begin with the standard point-mass dimensionless equations of motion in the vertical plane over a spherical nonrotating Earth. The negative specific energy were used in stead of time in the motion equations, both the equations and the optimization problem were simplified. The control variables, namely drag and lift, were treated as continuous piecewise-linear functions of the negative specific energy. By the Runge-Kutta methods, the trajectory optimization problem was transferred to nonlinear programming, which were solved by the Generalized Lagrange Multiplier. The optimal entry trajectories with different downrange distance of minimal accumulated heat load were gained, which satisfy the constraints of heating-rate, dynamic pressure and load factor. The characters of the optimal entry trajectories were discussed.