联立法求解月面上升段最优轨迹的快速收敛控制技术

Fast Convergence Control on Simultaneous Approach Based Trajectory Design during Lunar Ascent

为了更好地解决复杂约束下的航天器月面上升段在线轨迹规划问题,提出了一种求解最优轨迹的联立框架。首先利用有限元正交配置法将状态变量和控制变量完全离散化,得到一个非线性规划命题。考虑到命题中含有较多的不等式约束并且会随着有限元的增加而增加,故采用内点算法对非线性规划命题进行求解。离散化后的非线性规划命题的规模大幅度增加,导致了优化计算难度的加大和求解时间的增加,为了便于联立法的在线应用,采用收敛深度控制策略从平衡解的精度和计算效率的角度来改进优化算法的实时性。以某航天器载人返回任务月面上升段场景为算例进行仿真,结果表明基于联立法求得的最优控制量序列得到的飞行轨迹满足轨道根数的精度要求,同时利用收敛深度控制策略可以实现快速收敛控制。

In order to solve the trajectory optimization problem under complex constraints of manned spacecraft, a trajectory optimization algorithm based on simultaneous strategies was proposed in this study. Firstly, the optimal control problem was discretized with Radau collocation mode, and then a nonlinear programming was obtained. Interior point method was utilized to solve the nonlinear pro- gramming, which had many inequalities and the number of inequalities would increase as the num- ber of finite elements increases. The scale of the nonlinear programming rose considerably since the state and control variables were both discretized by simultaneous approach, and then the computa- tional difficulty and solution time were increased. For online application of the simultaneous ap- proach, convergence depth control strategy was adopted to enhance the optimization algorithm by balancing the solution precision and computational cost. Simulation was made under the scene of a certain manned spacecraft returning from lunar surface, the numerical results showed that the preci- sion of the orbit elements gotten by simulation with the optimized control variables could satisfy the requirement, and fast convergence control could be realized with the convergence depth control strat- egy.