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基于双层凸优化模型的月面运载器大范围转移最优轨迹规划方法

Large-Scale Lunar Transportation Trajectory Optimal Programming Method Based on the Bilevel Convexification Model

  • 摘要: 针对月面大范围转移运载器垂直起降、机动次数多且着陆精度要求高的问题,提出了一种基于双层凸优化模型的最优轨迹规划方法。首先,建立运载器质心运动方程,在考虑初始位置、终端位置、速度约束与推力约束等条件下,构建大范围轨迹优化模型,对非线性最优问题进行线性化与离散化;其次,将大范围最优轨迹规划问题转换为双层凸优化问题,将动力上升段、大范围动力飞行段、垂直下降段的最优化问题作为内层凸优化问题,通过内点法求解,同时结合燃料最优化目标,设计目标函数,作为外层凸优化问题,通过梯度下降法迭代计算,得到大范围垂直起降的燃料最优轨迹。仿真结果表明,提出的算法可得到运载器大范围转移轨迹的燃料最优解,满足月面运载器高精度软着陆的任务需求;在考虑位置误差的情况下进行蒙特卡洛仿真,结果表明算法具有较好的鲁棒性。

     

    Abstract: In order to solve the trajectory planning problem of the launch vehicle during the large-scale lunar transportation, which involves vertical takeoff and landing, multiple maneuvers, and high landing accuracy requirements. Firstly, the equations of motion of the vehicle's center of mass are established, and a large-scale trajectory optimization model is constructed considering initial position, terminal position, velocity constraints, and thrust constraints. The nonlinear optimization problem is linearized and discretized using convex optimization methods; Secondly, the large-scale optimal trajectory planning problem is converted into a bilevel convex optimization problem. The optimization problems in the dynamic ascent phase, the large-scale dynamic flight phase, and the vertical descent phase are treated as the inner layer convex optimization problems, and solved using the interior point method. At the same time, combined with the fuel optimization purpose, the objective function is designed as the outer layer convex optimization problem, and iterative calculations are performed using the gradient descent method, obtain the optimal fuel trajectory for a wide range of vertical takeoff and landing. Simulation experiments show that the algorithm proposed in this paper ensure the vertical landing of the vehicle which meets the requirements of high-precision landing. Monte Carlo simulation is conducted considering position errors, and the results show that the algorithm has good robustness.

     

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