非合作目标交会的双层MPC全局轨迹规划控制

针对空间非合作目标近距离视线交会中的全局最优鲁棒轨迹规划与控制问题，提出了基于高斯伪谱方法（GPM）和线性时变模型预测控制（LTVMPC）的双层模型预测控制（MPC）算法。在轨迹规划方面，以视线坐标系下的相对轨道动力学为模型、能量最少和控制精度最优为性能指标构建最优控制问题，利用GPM精度高、收敛速度快的特点将最优控制问题转化为易于求解的全局非线性规划问题，在MPC框架下求解得到全局最优的标称轨迹，克服了传统的MPC不适用于全局大范围非线性规划的缺点；在轨迹跟踪控制方面，考虑预测时域内状态转移矩阵的时变特性，设计了LTVMPC算法对标称轨迹进行追踪，避免了存在不确定性时轨迹的重规划，从而降低在线计算量，保证算法在线自主实施，并且采用滚动优化的策略使算法对不确定性具有鲁棒性。由于规划层和控制层考虑的约束相同，因此规划的轨迹是可控、可达的。数字仿真表明，在燃料消耗和交会时间等方面，提出的方法均显著优于传统的MPC方法，相较于传统的MPC方法，新算法的交会时间减少50%左右，燃料消耗降低30%以上。

Global trajectory planning and control of rendezvous of non-cooperative targets based on double-layer MPC

For the global optimal problem of trajectory planning and tracking control in ultra-close Line-of-Sight (LOS) rendezvous of non-cooperative targets, a double-layer Model Predictive Control (MPC) algorithm is proposed based on the Gaussian Pseudo-spectral Method (GPM) and Linear Time-Varying Model Predictive Control (LTVMPC). In the layer of trajectory planning, an optimization model is established with minimum fuel and optimal control accuracy as performance indicators. The global optimal nominal trajectory is obtained by the GPM method in the MPC framework, which overcomes the disadvantage that traditional MPC is not suitable for global large-scale nonlinear programming. In the layer of trajectory tracking control, considering the time-varying characteristics of the state transition matrix in the prediction horizon, LTVMPC is used to track the nominal trajectory, so as to avoid re-planning of the trajectory in the presence of uncertainty and thus reduce online calculation and ensure online autonomous implementation of the algorithm. Due to the same constraints considered by the planning layer and the control layer, the planning trajectory is controllable and reachable. The simulation results show that the proposed method is significantly better than the traditional MPC method in terms of fuel consumption and rendezvous time. Compared with those of the traditional method, the rendezvous time and fuel consumption based on the proposed method are reduced by about 50% and 30%, respectively.