航天器近距离相对运动的鲁棒约束模型预测控制

Spacecraft proximity relative motion under robust constrained model predictive control

航天器在轨服务对近距离相对运动精确控制的需求越来越强.通过引入集合理论,采用鲁棒可变时域模型预测控制和混合整数线性规划,解决了航天器近距离相对运动的鲁棒控制问题,便于处理控制约束和状态约束,对未知有界干扰、推力误差和导航误差具有鲁棒性.首先,针对航天器近距离相对运动过程中向任意目标集的有限时间机动问题,采用离散化C-W(Clohessy-Wiltshire)动力学模型、时间-能量组合优化目标函数和线性约束表示建立了控制问题模型;其次,给出了基于约束压缩的鲁棒可变时域模型预测控制算法,可以确保鲁棒可行和鲁棒完成;引入i-步鲁棒可控集分析问题可行性,通过集合运算将导航误差处理成有界干扰,采用混合整数线性规划完成了控制器设计.最后,数值仿真验证了模型的有效性.

With the development of on-orbit service, there is an increasing desire to control spacecraft proximity operations precisely. By employing the set theory, the mixed-integer linear programming（MILP） and the variable horizon model predictive control（MPC）, we solve the robust control problem of spacecraft proximity operations, considering control constraints, state constraints, unknown bounded disturbance, control error and navigation error. Firstly, the finite-time maneuvering with a predetermined target set is formulated by the discrete C-W dynamics, the time-fuel cost function and the linear constraints. Secondly, the robust variable horizon MPC algorithm is introduced to ensure the robust feasibility and the finite-time entry of the target set. The feasibility is analyzed by using the i-step robust controllable set. The navigation error is treated as a bounded disturbance by set operations. The controller is implemented using MILP optimization. Finally, the simulation results show that the controller is efficient and robust.