基于误差模型的多约束鲁棒编队控制器的设计

Design of multi-constraint robust formation controller based on error model

无人机(unmanned aerial vehicle,UAV)编队是一个复杂的非线性系统,四旋翼无人机虽然具有诸多优点,但是其动力学模型却是非线性、耦合、欠驱动的,并且物理约束、模型的不确定性以及外界干扰等因素会显著降低基于模型控制器的控制性能。因此,针对四旋翼的编队问题,提出了一种基于误差模型的多约束模型预测控制(model predictive control,MPC)策略。利用拉格朗日-欧拉公式建立无人机的三维空间(three-dimensional,3D)模型,并将四旋翼模型分为旋转子系统(rotational subsystem,RS)和平移子系统(translational subsystem,TS),分别针对2个子系统设计对应的多约束模型预测控制器,增广模型中嵌入了积分器,因此能够消除外部干扰引起的跟踪误差。相较于通常情况下的MPC(regular MPC,RMPC),文中所采用的经过修改的MPC(modified MPC,MMPC),通过对成本函数进行合理修改,不仅能够保证控制器在求解过程中子系统的渐近稳定性,也同时保证了闭环系统的稳定性。在此基础上,对以上算法进行了稳定性分析。仿真结果表明,MMPC不仅具有编队良好的路径跟踪能力,还能够保证在多约束和干扰存在的情况下,取得良好的控制性能。

UAVs formation is a complex nonlinear system. Although quadrotor has many advantages, its dynamics model is nonlinear, coupled, and under driven. For model-based controller design, physical constraints, model uncertainties and external disturbances significantly deteriorate control performance. Therefore, a multi-constraints MPC strategy based on error model is proposed for the quadrotor formation. Firstly, a 3 D model for quadrotor is established by using the Lagrange-Euler formulation, in which the model is divided into RS and TS. The corresponding multi-constraint MPC is designed for the two subsystems respectively. The tracking errors caused by external disturbances can be eliminated because of the integrator embedded in the augmented model. Comparing with RMPC, by making reasonable modifications to the cost function, the asymptotic stability of the open loop and the closed-loop subsystem can be ensured by MMPC. Moreover, the stability analysis of the above-mentioned algorithm is carried out. The simulation results show that the controller of the formation can not only achieve good path tracking, but also robustness to the multiple constraints and disturbances.