In this article, a robust nonlinear model predictive control (NMPC) scheme is proposed for the visual servoing of quadrotors subject to external disturbances. By using the virtual camera approach, the image moments are defined in the virtual camera plane and adopted as visual features to derive the decoupled image kinematics. As a result, the image-based visual servoing (IBVS) system model is established by integrating the image kinematics and quadrotor dynamics. To handle the visibility constraint, a robust NMPC scheme is developed for the IBVS of the quadrotor such that the visual target can stay within the field of view of the camera. In addition, based on the Lipschitz condition, the tightened state constraints are constructed to tackle external disturbances. The sufficient conditions on guaranteeing recursive feasibility of the proposed NMPC algorithm are derived. Furthermore, we theoretically show that the tracking error will converge to a small set around the origin in finite time under some derived conditions. Finally, simulation studies and experimental tests are conducted to verify the efficacy of the proposed method.

中文翻译：

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基于稳健非线性模型预测控制的四旋翼无人机视觉伺服

在本文中，提出了一种鲁棒的非线性模型预测控制（NMPC）方案，该方案用于受到外部干扰的四旋翼的视觉伺服。通过使用虚拟相机方法，可以在虚拟相机平面中定义图像矩，并将其用作视觉特征以导出解耦的图像运动学。结果，通过集成图像运动学和四旋翼动力学，建立了基于图像的视觉伺服（IBVS）系统模型。为了处理可见性约束，针对四旋翼飞行器的IBVS开发了鲁棒的NMPC方案，以使视觉目标可以停留在摄像机的视场内。此外，基于Lipschitz条件，构造了严格的状态约束以应对外部干扰。推导了保证所提NMPC算法递归可行性的充分条件。此外，我们从理论上证明，在某些导出条件下，跟踪误差将在有限时间内收敛到原点周围的一小部分。最后，进行了仿真研究和实验测试，以验证该方法的有效性。