A Study on Advanced Visual Servo Systems Design via Nonlinear Model Predictive Control

具有视觉反馈的机械系统运动控制是人类的一项基本能力。已提出的应用范围广泛，涉及制造业、汽车转向等领域。视觉反馈控制是非线性控制理论与力学几何框架、图像处理交叉的一门重要学科。本文从非线性控制理论的角度对机械臂视觉反馈控制进行了研究。首先，将相对刚体运动的三维视觉反馈控制问题视为图像特征位置的镇定问题；利用SE(3)的表示，导出了目标物体与摄像机之间的相对刚体运动动力学。根据三维视觉反馈系统的无源性和旋转矩阵的性质，导出了保证系统渐近稳定的李雅普诺夫意义上的视觉反馈控制器。其次，本研究的主要贡献是通过非线性模型预测控制的视觉反馈控制的设计和分析。基于控制Lyapunov函数和相应的反馈控制律，提出了三维视觉反馈系统的非线性模型预测稳定控制方案。该方案采用代价函数作为李雅普诺夫函数来建立稳定性。

Motion control of the mechanical systems with visual feedback is a basic ability of human being. Appli cations that have been proposed widely span manufacturing, car steering and so on. Moreover, the visual feedback control is an important discipline that lies at the intersection between nonlinear control theory and geometric framework of the mechanics and image processing. This research deals with the visual feedback control of robotic manipulators in nonlinear control theoretical aspect.Firstly, the 3-D visual feedback control problem of the relative rigid body motion is considered as the stabilization problem with respect to the image feature position. By using the representation of SE(3), the relative rigid body motion dynamics between the target object and the camera has been derived. The passivity of the 3-D visual feedback system and the rotational matrix property derive the visual feedback controller to guarantee the asymptotic stability, in the Lyapunov sense.Next, the principal contribution of this research is the design and analysis of the isual feedback control via the nonlinear model predictive control. Based on the control Lyapunov function and the corresponding feedback control law, the stabilizing nonlinear model predictive control scheme for the 3-D visual feedback system has been proposed. The proposed scheme has employed the cost function as a Lyapunov function for establishing stability.