Modeling and Control of Parallel Manipulator Driven by Linear Ultrasonic Motors

Zhang Quan;Zhu Benliang;Zhou Liping;Jin Jiamei;Zhang Jianhui;State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics;School of Mechanical and Automotive Engineering,South China University of Technology;

Linear ultrasonic motors Parallel manipulator Dynamic model Contour error

The demand for precise positioning manipulators with a large workspace has increased dramatically due to their role in semiconductor manufacturing,medical surgery and automatic microassembly. In this paper,a planar parallel manipulator( PPM) actuated by three linear ultrasonic motors ( LUSMs) for high accuracy positioning is designed. With the aim to realize accurate trajectory tracking control of the proposed 3-PRR PPM,a model and contour error based controller is developedaccording to the dynamic model of the parallel manipulator. The dynamic modeling procedure is as follows: firstly,based on the closed-loop constraints of the parallel structure,kinematic analysis of the manipulator is carried out,and the inverse kinematics solution is obtained. Then thevelocities and accelerations of each part,such as rigid linkage,sliders of the motor,and the moving platform,are analyzed in order to derivethe corresponding Jacobian matrices between different coordinates. Finally,the dynamic model of the parallel manipulator is developed using virtual work principle. In a motion trackingtask,it is much more important to minimize the component of the error vector that is the normal with respect to the reference trajectory. This component of the error vector is referred to as the contour error. According to contour error theory,minimizing independent axial errors may not minimize the contour error and conversely,it is possible to have a small contour error while having large axial errors. Hence the contour error based control method is adopted to achieve precise motion tracking in this paper. The contour errorsof three planar degrees of freedom are formulated based on tangential approximation approach,and then a model and contour error based controller is developed using the feedback linearization principle.The stability of the proposed control law is proved based on Lyapunov theory. To guarantee the accuracy of the proposed control algorithm,a kinematic calibration is performed to obtain the real kinematic parameters before the control experiment. The actual position of the moving platform is captured by the CCD camera,and the error cost function is optimized by the particle swarm optimization( PSO)algorithm. Experimental results show that,the trajectory tracking errors of X and Y axes can be reduced to 15 μm using the proposed controller,which improves the motion tracking accuracy of the moving platform. The results also present that the tangential approximation approach has the better ability to approximate the real contour error.