IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 4, OCTOBER 2009

Design, Fabrication, and Visual Servo Control of an XY Parallel Micromanipulator With Piezo-Actuation Qingsong Xu, Yangmin Li, Senior Member, IEEE, and Ning Xi, Fellow, IEEE

Abstract—This paper presents a complete design and development procedure of a new XY micromanipulator for two-dimensional (2-D) micromanipulation applications. The manipulator possesses both a nearly decoupled motion and a simple structure, which is featured with parallel-kinematic architecture, flexure hinge-based joints, and piezoelectric actuation. Based on pseudo-rigid-body (PRB) simplification approach, the mathematical models predicting kinematics, statics, and dynamics of the XY stage have been obtained, which are verified by the finite-element analysis (FEA) and then integrated into dimension optimization via the particle swarm optimization (PSO) method. Moreover, a prototype of the micromanipulator is fabricated and calibrated using a microscope vision system, and visual servo control employing a modified PD controller is implemented for the accuracy improvement. The experiments discover that a workspace size of 260 m 260 m with a 2-D positioning accuracy and repeatability around 0.73 and 1.02 m, respectively, can be achieved by the micromanipulator. Note to Practitioners—Designing a decoupled XY micromanipulator for the applications such as scanning probe microscope and biological cell manipulation is the major concern of this research, and a new manipulator employing parallel mechanism with flexure hinges is proposed. The dimensions of the XY stage are optimized with respect to precision and accuracy under constraints on its kinematics, statics, and dynamics performances. The manipulator is fabricated from Al alloy via the wire-electrical discharge machining (EDM) process. In order to compensate for the nonlinearity introduced by the piezoelectric actuator (PZT), joint level feedback control is adopted. To ensure the manipulation accuracy performed by the micromanipulator, both kinematic calibration and online servo control are carried out by processing images captured through a microscope vision system. The experimental results show that the designed micromanipulator is sufficient for applications with not rigorous requirements, whereas its accuracy can be further improved which heavily depends on measuring instruments available. Index Terms—Flexure mechanism, micromanipulation, motion control, parallel mechanism, piezoelectric actuation, visual servoing.

Manuscript received November 22, 2007; revised March 13, 2008. First published July 10, 2009; current version published September 30, 2009. This paper was recommended for publication by Associate Editor M. Zhang and Editor M. Wang upon evaluation of the reviewers’ comments. This work was supported in part by the research committee of the University of Macau under Grant UL016/08-Y2/EME/LYM01/FST and in part by the Macao Science and Technology Development Fund under Grant 016/2008/A1. Q. Xu and Y. Li are with the Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Taipa, Macao SAR, China (e-mail: [email protected]; [email protected]). N. Xi is with the Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824-0590 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASE.2009.2021980

I. INTRODUCTION LONG with the increasing of activities around the research and development in micro and nanoscales technology, micromanipulators with ultrahigh precision play more and more important roles in such applications as biological cell manipulation, optical fibers alignment, microcomponent assembly, and scanning probe microscopes [e.g., atomic force microscope (AFM)], etc. In order to suit the said situations, the manipulators are expected to be designed with high resolution, high repeatability, and high bandwidth capabilities, while the manipulators themselves may be in macroscale with the size of tens to hundreds of millimeters instead. The design of a proper micromanipulator satisfying all of the requirements is a challenging systematic work since it requires a multidisciplinary consideration of all issues involving kinematic schemes, mechanical joints, materials, fabrication, actuators, sensors, control schemes, and so on. In view of the cooperative contribution of parallel mechanism and compliant mechanism to an ultrahigh precision with compact size, a compliant parallel micromanipulator (CPM) featuring with parallel kinematic structure and flexure hinge-based joints is preferred for the pertinent applications [1], [2]. As an evidence, numerous CPMs with various types of motion have been proposed in the literature, e.g., [3]–[6]. In particular, due to its promising applications in micro/nanomanipulation fields, the XY CPM is the concentration of this paper. Many XY CPMs have been designed and investigated in recent works [7]–[11]. Nevertheless, most previous works on XY CPMs propose either a simple structure resulting in a coupled CPM [8]–[10] or a decoupled CPM which is at the expense of complicated structure [11]. In order to benefit the control scheme implementation and prototype fabrication in practice, a CPM with both a decoupled motion and a simple structure is desirable. In the current research, a new XY CPM making a compromise between the structure complexity and motion decoupling is proposed with a workspace of hundreds of micrometers. Moreover, a complete investigation is attempted to illustrate the design and development procedure for a CPM with ultrahigh precision since such a comprehensive work is lack in the literature. Once a proper control algorithm is implemented, the accuracy of the micromanipulator heavily depends on the measuring instruments adopted. Due to the CPM delivers only a planar motion, its output motion can be measured by resorting to displacement sensors such as capacitive or laser type [8] with a nanometer-level resolution. However, such kinds of high-performance sensors are very expensive although they are commercially available. As an alternative, a low-cost microscope

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the CPM performances by resorting to computer simulations. Here, the pseudorigid-body (PRB) model concept [13] is utilized to facilitate the design and evaluation of CPM. In order to develop a PRB model for the CPM, all of the flexure hinges are replaced by a traditional revolute joint combined with a torsional spring [14], while other elements are all considered as rigid bodies instead. Fig. 1. Schematic diagram of the XY CPM.

III. MODELING OF THE XY CPM A. Parasitic Motion Analysis

vision system is employed in the current research as a noncontact motion sensor to implement both kinematic calibration and closed-loop visual servo control strategy so as to improve the accuracy of the developed CPM up to (sub) micrometer level for micropositioning applications. Whereas before the development of the CPM, the architecture parameters need to be optimized with respect to desired performances. In order to characterize the CPM properties for dimension optimization, the establishment of mathematical models predicting kinematics, statics, and dynamics of the stage is indispensable. In the rest of this paper, the design, modeling, dimension optimization and fabrication for the new XY CPM are presented in Sections II–IV, respectively. Afterwards, the kinematic calibration, visual servo control and performance evaluation of the CPM are elaborated in Sections V and VI in sequence. Then, the achievements and limitations of the conducted research are summarized in Section VII with future works indicated. II. ARCHITECTURE DESCRIPTION OF AN XY CPM The key technique to design a decoupled 2-DOF CPM is to plane and parasitic eliminate its parasitic rotation in the translation or crosstalk coupling between the and axes. As illustrated in Fig. 1, the parallelogram flexure is adopted to eliminate the parasitic rotation of the stage. The XY stage employs flexure hinges at all joints, and consists of a mobile platform and two limbs with identical kinematic structure. Each limb consists of a parallelogram including four flexure revolute (R) hinges, and a flexure prismatic (P) hinge with lever in sequence. The P joint within each limb is fixed at the base via three fixing screws and actuated by a linear actuator. In view of the requirements of greater actuation force, higher stiffness, and faster response characteristics for the actuator, the piezoelectric actuator (PZT) is adopted to drive the stage. The main problems concerning flexure hinge are the center-shift and stress concentration phenomena [12], which lead to a degraded accuracy and fatigue risk of the CPM, respectively. Thus, the hinge with right circular shape is adopted since it possesses the smallest center-shift compared to other types, and the material with higher ratio of yield strength to Young’s modulus (such as Ti alloy, Al alloy, stainless steal, etc.) is selected to fabricate the stage. Additionally, the stroke of the adopted PZT is enlarged by utilizing the lever amplification mechanism. In the early design stage for the XY CPM, the main objective is to establish simple yet accurate enough models to predict

With reference to Fig. 2, under the situation that the CPM is driven by the first PZT, the parasitic translations induced by limbs 1 and 2 can be expressed as follows based on the PRB model: (1) (2) where in view that and are in units of millimeter, while is in unit of micrometer, i.e., , , the corresponding approximations are adopted (3) (4) Taking into account the directions of the parasitic motions, one can see that is along the positive axis, while is along the negative -direction instead. In accordance with the relationship between and , three cases may occur. To eliminate the parasitic motions in direction, the case of is expected. Accordingly, in view of (1) and (2), one can deduce that (5) Due to a symmetric structure of the CPM, it is observed that if the CPM is designed with parameters satisfying (5), the output translational motion is decoupled. Then, we have (6) (7) Another factor that may cause parasitic motions of the stage arises from the flexure hinges themselves. Although the employed right circular notch hinge has better accuracy than other types, the shift of rotation center and the compliances in other working directions still exist. Referring to Fig. 2, one can see ) is that the rotation around the axis (with stiffness the working direction of the flexure hinge. However, the hinges within legs also bear the loads along and axes (with stiffness and ) during the operation. In order to make the flexure hinge more sensitive to the rotation about the working direction and more unsensitive to the passive directions, the following two stiffness ratios should be designed as small as possible

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Fig. 2. Parameters and parasitic translations of the XY CPM.

Based upon the approximate stiffness equations given in [14], the stiffness ratios can be expanded in terms of the hinge parameters

(9) which are valid in the range of (10) so as to keep the deviations with respect to the exact models within 10% [15]. In order to design a CPM with minimum parasitic motion, both and should be reduced. Accordingly, a possible objective function for minimization can be assigned as follows: (11)

with (13) where is Young’s modulus of the material, and denotes the theoretical amplification ratio of the lever. The output displacement of the actuation P joint in limb 1 to the CPM mobile platform along brings a displacement the direction, which causes the same displacement to limb 2 in direction accordingly, as shown in Fig. 2. The displacement will then lead the four hinges constructing the parallelogram of . Likewise, the stiffness of limb limb 2 to rotate with an angle 2 in the direction can be calculated as (14) which allows the generation of the partial actuation force compensating for the internal force associated with limb 2 (15)

where

represents a set of CPM parameters to be optimized.

B. Statics Analysis 1) Static Forces Generation: Differing from the statics of a conventional parallel manipulator, the statics of a CPM solves the actuation forces which are expected to balance both external forces applied on the end-effector and internal forces arised from the deformations of flexure elements. Under the assumption of absence of external forces, the forces created by PZT should be equivalent to internal elastic forces due to the flexure hinges at the statics state. In what follows, we assume that limb 1 of the CPM is actuated by a PZT with a force and corresponding input displacement , whereas the PZT inscribed in limb 2 remains undriven. Concerning limb 1, the deformation mainly comes from the five hinges of the actuation P joint, as shown in Fig. 2. Hence, contributing to the counteraction of the the actuation force internal force in limb 1 can be calculated by a potential energy analysis as (12)

Consequently, the actuation force which induces a disof the CPM can be calculated as the summation placement and . In sequence, the actuation stiffness of the XY of CPM, i.e., the relationship between the actuation force and corresponding displacement, can be determined as follows: (16) 2) Statics Test With FEA: Considering the XY CPM with parameters described in Table I, we assume that the input disis applied on the actuation P joint asplacement sociated with limb 1. The actuation force and stiffness can be and , recomputed as spectively. The FEA is performed with ANSYS to validate the derived statics equation, where the 20-node element SOLID186 is adopted to mesh the solid model and the input displacement is assigned on the first actuation P joint. After the simulation, the deformed shape is shown in Fig. 3, and the actuation force . Furthermore, the actuation is determined as can be obtained by the FEA. stiffness

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frequency is concerned. Based on the theory of vibrations, the natural frequency of the CPM can be calculated as . With main parameters described in Table I, the natural fre. quency of the XY stage can be calculated as Moreover, the modal analysis performed with FEA via ANSYS exhibits that the first two natural frequencies are almost the same due to a symmetric structure of the CPM. Besides, compared to the FEA result (23.83 Hz), the dynamic model overestimates the natural frequency of the stage with a derivation around 15.7%.

TABLE I MAIN PARAMETERS OF THE XY CPM

IV. DIMENSION OPTIMIZATION AND PROTOTYPE DEVELOPMENT Before developing a CPM for practical application, it is a key step to determine its dimensions by taking into account its performances simultaneously. In this paper, the true values for the CPM stiffness and natural frequency are taken to be those generated from the FEA. In view of the deviations of the analytical models from the simulation results around 15%, a compensation factor is adopted in the optimization process to correct the derived models. A. Objective Function Fig. 3. Finite-element model of the XY stage.

Taking the FEA results as the benchmark, one can observe that the derived model underestimates the actuation stiffness with a deviation around 14.9%. C. Dynamics Analysis 1) Dynamic Modeling: In order to obtain a dynamic model of the XY CPM based on the Lagrangian approach, the variables are chosen as the generalized coordinates. With the assumption that the potential energies come from elastic deformations of the CPM, both potential and kinetic energies of the CPM can be expressed in terms of the selected coordinates and their derivatives. Then, a necessary calculation allows the derivation of dynamic equation (17) where is the mass matrix, is the stiffness matrix, and denotes the vector for the actuation forces, respectively, with the following notations: (18) (19) where is the mass of the mobile platform, and the masses to are indicated in Fig. 2. It is observed that the effect of damping is not included in the dynamic model (17) due to the approximations in the kinematic equations, which also indicates that the damping ratio of the CPM is very small. 2) Modal Analysis and FEA Validation: The modal analysis is necessary for the CPM design as far as the control

With the goal of enhancing the accuracy property of the CPM, the main objective for the dimension optimization is to obtain a CPM with minimum parasitic motions subject to other performance constraints, and the optimal design problem is stated below. • Variables to be optimized: , , , , and . expressed by (11). • Minimize: Objective • Subject to: . 1) Actuation stiffness value . 2) Natural frequency 3) Elimination of parasitic motion guaranteed by (5). 4) Accuracy valid range ensured by (10). , 5) Parameter ranges: , , , and . In the current optimization, five parameters need to be optimized. As far as constraint conditions are concerned, the actuation stiffness of the CPM should not exceed the stiffness of the adopted PZT, i.e., . The natural frequency should be no less than two times of the frequency of the servo system (that in this study) so as to avoid exciting is taken as resonance of the system. Besides, since the CPM will be manufactured by the wire-EDM (electrical discharge machining) process, the width of the thinnest portion for the notch hinge should be no less than 0.3 mm corresponding to the maximum tolerance of 0.01 mm. In addition, the minimum value of the distance is restricted by the length of the adopted PZT (132 mm) with the addition of proper assembly spaces, and the upper bounds for design variables are all restricted so as to generate a compact manipulator. B. Optimization and Results The particle swarm optimization (PSO) is adopted in this research since PSO has a better convergent performance for the

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TABLE II OPTIMIZED DIMENSIONS FOR THE XY STAGE

Fig. 5. Diagram of the hardware allocation.

Fig. 6. Frames of image and task spaces for the end-effector.

Fig. 4. Photograph of the XY CPM prototype and experimental setup.

robot manipulator design [16], [17]. The optimization is implemented with MATLAB, and the optimized CPM dimensions are described in Table II. Moreover, the conducted FEA simulations show that the optimized CPM possesses an actuation stiffness of 173.3 N/mm and a natural frequency of 23.8 Hz, which all satisfy the assigned performance demands generally. Besides, the manipulator has with a maximum crosstalk a workspace size of of 3.1% between the two working axes. It is noticeable that the natural frequency can be improved by reducing the overall size of the manipulator. In addition, the parasitic motions can be further lessened by making use of a nonlinear modeling of the stage for the design, which requires more computational efforts. C. Prototype Fabrication and Experimental Setup The prototype of the XY CPM with the optimized parameters is developed as graphically shown in Fig. 4. The stage is fabricated from Al 7075 alloy, which is actuated by two PZT (PAZ015 from Thorlabs, Inc.) with a stroke of and closed-loop resolution of 25 nm. The PZT is driven by a two axis controller (BPC002 from Thorlabs) with a voltage range of 0 to 75 V, and the PZT has an embedded strain gage sensory feedback to compensate for the nonlinearity effects. Moreover, a microscope vision system is used to detect the planar motion of the CPM. As shown in Fig. 4, the system consists of a lighting system, an inverted optical microscope, a CCD camera (from Watec Co., Ltd.), a PCI-based image acquisition board (from 10Moons Technology Development Co., Ltd.), and

a personal computer (Intel Pentium 4 CPU 3.00 GHz, 512 MB RAM) with image processing and control algorithms. The microscope allows a magnification ratio of 68 to 476 (calibrated on a 14-inch screen) and the lighting system gives a bright field of view (FOV). In addition, the image acquisition board can capture images (720 pixel 576 pixel) with the maximum acquisition rate of 15 frames/s. The hardware connection is illustrated in Fig. 5. Besides, an AFM probe (contact mode, from BudgetSensors, Innovative Solutions Bulgaria Ltd.) is rigidly mounted on the output platform of the CPM as an end-effector. The main parameters of the AFM probe are depicted in Fig. 6, where the . width of the probe cantilever is 50 V. KINEMATIC CALIBRATION A. Kinematic Relationships To execute either open-loop or closed-loop kinematic control of the CPM, it is necessary to calibrate the relationship between the input and output kinematics. Furthermore, since the motion of the CPM will be captured by resorting to the vision system, the relationships among the image space, task space, and joint space need to be calibrated. During the image processing, the coordinate relationship between the task and image spaces is shown in Fig. 6, where an is set in the image space. In the task image frame is assigned at the home pospace, a reference frame and sition of the AFM probe tip. With describing the position vector of point in image space and task space, respectively, the position for an object in task space can be transformed into the image space through a rotation matrix and a position vector , i.e.,

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Fig. 7. Procedures for the image processing. (a) Acquired image; (b) crop a region; (c) convert to gray image; (d) increase the image contrast; (e) convert to BW image; (f) identify the probe edge and tip center.

where

B. Calibration and Results

(21) and denotes the inverse of image resolution which is in unit . of Differentiating (20) with respect to time, yields (22) where (23) is a Jacobian matrix relating the velocity in image space to that in task space. In addition, the kinematics between the image and joint spaces can be directly related by (24) is defined as the image Jacobian to be calibrated. where , which indicates that Moreover, one can derive that the image Jacobian contains the impacts of both and the robot . Assume that remains constant during Jacobian the manipulation, it can be calibrated in the following ways.

In the calibration, the largest magnification ratio is set to generate the highest image resolution. The MATLAB software with Image Acquisition Toolbox and Image Processing Toolbox are utilized to acquire and process the images. Once the image of the AFM probe is obtained, it is processed according to the procedures, as illustrated in Fig. 7. First, the region contains the AFM probe and covers its motion range, which is cropped out from the whole image as shown in Fig. 7(b) to reduce the following processing time. For the convenience of processing as shown in Fig. 7(c), the color image is then converted into the gray style by eliminating the hue and saturation information while retaining the luminance. Then, the image contrast is increased by adjusting the image intensity values, as described in Fig. 7(d) for further processing. Afterwards, a binary BW (black-and-white) image in Fig. 7(e) is generated by using a selected threshold, and the output image has values of 1 (white) for all pixels in the input image with luminance greater than the threshold and 0 (black) for all other pixels. At last, as depicted in Fig. 7(f), the exterior boundaries of objects in the BW image are extracted, the boundary of the AFM cantilever is picked out, and the center point of the probe tip is determined in sequence. After image processing, the width of the AFM cantilever in image space is calculated as the mean value of 10 experimental data calibrated separately. The image resolution is then determined as

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The block diagram for the visual servo motion control is derepresents the desired displacescribed in Fig. 8, where ment vector in image space. It can be observed that the introduced servo controller actually adopts a PD plus two integrators control scheme. Generally, the output of the PD controller is in the form of acceleration signal, i.e., (31)

Fig. 8. Block diagram of visual servo control for the XY CPM.

In addition, it is tested that the workspace size of the CPM is . about , a total of For the sake of calibrating the image Jacobian sets of increments for the input and output displaceand ) should be recorded, which in accordance ments ( with (24), should satisfy the relationship [18] (26) where (27) (28) Accordingly, the calibrated

can be obtained as (29)

For in the experiment, the following Jacobian matrix is calibrated: (30) which indicates that the XY CPM has a nearly decoupled motion. Once the CPM moves along only the - and -axes, the parasitic translations or crosstalks in the other axis are 6.8% and 6.4%, respectively. However, for practical micromanipulation, such large coupling errors should not be neglected, which can be compensated by a closed-loop control implemented in the following discussions. VI. VISUAL FEEDBACK CONTROL AND PERFORMANCE EVALUATION According to the demands in different situations, various types of control schemes for a CPM have been proposed in the literature, and it has been shown that machine vision is an efficient tool for the servo control of micromanipulation system [19]–[24]. In this research, the image-based control is adopted for the motion control due to its attractive properties. Besides, the joint level control based on the strain gage displacement sensor embedded in the PZT actuator is implemented to eliminate nonlinearities in PZT [25]. A. Motion Control Algorithm Although many advanced control techniques have been proposed already, the proportional-integral-derivative (PID) control is employed here due to its simple architecture and wide applications in practice.

of the PZT, where which gives the acceleration and denote the displacement and veand are the proportional and derivative locity errors, and matrices, respectively. The two serially connected integral controller allows the generation of PZT displacement . Besides, the system becomes a type-II system with the adding of two integrators, which enables zero steady-state error for either a unit step or a unit ramp input. It can be shown that the current controller enables a more rapid response of the system with less steady-state error than the one presented in [26], where only one integrator is adopted to give the PZT displacement. Moreover, a single rate model with the video sampling rate is adopted to design the control system for the reason of simplicity. The control command can be generated in a digital computer as follows. , where and 1) . . 2) . 3) During the procedure, saturation functions are used to limit the resulted acceleration, velocity, and displacement within the corresponding predefined maximum values, respectively. B. Step Response and Control Results With the visual servo control, the closed-loop step response of the CPM is first generated. It is desired to locate the end-efto the center point of the fector from its home position workspace and then return to the initial position. In view of the natural frequency of the designed CPM (less than 24 Hz) as well as the period required for the image acquisition and pro, which correcessing, the time interval is set as sponds to a control frequency of 11 Hz to avoid the resonance of the CPM structure. In the experiment, the control parameters and are tuned empirof ically to eliminate both overshoot and oscillation, and the step responses in two axes of the image space are plotted in Fig. 9. From the step response curves, one can see that the system arrives at the steady state quickly after 1 second with a zero steady-state error approximately. Moreover, a time delay of can be observed from the step response plots, which is introduced by the vision system arising from the time required to capture and process the image. In many applications such as scanning probe microscopes and biological cell injection [21], [22], the line path with constraints on velocity and acceleration is sufficient. Hence, a line trajectory (with maximum velocity and acceleration: 5 and 2 ) is selected to test the performances of the online feedback control, and the experimental results are illustrated in

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Fig. 9. Closed-loop step response in U and V axes of image space.

Fig. 11. Hysteresis test results of the CPM motion. (a) General view. (b) Magnified view.

observation of the tracking errors reveals that the errors in a trajectory are proportional to the velocity in general, as shown in Fig. 10(b). C. Performance Evaluation and Discussions

Fig. 10. Control results of visual servo motion control.

Fig. 10. It is observed that the maximum tracking errors in the , two directions are about 2.5 pixel corresponding to 2.05 which are only 1/3 of the open-loop control errors. A further

In order to check the hysteresis of the CPM, one PZT is actuwith a step size of 0.5 and ated to stretch from 0 to 100 then back to the home position for the open-loop system with only the joint feedback controller, while the other PZT keeps undriven. The experimental results are shown in Fig. 11. From Fig. 11(a), one can see that the hysteresis of the system is neglectable thanks to the role of the employed PID joint controller, whereas the parasitic motion in the vertical direction ( axis) is obvious, which can be predicted by the calibrated image Ja. Furthermore, from the magnified view of the plot cobian in Fig. 11(b), the resolution, i.e., the step size of 1 pixel correof the CPM motion can be observed. It sponding to 0.82 means that the CPM resolution is tightly related to that of the displacement detecting system. Then, the 2-D positioning accuracy and repeatability of the CPM end-effector are tested by employing a visual servo controller. It is desired to position the end-effector from home posito the center of the workspace along a 45 direction. tion At the steady state when the CPM has been commanded to position the end-effector to the destination, the deviation between the real and desired positions indicates the positioning accuracy of the CPM. This experiment has been repeated ten times for accuracy evaluation, and the results are shown in Fig. 12. The CPM accuracy is defined as the deviation of mean value of the for results from the destination, which is calculated as 0.73

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Fig. 12. Positioning error of the CPM in two axes.

Fig. 13. Two-dimensional positioning error versus velocity.

the 2-D micropositioning. Moreover, the positioning repeatability is defined as the standard deviation (SD) of the ten sam. Therefore, ples of results, which has been computed as 1.02 the precision of the development micromanipulation system is for 2-D. Besides, as the rising of the constant velocity , the tracking errors in terms of the maximum and mean errors (in both and directions) are illustrated in Fig. 13. It is obvious that the tracking accuracy is deteriorated as the increasing of velocity, which reveals that the tracking error is proportional to the velocity again. As far as the limitations of the current vision micromanipulation system are concerned, one can observe that the control frequency is limited by the long time interval for image acquisition and feature extraction. On the other hand, the accuracy of the CPM is up to micrometer level due to a not high enough resolution of the employed vision system. Although the subpixel technology slicing one pixel into multiple subpixel grid can be used to enhance the image resolution, the image processing time will be further increased, which reduces the control frequency and introduces more time delay in the system as a result. Therefore, in order to implement a perfect visual control system, the image acquisition hardware with a quick processing speed and microscope with a large magnification ratio are indispensable. From this point-of-view, the accuracy characterization of the micromanipulator is dependant on the adopted measuring instruments greatly. VII. CONCLUSION This paper is focused on the design and development of a new precision XY micromanipulator, which possesses a relatively

simple structure and nearly decoupled motion. Based on the PRB simplification model, the parasitic motions of the manipulator have been analyzed in details. The statics and dynamics models are derived and validated through the FEA via ANSYS. Moreover, the optimal design for the CPM is accomplished by resorting to PSO approach in order to achieve the desired performances. A prototype has been fabricated for experimental studies. Based on a microscope vision system, the kinematic calibration and closed-loop motion control of the micromanipulator has been conducted. Due to a relatively low natural frequency of the CPM, the control frequency of 11 Hz is adopted to avoid the resonance of the structure. The experimental results , the designed show that, under a motion resolution of 0.82 micromanipulator has a workspace around with a positioning accuracy 0.73 and repeatability 1.02 in 2-D micropositioning. The tracking error is proportional to the velocity of the end-effector. It has been shown that although the designed XY CPM is not fully decoupled, an ultrahigh precision can still be achieved by means of visual servo control. The major limitations of the current feedback control and performance characterization lie in the low natural frequency of the CPM and resolution of the microvision detecting system. In order to suit applications with rigorous accuracy requirements, the natural frequency of the micromanipulator should be increased, and the hardware with higher resolution and sampling rate is expected to be integrated in the servo control loop. Such efforts will be conducted in our next step research towards a practical micromanipulation task. On the other hand, the design of a fully decoupled CPM will be attempted in our future work as well to save the efforts on feedback control, i.e., to achieve the ultrahigh precision by means of a proper calibration only.

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Yangmin Li (M’98–SM’04) received the B.S. and M.S. degrees from Jilin University, Changchun, China, in 1985 and 1988, respectively, and the Ph.D. degree from Tianjin University, Tianjin, China, in 1994, all in mechanical engineering. He is currently a Professor of Electromechanical Engineering at the University of Macau, where he also directs the Mechatronics Laboratory. He has authored about 200 scientific papers, and has served 70 international conference program committees. His research interests include micro/nanomanipulation, nanorobotics, micromanipulator, mobile robot, modular robot, multibody dynamics and control. Dr. Li is a member of the American Society of Mechanical Engineers (ASME). He currently serves as Technical Editor of the IEEE/ASME TRANSACTIONS ON MECHATRONICS, a council member and an Editor of the Chinese Journal of Mechanical Engineering, and a member of editorial board of the International Journal of Control, Automation, and Systems.

Ning Xi (S’89–M’95–F’07) received the B.S. degree in electrical engineering from the Beijing University of Aeronautics and Astronautics, Beijing, China, and the M.S. and D.Sc. degrees in systems science and mathematics from Washington University, St. Louis, MO, in 1989 and 1993, respectively. Currently, he is the John D. Ryder Professor of Electrical and Computer Engineering at Michigan State University, East Lansing. His research interests include robotics, manufacturing automation, micro/nanomanufacturing, nanosensors and devices, and intelligent control and systems. Dr. Xi received the Best Paper Award at the IEEE/RSJ International Conference on Intelligent Robots and Systems in August 1995. He also received the Best Paper Award at the 1998 Japan-U.S. Symposium on Flexible Automation. He was awarded the First Early Academic Career Award by the IEEE Robotics and Automation Society in May, 1999. He also received the Best Paper Award from the IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING in 2007. He was awarded the SPIE Nano Engineering Award in 2007. In addition, he is also a recipient of the U.S. National Science Foundation CAREER Award.

Qingsong Xu received the B.S. degree in mechatronics engineering (Hon) from Beijing Institute of Technology, Beijing, China, in 2002, and the M.S. and Ph.D. degrees in electromechanical engineering from the University of Macau, Macao, China, in 2004 and 2008, respectively. He is currently a Postdoctoral Fellow at the University of Macau. His current research interests include mechanism design, kinematics, dynamics, and control of parallel robots, micro/nanorobots, and mobile robots with various applications.

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