This article demonstrates an iterative approach for precise parallelism and gap control of two platforms. In order to achieve this goal, three linear actuators were used to adjust the posture and distance of one platform with respect to the other. Besides, motion coupling between three actuators was considered and compensated for by a model-based iterative control method. The features of the proposed method are a simple actuating mechanism, efficient sensing architecture, and robust iterative control for permissive modelling uncertainties. Experimental results show that, within 0.3 s, the desired parallelism and gap can be achieved with errors in the sensor resolution level. Therefore, the proposed method is suitable for precise parallelism and gap control of two platforms.
CarmoJPRochaRPBartekM. (2012) A review of visible-range Fabry-Perot microspectrometers in silicon for the industry. Optics & Laser Technology44: 2312–2320.
2.
ChablatDWengerPhMajouF. (2004) An interval analysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machines. The International Journal of Robotics Research23(6): 615–624.
3.
ChitnisVTVaradanKRashmiMS. (1990) Automatic mask-to-wafer alignment and gap control using moire interferometry. SPIE Proceedings, Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection1332: 613–622.
DasguptaBMruthyunjayaTS (1998) Closed-form dynamic equations of the general Stewart platform through the Newton-Euler approach. Mechanism and Machine Theory33(7): 993–1012.
6.
GengZHaynesLSLeeJD. (1992) On the dynamic model and kinematic analysis of a class of Stewart platforms. Robotics and Autonomous Systems9(4): 237–254.
7.
GoughVE (1956) Contribution to discussion of papers on research in automobile stability, control and tyre performance. Proceedings of the Automotive Division of the Institution of Mechanical Engineers171: 392–394.
8.
HladowskiLGalkowskiKRogersE. (2007) A new iterative learning control scheme for linear time-varying discrete systems. In: 3rd IFAC workshop on periodic control systems, St Petersburg, Russia.
9.
HungS-KHwuE-TChenM-Y. (2007) Dual-stage piezoelectric nano-positioner utilizing a range-extended optical fiber Fabry-Perot interferometer. IEEE/ASME Transactions on Mechatronics13(3): 291–298.
10.
IsaacsonE (1966) Analysis of Numerical Methods. New York, NY: John Wiley & Sons.
11.
KelaiaiaRCompanyOZaatriA (2012) Multiobjective optimization of parallel kinematic mechanisms by the genetic algorithms. Robotica30: 783–797.
12.
KurodaRMiyazakiTSakaiK. (1996) Method of detecting positional displacement between mask and wafer, and exposure apparatus adopting the method. Patent 5508527, USA.
13.
LeeKM (1991) A three-degrees-of-freedom micromotion in-parallel actuated manipulator. IEEE Transactions on Robotics and Automation7(5): 634–641.
14.
LeeSSongJChoiW. (2003) Position control of a Stewart platform using inverse dynamics control with approximate dynamics. Mechatronics13(6): 605–619.
15.
LevinsonHJ (2010) Principle of Lithography. Bellingham, WA: SPIE Press.
16.
LopesAM (2009) Dynamic modeling of a Stewart platform using the generalized momentum approach. Communications in Nonlinear Science and Numerical Simulation14(8): 3389–3401.
17.
MillerK (2004) Optimal design and modeling of spatial parallel manipulators. The International Journal of Robotics Research23(2): 127–140.
18.
RubenSDTsaoTCHockenRR. (2009) Mechatronics and control of a precision motion stage for nano-manufacturing. In: Proceedings of dynamic systems and control conference.
19.
SeoTWKimHSKangDS. (2008) Gain-scheduled robust control of a novel 3-DOF micro parallel positioning platform via a dual stage servo system. Mechatronics18(9): 495–505.
20.
StewartD (1965) A platform with six degrees of freedom. Proceedings of the Institution of Mechanical Engineers180(15): 371–386.
TsaiLW (2000) Solving the inverse dynamics of Stewart-Gough manipulator by the principle of virtual work. Journal of Mechanical Design122(1): 3–9.
23.
Van den BrinkMAStoeldraijerJMDLindersHFD (1992) Overlay and field-by-field leveling in wafer steppers using an advanced metrology system. SPIE Integrated Circuit Metrology, Inspection, and Process Control VI1673: 330–344.
24.
WangJWuJWangL. (2009) Dynamic feed-forward control of a parallel kinematic machine. Mechatronics19(3): 313–324.
25.
WuJWangJWangL. (2009) Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy. Mechanism and Machine Theory44: 835–849.
26.
YunjiangL (2006) Optimal design of parallel manipulators. PhD Thesis, Hong Kong University of Science and Technology, Hong Kong.
27.
ZhangJHuangDLuC (2007) Research on dynamic model and control strategy of auto-leveling system for vehicle-borne platform. In: IEEE international conference on mechatronics and automation, Harbin, China, pp. 973–977.
28.
ZhaoYGaoF (2009) Inverse dynamics of the 6-DOF outparallel manipulator by means of the principle of virtual work. Robotica27(2): 259–268.
29.
ZhouJLiuGZhangX. (2011) A method of gap control based on the principle of equal thickness interference for HARNS fabrication. Microsystem Technologies17: 101–107.
