Optimum calibration of a parallel kinematic manipulator using digital indicators

Abstract

This paper presents a calibration method for parallel manipulators using a measurement system specially installed on an external fixed frame. The external fixed frame is important as an error reference for calibration in certain operations, such as in the configuration of a parallel manipulator functioning as a machine tool where the workpiece is fixed to a worktable. The pose of the end-effector is measured using three digital indicators installed on the external fixed frame. To enable measurement, the end-effector is assumed to be a plane large enough that all digital indicators could touch. The error is defined as the difference between the theoretical and actual readings of the digital indicators. The geometric parameters of the parallel manipulator are optimized to minimize this error. This calibration method is low cost and feasible for compensating geometric parameter errors for a parallel manipulator. Optimal pose selection for the calibration is achieved using a swarm intelligence search algorithm. The method is implemented on a prototype of a six degrees-of-freedom (DOFs) Gough-Stewart platform constructed to function as a machine tool.

Keywords

Calibration / Parallel kinematic manipulator (PKM) / Digital indicator

References

[1] Jáuregui JC, Hernández EE, Ceccarelli M, Carlos LC, Alejandro García. Kinematic calibration of precise 6-DOF Stewart platform-type positioning systems for radio telescope applications. Front Mech Eng, 2013, 8(3): 252-260.

[2] Shi H, Su H-J, Dagalakis N, Kramar JA. Kinematic modeling and calibration of a flexure based hexapod nanopositioner. Precis Eng, 2013, 37(1): 117-128.

[3] Masory O, Wang J, Zhuang H (1993) On the accuracy of a Stewart platform: part II: kinematic calibration and compensation. In: Proceedings of IEEE conference on robotics and automation, pp 114–120

[4] Meng G, Li TM, Yin WS (2003) Calibration method and experiment of Stewart platform using a laser tracker. In: International conference on systems, man and cybernetics, pp 2797–2802

[5] Zhuang H, Yan J, Masory O. Calibration of Stewart platform and other parallel manipulators by minimizing inverse kinematic residuals. J Robotics Syst, 1998, 15(7): 396-406.

[6] Daney D. Kinematic calibration of the Gough platform. Robotica, 2003, 21(6): 677-690.

[7] Renaud P, Andrew N, Pierrot F, Martinet P (2004) Combining end-effector and legs observation for kinematic calibration of parallel mechanisms. In: IEEE international conference on robotics and automation, pp 4116–4121

[8] Cong D, Yu D, Han J (2006) Kinematic calibration of parallel robots using CMM. In: The sixth world congress on intelligent control and automation (WCICA), pp 8514–18

[9] Besnard S, Khalil W (1999) Calibration of parallel robots using two inclinometers. In: Proceedings of IEEE international conference on robotics & automation, pp 1758–1763

[10] Zhuang H. Self-calibration of parallel mechanisms with a case study on Stewart platform. IEEE Trans Robotics Autom, 1997, 13(3): 297-387.

[11] Wang D, Bai Y (2012) Calibration of Stewart platforms using neural networks. In: IEEE international conference on evolving and adaptive intelligent systems, pp 170–175

[12] Bai Y, Zhuang H, Wang D. Apply fuzzy interpolation method to calibrate parallel machine tools. Int J Adv Manuf Technol, 2012, 60(2): 553-560.

[13] Lee MK, Kim TS, Park KW, Kwon SH. Constraint operator for kinematic calibration of a parallel mechanism. J Mech Sci Technol, 2003, 17(1): 23-31.

[14] Kim TS, Park KW, Lee MK. Study on observability of a parallel-typed machining center using a single planar table and digital indicators. Mech Mach Theory, 2006, 41(10): 1147-1156.

[15] Nanua P, Waldron KJ, Murthy V. Direct kinematic solution of a Stewart platform. IEEE Trans Robotics Autom, 1990, 6(4): 438-444.

[16] Merlét JP. A formal-numerical approach for robust in-workspace singularity detection. IEEE Trans Robotics, 2007, 23(3): 393-402.

[17] Wang S-M, Ehmann KF. Error model and accuracy analysis of a six-DOF Stewart platform”. J Manuf Sci Eng, 2002, 124(2): 286-295.

[18] Patel AJ, Ehmann KF. Volumetric error analysis of a Stewart platform-based machine tool. Ann CIRP Manuf Technol, 1997, 46(1): 287-290.

[19] Wang J, Masory O (1995) On the accuracy of Stewart platform: part I the effect of manufacturing tolerances. In: Proceedings of IEEE international conference on robotics and automation, pp 114–120

[20] Terrier M, Dugas A, Hascoet JY. Qualification of parallel kinematics machines in high speed milling on free form. Int J Mach Tool Manuf, 2004, 44(7–8): 865-877.

[21] Besnard S, Khalil W (2001) Identifiable parameters for parallel robots kinematic calibration. In: Proceedings of IEEE international conference on robotics and automation, pp 2859–2866

[22] Patel AJ, Ehmann KF. Calibration of a hexapod machine tool using a redundant leg. Int J Mach Tools Manuf, 2000, 40(4): 489-512.

[23] Merlét JP (1999) Parallel robots: open problems. In: Proceedings of ninth international symposium of robotic research, pp 27–32

[24] Nahvi A, Hollerbach JM (1996) The noise amplification index for optimal pose selection in robot calibration. In: IEEE international conference on robotics and automation, pp 647–654

[25] Daney D (2002) Optimal measurement configurations for Gough platform calibration. In: IEEE international conference on robotics and automation, pp 147–152

[26] Daney D, Madeline B, Papegay Y. Choosing measurement poses for robot calibration with the local convergence method and Tabu search. Int J Robotics Res, 2005, 24(6): 501-518.

[27] Yang X-S, Deb S (December, 2009) Cuckoo search via Lévy flights. In: World congress on nature and biologically inspired computing (NaBIC 2009), pp 210–214