Abstract
This paper presents a new perspective on the calibration of industrial robotics systems by describing robot position errors as time varying variations of the actual positions of the end-effector from the target position, the error calibration of a robotics manipulator is treated as a “process” rather than a “state”. Therefore the theory of variations is applicable. The importance of distinguishing the two kinds of variations, namely random system variations and assignable variations, in a robot calibration process is demonstrated through a Monte Carlo simulation.
Statistical process control techniques provide a tool for measuring and characterising the position errors of robotics manipulators. Their application in this work, not only focuses on the development of mathematical formulation of calibration models, but provides a deeper understanding of the randomness of the errors in robot systems.
It is also shown that if a robot system is adjusted for its random errors to compensate for undesirable results, the resulting output will be worse than if the robot system alone was not adjusted.
Similar content being viewed by others
References
L. J. Everett, M. Driels and B. W. Mooring, “Kinematic modelling for robot calibration”,Proceedings of the 1987 IEEE International Conference on Robotics and Automation, vol. 1, pp. 183, 1987.
Z. S. Roth, B. W. Mooring and B. Ravani, “An overview of robot calibration”,IEEE Journal of Robotics and Automation,3(5), pp. 121–128, 1987.
C. Wu, “The kinematic error model for the design of robot manipulators”,Proceedings of the American Control Conference, San Francisco, CA, pp. 497–502, 1983.
R. Ibarra and N. D. Perreira, “Determination of linkage parameter and pair variable errors in open chain linkages using a minimal set of pose measurement data”,ASME Journal of Mechanisms, Transmissions, and Automation in Design 108 (2), p. 159, 1986.
K. J. Waldron and A. Kumar, “Development of a theory of errors for manipulators”,Proceedings of the Fifth World Congress on the Theory of Machines and Mechanisms, pp. 821–826, 1987.
J. Denavit and R. S. Hartenberg, “A kinematic notation for lower pair mechanisms based on matrices”,ASME Journal of Applied Mechanics, vol. 41, p. 215, 1955.
D. E. Whitney, C. A. Lozinski and J. M. Rourke, “Industrial robot calibration method and results”,Proceedings of the 1984 International Computers in Engineering Conference and Exhibit, vol. 1, pp. 92–100, 1984.
J. Chen and L. M. Chao, “Positioning error analysis for robot manipulator with rotary joints”,Proceedings of the 1986 IEEE International Conference on Robotics and Automation, vol. 2, p. 1011, 1986.
S. A. Hayati, “Robot arm geometric link parameter estimation”,The 22nd Conference of IEEE Control System Society, Decision and Control, San Antonio, Texas, vol. 3, pp. 1477–1483, December 1983.
T. W. Hsu and L. J. Everett, “Identification of the kinematic parameters of a robot manipulator for positional accuracy improvement”,Proceedings of the 1985 Computers in Engineering Conference and Exhibition, pp. 263–267, 1985.
K. W. Veitschegger and C. H. Wu, “Robot accuracy analysis”,Proceedings of the IEEE Conference on Cybernetics and Society, p. 425, 1985.
K. W. Veitschegger and C. H. Wu, “Robot accuracy analysis based on kinematics”,IEEE Journal of Robotics and Automation,2(3), p. 171, 1986.
K. W. Veitschegger and C. H. Wu, “A method for calibrating and compensating robot kinematic errors”,Proceedings of the 1987 IEEE International Conference on Robotics and Automation, vol. 1, pp. 39–44, 1987.
S. A. Hayati and M. Mirmirani, “A software for robot geometry parameter estimation”,ASME Paper Presented at Robots West Conference, Anaheim, CA, November 1984.
B. W. Mooring, “The effect of joint axis misalignment on robot positioning accuracy”,ASME Proceedings of the 1983 International Computers in Engineering Conference and Exhibition, Chicago, vol. 2, pp. 151–155, 1983.
B. W. Mooring and G. R. Tang, “An improved method for identifying the kinematic parameters in a six axis robot”,ASME Proceedings of the 1984 International Computers in Engineering Conference and Exhibition, vol. 1, pp. 79–84, 1984.
H. W. Stone, A. C. Sanderson and C. P. Neumann, “Arm signature identification”,Proceedings of the 1986 IEEE International Conference on Robotics and Automation, San Francisco, CA, vol. 1, pp. 41–48, April 1986.
R. N. Vaishnav and E. B. Magrab, “A general procedure to evaluate robot positioning errors”,The International Journal of Robotics Research,6(1), pp. 81–86, Spring 1987.
J. Chen and Y. F. Chen, “Estimation of coordinate measuring machine error parameters”,Proceedings of the 1987 IEEE International Conference on Robotics and Automation, vol. 1, pp. 196–201, 1987.
Z. G. Qian and K. Kazerounian, “Kinematics identification of robotic manipulators”,Proceedings of 1st Applied Mechanisms and Robotics Conference, Cincinati, November 1989.
Z. G. Qian and K. Kazerounian, “Dynamic calibration for serial manipulators based on zero position analysis method”,Proceedings of ASME Design Automation Conference, Montreal, September 1989.
C. G. Atkenson, C. H. An and J. M. Hollerbach, “Rigid body load identification for manipulators”,Proceedings of the 24th IEEE Conference on Decision and Control, pp. 996–1001, December 1985.
A. Mukerjee and D. H. Ballard, “Self calibration in robot manipulators”,IEEE Transactions on Robotics and Automation, vol. 3, pp. 1050–1057, 1985.
P. G. Hoel,Introduction to Mathematical Statistics, 3rd edn, John Wiley & Sons, pp. 335–341, 1966.
H. Hacquebord, “Statistical thinking for leaders — profound knowledge for applying Dr Deming's management theory”, Management Seminar, 1991.
Shewart 1927.
W. E. Deming,Out of the crisis, MIT Center for Advanced Engineering Study, Cambridge, MA, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Qian, G.Z., Kazerounian, K. Statistical error analysis and calibration of industrial robots for precision manufacturing. Int J Adv Manuf Technol 11, 300–308 (1996). https://doi.org/10.1007/BF01351287
Issue Date:
DOI: https://doi.org/10.1007/BF01351287