For kinematic calibration of robots, we proposed using a low order Fourier series obtained by transforming the data for circular measurement paths. The errors of the realized paths were measured using a Double-Ball-Bar (DBB) system. Two nondimensional indices were proposed for evaluating the orthogonalities of the measurement paths and calibration parameters. An index was also proposed to evaluate the accuracy of the calibration with regard to measurement error. An algorithm for determining adequate measurement paths and an optimal set of a specified number of paths using these indices was also proposed. The effectiveness of the proposed method, indices, and algorithm was investigated through simulations and experiments with an experimental 6 dof in-parallel actuated worktable that we developed.
Issue Section:
Technical Papers
1.
Proc. Year 2000 Parallel Kinematic Machines Int. Conf., 2000.
2.
Takeda, Y., Funabashi, H., Kimura, M., and Hirose, K., 1999, “Development of a Spatial Six-Degree-of-Freedom In-Parallel Actuated Worktable With Rolling Spherical Bearings,” Proc. 9-th Int. Conf. Advanced Robotics (ICAR), pp. 551–556.
3.
Takeda, Y., Funabashi, H., Shen, G., Ichikawa, K., and Hirose, K., 2000, “Stiffness Analysis of a Spatial Six-Degree-of-Freedom In-Parallel Actuated Mechanism With Rolling Spherical Bearing,” Proc. Year 2000 Parallel Kinematic Machines Int. Conf., pp. 264–273.
4.
Takeda
, Y.
, and Funabashi
, H.
, 1995
, “Motion Transmissibility of In-Parallel Actuated Manipulators
,” JSME Int. J.
, 38
(4
), pp. 749
–755
.5.
Takeda
, Y.
, and Funabashi
, H.
, 1996
, “Kinematic and Static Characteristics of In-Parallel Actuated Manipulators at Singular Points and in Their Neighborhood
,” JSME Int. J.
, 39
(1
), pp. 85
–93
.6.
Takeda
, Y.
, Funabashi
, H.
, and Ichimaru
, H.
, 1997
, “Development of Spatial In-Parallel Actuated Manipulators With Six Degrees of Freedom With High Motion Transmissibility
,” JSME Int. J.
, 40
(2
), pp. 299
–308
.7.
Takeda
, Y.
, and Funabashi
, H.
, 1999
, “Kinematic Synthesis of In-Parallel Actuated Mechanisms Based on the Global Isotropy Index
,” J. of Robotics and Mechatronics
, 11
(5
), pp. 404
–410
.8.
Ota, H., Shibukawa, T., and Uchiyama, M., 2000, “Forward Kinematic Calibration Method for Parallel Mechanism Using Pose Data Measured by a Double Ball Bar System,” Proc. Year 2000 Parallel Kinematic Machines Int. Conf., pp. 57–62.
9.
Patel
, A. J.
, and Ehmann
, K. F.
, 2000
, “Calibration of a Hexapod Machine Tool Using a Redundant Leg
,” Int. J. Mach. Tools Manuf.
, 40
, pp. 489
–512
.10.
Vischer
, P.
, and Clavel
, R.
, 1998
, “Kinematic Calibration of the Parallel Delta Robot
,” Robotica
, 16
, pp. 207
–218
.11.
Wampler
, C. W.
, Hollerbach
, J. M.
, and Arai
, T.
, 1995
, “An Implicit Loop Method for Kinematic Calibration and Its Application to Closed-Chain Mechanisms
,” IEEE Trans. Rob. Autom.
, 11
(5
), pp. 710
–724
.12.
Nahvi, A., Hollerbach, J. M., and Hayward, V., 1994, “Calibration of a Parallel Robot Using Multiple Kinematic Closed Loops,” Proc. IEEE Int. Conf. Robotics and Automation, pp. 407–412.
13.
Zhuang
, H.
, Jiahua
, Y.
, and Masory
, O.
, 1998
, “Calibration of Stewart Platforms and Other Parallel Manipulators by Minimizing Inverse Kinematic Residuals
,” J. Rob. Syst.
, 15
, pp. 395
–405
.14.
Daney, D., 2002 “Optimal Measurement Configuration for Gough Platform Calibration,” Proc. IEEE Int. Conf. Robotics and Automation, pp. 147–152.
15.
Zhuang
, H.
, 1997
, “Self-Calibration of Parallel Mechanisms With a Case Study on Stewart Platforms
,” IEEE Trans. Rob. Autom.
, 13
, pp. 387
–397
.16.
Besnard, S., and Khalil, W., 2001, “Identifiable Parameters for Parallel Robots Kinematic Calibration,” Proc. 2001 IEEE Int. Conf. Robotics and Automation, pp. 2859–2866.
17.
Iurascu
, C. C.
, and Park
, F. C.
, 2003
, “Geometric Algorithms for Kinematic Calibration of Robots Containing Closed Loops
,” ASME J. Mech. Des.
, 125
, pp. 23
–32
.18.
Borm
, J. H.
, 1991
, “Determination of Optimal Measurement Configurations for Robot Calibration Based on Observability Measure
,” Int. J. Robot. Res.
, 10
(1
), pp. 51
–63
.19.
Driels
, M. R.
, and Pathre
, U. S.
, 1990
, “Significance of Observation Strategy on the Design of Robot Calibration Experiments
,” J. Rob. Syst.
, 7
(2
), pp. 197
–223
.20.
Hollerbach
, J. M.
, and Wampler
, C. W.
, 1996
, “The Calibration Index and Taxonomy for Robot Kinematic Calibration Methods
,” Int. J. Robot. Res.
, 15
(6
), pp. 573
–591
.21.
Nahvi, A., and Hollerbach, J. M., 1996, “The Noise Amplification Index for Optimal Pose Selection in Robot Calibration,” Proc. IEEE Int. Conf. on Robotics and Automation, pp. 647–654.
22.
Zhuang, H., Wang, K., and Roth, Z. S., 1994, “Optimal Selection of Measurement Configurations for Robot Calibration Using Simulated Annealing,” Proc. IEEE Int. Conf. on Robotics and Automation, pp. 393–398.
23.
Kakino, Y., Ihara, Y., and Shinohara, A., 1993, “Accuracy Inspection of NC Machine Tools by Double Ball Bar Method,” Carl Hanser Verlag.
24.
Innocenti
, C.
, 1998
, “Closed-Form Determination of the Location of a Rigid-Body by Seven In-Parallel Linear Transducers
,” ASME J. Mech. Des.
, 120
, pp. 293
–298
.25.
Salisbury
, J. K.
, and Craig
, J. J.
, 1982
, “Articulated Hands: Force Control and Kinematic Issues
,” J. Ferment. Bioeng.
, 1
(1
), pp. 4
–17
.26.
Forsythe, G. E., Malcolm, M. A., and Moler, C., B., 1977, Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs, NJ.
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