The future researched can be summarized as follows.
1. The closed-form solutions in this dissertation assume that the robot can move its end-effector without rotation to decouple the geometry relationships into several linear steps. However, the robot should have six or more degree-of-freedom to manipulate in this way. Therefore, developing a more general closed-form solution for the hand-eye-workspace calibration which can cope with the robot arm having less than six degree-of-freedom is worth a further study.
2. The results show that using a line laser is more efficient than that using a single beam laser since a line laser projection provides more abundant information at one hand pose. Therefore, the studies of using other structured lasers, such as a cross hair, parallel lines, a dot matrix, a circle, and a rectangle, are worth to develop in the future.
3. The effectiveness of each calibration method is sensitive to the image position errors from extraction of the laser spots. In the experiments, the image position of a laser spot is determined at centroid but it is not precise. An accurate model of a laser beam projection and a camera having a high resolution and a high dynamic range may be incorporated to improve the performance. Using a camera with higher resolution to observe the same area can obtain higher spacing resolution, hence the laser spot position can be determined more precisely. Using a camera with high dynamic range can well observe illumination of the laser spot and then, the laser spot can be well captured to apply a laser beam model.
4. The proposed robot kinematic calibration method is achieved under assumption of perfect plane. Robot calibration using a laser pointer projected onto a non-planar surface could be more practical for many applications. For example, using a pre-calibrated camera to observe a conveyor surface, which flatness is not well controlled, to periodically calibrate robot is useful to extend life-cycle of the system. The study on this topic is interesting.
Reference
[1] G. Flandin, F. Chaumette, and E. Marchand, “Eye-in-hand/eye-to-hand cooperation for visual servoing,” in IEEE Int. Conf. Robotics and Automation, vol.3, pp. 2741-2746, San Francisco, Apr. 2000.
[2] S. Hutchinson, G. D. Hager, and P. I. Corke, “A tutorial on visual servo control,”
IEEE Trans. Robotics and Automation, vol. 12, no. 5, pp. 651-670, Oct. 1996.
[3] Y. Shiu and S. Ahmad, “Finding the mounting position of a sensor by solving a homogeneous transform equation of the form AX = XB,” in IEEE Int. Conf.
Robotics and Automation, vol. 4, pp. 1666-1671, Mar. 1987.
[4] R.Y. Tsai and R.K. Lenz, “Real time versatile robotics hand/eye calibration using 3D machine vision,” in IEEE Int. Conf. Robotics and Automation, vol. 1, pp.
554-561, Philadelphia, PA . USA, Apr. 1988.
[5] J.C.K. Chou and M. Kamel, “Quaternions approach to solve the kinematic equation of rotation, AaAx=AxAb, of a sensor-mounted robotic manipulator,” in IEEE Int. Conf. Robotics and Automation, vol.2, pp. 656-662, Philadelphia, PA, USA, Apr. 1988.
[6] P. Liang, J. Feng, and S. Hackwood, “A general framework for robot hand-eye coordination,” in IEEE Int. Conf. Robotics and Automation, vol. 2, pp.
1082-1087, Philadelphia, PA, USA, Apr. 1988.
[7] Y.C. Shiu and S. Ahmad, “Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB,” IEEE Trans.
Robotics and Automation, vol. 5, no. 1, pp. 16-29, Feb. 1989.
[8] R.Y. Tsai and R.K. Lenz, “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Robotics and Automation, vol. 5, no. 3, pp. 345-358, Jun. 1989.
[9] J. Dias and A. de Almeida, H. Araujo, J. Batista, “Camera recalibration with hand-eye robotic system,” in Proc. Int. Conf. Industrial Electronics, Control and Instrumentation, vol. 3, pp. 1923-1928, Kobe, Japan, Oct. 1991.
[10] H. Zhuang and Z.S. Roth, “Comments on 'Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB',”
IEEE Trans. Robotics and Automation, vol. 7, no. 6, pp. 877-878, Dec. 1991.
[11] C.C. Wang, “Extrinsic calibration of a vision sensor mounted on a robot,” IEEE Trans. Robotics and Automation, vol. 8, no. 2, pp. 161-175, Apr. 1992.
[12] H. Zhuang and Y. C. Shiu, “A noise-tolerant algorithm for robotic hand-eye calibration with or without sensor orientation measurement,” IEEE Trans.
Systems, Man and Cybernetics, vol. 23, no. 4, pp. 1168-1175, Jul./Aug. 1993.
[13] H. Zhuang, Z.S. Roth, and R. Sudhakar, “Simultaneous robot/world and
tool/flange calibration by solving homogeneous transformation equations of the form AX=YB,” IEEE Trans. Robotics and Automation, vol. 10, no. 4, pp.
549-554, Aug. 1994.
[14] H. Zhuang and Q. Zhihua, “A new identification Jacobian for robotic hand/eye calibration,” IEEE Trans. on Systems, Man and Cybernetics, vol. 24, no. 8, pp.
1284-1287, Aug. 1994.
[15] F.C. Park and B.J. Martin, “Robot sensor calibration: solving AX=XB on the Euclidean group,” IEEE Trans. Robotics and Automation, vol. 10, no. 5, pp.
717-721, Oct. 1994.
[16] R. Horaud and F. Dornaika, “Hand-eye calibration,” The international journal of robotics research, vol. 14, no. 3, pp. 195-210, Jun. 1995.
[17] G.D. van Albada and J.M. Lagerberg, A. Visser, L.O. Hertzberger, “A low-cost pose-measuring system for robot calibration,” Robotics and Autonomous Systems, vol. 15, no. 3, pp. 207-227, Aug. 1995.
[18] Y.-C. Lu and J.C.K. Chou, “Eight-space quaternion approach for robotic hand-eye calibration,” in IEEE Int. Conf. Systems, Man and Cybernetics, vol.4, pp. 3316-3321, Vancouver, BC, Canada, Oct. 1995.
[19] K. Daniilidis, E. Bayro-Corrochano, “The dual quaternion approach to hand-eye calibration,” in Int. Conf. Pattern Recognition, vol. 1, pp. 318-322, Vienna, Aug.
1996.
[20] S. Remy, M. Dhome, J.M. Lavest, and N. Daucher, Hand-eye calibration, in IEEE/RSJ Int. Conf. Intelligent Robots and Systems, vol. 2, pp. 1057-1065, Grenoble, France, Sep. 1997.
[21] F. Dornaika and R. Horaud, “Simultaneous robot-world and hand-eye calibration,”
IEEE Trans. Robotics and Automation, vol. 14, no. 4, pp. 617-622, Aug. 1998.
[22] K. Daniilidis, “Hand-eye calibration using dual quaternions,” The international journal of robotics research, vol. 18, no. 3, pp. 286-298, Mar. 1999.
[23] R.L. Hirsh, G.N. DeSouza, and A.C. Kak, “An iterative approach to the hand-eye and base-world calibration problem,” in IEEE Int. Conf. Robotics and Automation, vol. 3, pp. 2171-2176, Seoul, Korea, May 2001.
[24] J. Schmidt, F. Vogt, and H. Niemann, “Robust Hand-Eye Calibration of an Endoscopic Surgery Robot Using Dual Quaternions,” Pattern Recognition, vol.
2781, pp. 548-556, 2003.
[25] I. Fassi and G. Legnani, “Hand to sensor calibration: A geometrical interpretation of the matrix equation AX=XB,” Journal of Robotic Systems, vol. 22, no. 9, pp.
497-506, Sep. 2005.
[26] T. Heikkila, M. Sallinen, T. Matsushita, and F. Tomita, “Flexible hand-eye calibration for multi-camera systems,” in IEEE/RSJ Int. Conf. Intelligent Robots and Systems, vol. 3, pp. 2292-2297, Takamatsu, Japan, Oct./Nov. 2000.
[27] H. Malm, A. Heyden, “Simplified intrinsic camera calibration and hand-eye calibration for robot vision,” in IEEE/RSJ Int. Conf. Intelligent Robots and Systems, vol. 1, pp. 1037-1043, Las Vegas, Nevada, Oct. 2003.
[28] H. Malm and A. Heyden, “Extensions of Plane-Based Calibration to the Case of Translational Motion in a Robot Vision Setting”, in IEEE Trans. on Robotics, vol.
22, no. 2, pp. 322-333, Apr. 2006.
[29] K.H. Strobl and G. Hirzinger, “Optimal Hand-Eye Calibration,” in IEEE/RSJ Int.
Conf. Intelligent Robots and Systems, pp. 4647-4653, Beijing, China, Oct.
2006.
[30] K.H. Strobl and G. Hirzinger, “More accurate camera and hand-eye calibrations with unknown grid pattern dimensions,” in IEEE Int. Conf. Robotics and
Automation, pp. 1398-1405, Pasadena, CA, USA, May 2008.
[31] A. Malti and J.P. Barreto, “Robust hand-eye calibration for computer aided medical endoscopy,” in IEEE Int. Conf. Robotics and Automation, pp. 5543-5549, Anchorage, Alaska, USA, May 2010.
[32] A. Li, L. Wang, and D. Wu, “Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product,” Int. Journal of the Physical Sciences, vol. 5, no.10, pp. 1530-1536, Sep. 2010.
[33] C.S. Gatla, R. Lumia, J. Wood, and G. Starr, “Calibrating Pan-Tilt Cameras in Robot Hand-Eye Systems Using a Single Point,” in IEEE Int. Conf. Robotics and Automation, pp. 3186-3191, Roma, Italy, May Apr. 2007.
[34] X. Haixia, W. Yaonan, C. Wei, and L. Juan, “A self-calibration approach to hand-eye relation using a single point,” in Int. Conf. Information and Automation, pp. 413-418, Zhangjiajie, China, Jun. 2008.
[35] A. Jordt, N.T. Siebel, and G. Sommer, “Automatic high-precision self-calibration of camera-robot systems,” in IEEE Int. Conf. Robotics and Automation, pp.
1244-1249, Kobe, Japan, May 2009.
[36] S. D. Ma, “A self-calibration technique for active vision systems,” IEEE Trans.
Robotics and Automation, vol. 12, no. 1, pp. 114-120, Feb. 1996.
[37] G.Q. Wei, K. Arbter, and G. Hirzinger, “Active self-calibration of robotic eyes and hand-eye relationships with model identification,” IEEE Trans. Robotics and Automation, vol. 14, no. 1, pp. 158-166, Feb. 1998.
[38] N. Andreff, R. Horaud, and B. Espiau, “Robot hand-eye calibration using structure-from-motion,” The international journal of robotics research, vol. 20, no. 3, pp. 228-248, Mar. 2001.
[39] H. Malm and A. Heyden, “A new approach to hand-eye calibration,” in Proc. Int.
Conf. Pattern Recognition, vol. 1, pp. 525-529, Barcelona, Spain, Sep. 2000.
[40] H. Malm and A. Heyden, “Self-calibration from image derivatives for active vision systems,” in Int. Conf. Control, Automation, Robotics and Vision, vol. 2, pp. 1116-1121, Singapore, Dec. 2002.
[41] M. Staniak and C. Zieliński, “Structures for visual servos,” Robotics and Autonomous Systems, vol. 58, no. 8, pp. 940-945, Aug. 2010.
[42] Y. Liu, Y. Shen, N. Xi, R. Yang, X. Li, G. Zhang, and T. A. Fuhlbrigge, “Rapid Robot/Workcell Calibration Using Line-based Approach,” in IEEE Int. Conf.
Automation Science and Engineering, pp. 510-525, Washington DC, USA, Aug.
2008.
[43] S. Lei, L. Jingtai, S. Weiwei, W. Shuihua, and H. Xingbo, “Geometry based robot calibration method,” in IEEE Int. Conf. Robotics and Automation, vol. 2, pp.
1907-1912, New Orleans, LA, Apr. 2004.
[44] J.S. Hu, M.C. Chien, Y.J. Chang, Y.C. Chang, S.H. Su, J.J. Yang, and C.Y. Kai,
“A Robotic Ball Catcher with Embedded Visual Servo Processor,” in IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 2513-2514, Taipei, Taiwan, Oct.
2010.
[45] L. Sun, J. Liu, W. Sun, and S. Wu, X. Huang, “Geometry-based robot calibration method, in IEEE Int. Conf. Robotics and Automation, vol. 2, pp. 1907-1912, New Orleans, LA, USA, Apr./May 2004.
[46] J.S. Hu and Y.J. Chang, “Calibration of an Eye-to-Hand System Using a Laser Pointer on Hand and Planar Constraints,” in IEEE Int. Conf. Robotics and Automation, pp. 982-987, Shanghai, China May 2011.
[47] J.S. Hu and Y.J. Chang, “Eye-Hand-Workspace Calibration Using Laser Pointer Projection on Plane Surface,” Industrial Robot: An International Journal, vol. 39,
no. 2, pp. 197-207, 2012.
[48] D. Brown, “Close-range camera calibration,” Photogrammetric engineering, vol.
37, pp. 855-866, 1971.
[49] J. Heikkila and O. Silven, “A Four-step Camera Calibration Procedure with Implicit Image Correction,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1106-1112, Jun. 1997.
[50] Z. Zhang, “A Flexible New Technique for Camera Calibration,” IEEE Trans.
Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1330-1334, Nov.
2000.
[51] P.F. Sturm and S.J. Maybank, “On plane-based camera calibration: A general algorithm, singularities, applications,” in IEEE Int. Conf. Computer Vision and Pattern Recognition, pp. 432-437, Fort Collins, CO , USA, 1999.
[52] Zhang, Z., “Camera calibration with one-dimensional objects.” IEEE Trans.
Pattern Analysis and Machine Intelligence, vol. 26, no. 7, pp. 892-899, Jul.
2004.
[53] R. Shapiro, “Direct linear transformation method for three-dimensional cinematography,” Research Quarterly, vol. 49, pp. 197-205, 1978.
[54] R. I. Hartley and A. Zisserman, Multiple View Geometry in computer vision, 2nd ed., Cambridge University Press, 2003.
[55] B. Horn, “Closed-form solution of absolute orientation using unit quaternions,”
Journal of the Optical Society of America A, vol. 4, pp. 629-642, 1987.
[56] J.-Y. Bouguet, Camera calibration toolbox for Matlab.
http://www.vision.caltech.edu/bouguetj/calib_doc/.
[57] Z. S. Roth, B. W. Mooring, and B. Ravani, “An overview of robot calibration,”
IEEE Journal of Robotics and Automation, vol. 3, pp. 377-385, 1987.
[58] J. M. Hollerbach and C. W. Wampler, “The calibration index and taxonomy for robot kinematic calibration methods,” The International Journal of Robotics Research, vol. 15, p. 573, 1996.
[59] B. W. Mooring, Z. S. Roth, and M. R. Driels, Fundamentals of manipulator calibration: Wiley New York, 1991.
[60] G. Alici and B. Shirinzadeh, “Laser interferometry based robot position error modelling for kinematic calibration,” in IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pp. 3588-3593, 2003.
[61] S. Aoyagi, A. Kohama, Y. Nakata, Y. Hayano, and M. Suzuki, “Improvement of robot accuracy by calibrating kinematic model using a laser tracking system-compensation of non-geometric errors using neural networks and selection of optimal measuring points using genetic algorithm,” in IEEE/RSJ Int.
Conf. Intelligent Robots and Systems, pp. 5660-5665, 2010.
[62] A. Rauf, A. Pervez, and J. Ryu, “Experimental results on kinematic calibration of parallel manipulators using a partial pose measurement device,” IEEE Trans.
Robotics, vol. 22, pp. 379-384, 2006.
[63] P. Renaud, N. Andreff, J.-M. Lavest, and M. Dhome, “Simplifying the kinematic calibration of parallel mechanisms using vision-based metrology,” IEEE Trans.
Robotics, vol. 22, pp. 12-22, 2006.
[64] J. H. Jang, S. H. Kim, and Y. K. Kwak, “Calibration of geometric and non-geometric errors of an industrial robot,” Robotica, vol. 19, pp. 311-321, 2001.
[65] W. S. Newman and D. W. Osborn, “A new method for kinematic parameter calibration via laser line tracking,” in IEEE Int. Conf. Robotics and Automation, vol. 2, pp. 160-165, 1993.
[66] Y. Liu, Y. Shen, N. Xi, R. Yang, X. Li, G. Zhang, and T. A. Fuhlbrigge, "Rapid robot/workcell calibration using line-based approach," in IEEE Int.
Conf.Automation Science and Engineering, pp. 510-515, 2008.
[67] L. Yong, et al., "An automated method to calibrate industrial robot joint offset using virtual line-based single-point constraint approach," in IEEE/RSJ Int. Conf.
Intelligent Robots and Systems, pp. 715-720, 2009.
[68] I. W. Park, et al., "Laser-Based Kinematic Calibration of Robot Manipulator Using Differential Kinematics," IEEE/ASME Trans. Mechatronics, vol. PP, pp.
1-9, 2011.
[69] H. Zhuang and Z. S. Roth, Camera-aided robot calibration, CRC Press, 1996.
[70] J. Denavit and R. S. Hartenberg, "A kinematic notation for lower-pair mechanisms based on matrices," ASME Trans J. Appl. Mech, vol. 23, pp.
215-221, 1955.
[71] M. R. Driels, W. Swayze and S. Potter, “Full-pose calibration of a robot manipulator using a coordinate-measuring machine,” The International Journal of Advanced Manufacturing Technology, vol. 8, pp. 34-41, 1993
[72] J.-Y. Bouguet, Camera calibration toolbox for Matlab.
http://www.vision.caltech.edu/bouguetj/calib_doc/.
[73] P. I. Corke, "A robotics toolbox for MATLAB," Robotics & Automation Magazine, IEEE, vol. 3, pp. 24-32, 1996.
[74] Y. I. Abdel-Aziz and H. M. Karara, “Direct linear transformation into object space coordinates in close-range photogrammetry”, in Proc. of the Symposium on Close-Range Photogrammetry, Urbana, pp. 1-18, 1971.
[75] R. Shapiro, “Direct linear transformation method for three-dimensional cinematography”, Research Quarterly, vol. 49, pp. 197– 205, 1978.
[76] H. Bacakoglu and M. S. Kamel, “A three-step camera calibration method”, IEEE IEEE Trans. Instrumentation and Measurement, vol. 46 no. 5, pp. 1165-1172, 1997.
[77] R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses”, IEEE Journal of Robotics and Automation, vol. 3, no.4, pp. 323-344, 1987.
[78] H. Zhuang, Z. S. Roth, X. Xu, and K. Wang, “Camera calibration issues in robot calibration with eye-on-hand configuration”, Robotics and Computer-Integrated Manufacturing, vol. 10, no. 6, pp. 401-412, 1993.
[79] B.K. Ghosh, T.J. Tarn, N. Xi, Z. Yu, and D. Xiao, “Robotic motion planning and manipulation in an uncalibrated environment”, IEEE Robotics and Automation Magazine, vol. 5, no. 4, pp. 50-57, 1998.
[80] R. Willson, Modeling and Calibration of Automated Zoom Lenses, Ph.D. thesis, Department of Electrical and Computer Engineering, Carnegie Mellon University, 1994.