基于空间离散化的机器人位置校正方法研究
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摘要
精度是衡量机器人实用性的重要参数。随着机器人技术的快速发展,工业生产对机器人的精度要求也日益提高。为了提高机器人的工作质量,使其满足高精度的工作要求,就要不断深入研究工业机器人位置校正方法。本文提出了一种新的工业机器人位置校正方法,即采用测量机器人与工业机器人末端对接,工业机器人带动测量机器人在工业机器人工作空间网格点上测量末端位置,与名义位置相比较,得到工业机器人工作空间误差网格,将其转化到名义坐标空间网格,建立误差数据库。工业机器人工作时,调用空间误差数据库,择优选择空间插值点进行空间误差插值,对名义位置进行补偿。再用测量机器人对补偿后的工业机器人重新测量,对误差补偿性能进行评价。对FANUC_M_6iB机器人运动学分析,介绍了两种机器人工作空间的求解方法,求解出了机器人的工作空间。对机器人工作空间采用了映射法原理进行网格划分,进而进行工作空间的离散化,建立空间误差网格模型。对于网格节点外的位置校正采用双线性插补方法插补。阐述了FARO测量手臂的工作原理,建立了测量臂的数学模型,为网格节点测量结果的数值变换和误差求解奠定了基础。最后利用Matlab的较强的数学计算功能和Access足量的数据存储功能,与工业机器人控制软件相结合,采用Visual C++编写机器人位置校正软件。
Accuracy is a very important parameter to evaluate the practicality of the robot. With the rapid development of robotics, industrial production requires that the quality of robot being improved day by day. In order to improve the work quality of robot, to make the requirement of robot high precision, it is necessary to develop in-depth study of industrial robot calibration method. The dissertation put forward an industrial robot position calibration method. By a hinge linking up the end of industrial robot and measurement robot, the measurement robot is driven by the industrial robot to measure the end position at the space grid of industrial robots automatically. Compared with the nominal position, we can get the space error grid of industrial robots and transform the space error into the nominal coordinate’s space error grid and establish the error database. When industrial robot is working, the space error database is invoked and the space interpolation point is selected for space error interpolation to compensate the nominal position. The industrial robot compensated is re-surveyed by measurement robot and evaluate the performance of the error compensation. The dissertation elaborated the FANUC_M_6iB robot kinematics analysis, introduces two kinds of robot work space solution method and solved the robot work space. The robot work space was meshed based on mapping method principle, and then discrete working space. Construct the model of space error grid. With the location outside the grid node calibrated using bilinear interpolation method. The dissertation introduced the working principle of FARO arm, set up the mathematical model of measuring arm, and laid foundation for numerical transform and error solving of the grid node measurements. At last, the dissertation adopts Matlab‘s strong math calculation functions and Access‘s adequate data storage functions, combined with industrial robot control software, adopts Visual C++ to compile the robot position calibration procedures.
Accuracy is a very important parameter to evaluate the practicality of the robot. With the rapid development of robotics, industrial production requires that the quality of robot being improved day by day. In order to improve the work quality of robot, to make the requirement of robot high precision, it is necessary to develop in-depth study of industrial robot calibration method. The dissertation put forward an industrial robot position calibration method. By a hinge linking up the end of industrial robot and measurement robot, the measurement robot is driven by the industrial robot to measure the end position at the space grid of industrial robots automatically. Compared with the nominal position, we can get the space error grid of industrial robots and transform the space error into the nominal coordinate’s space error grid and establish the error database. When industrial robot is working, the space error database is invoked and the space interpolation point is selected for space error interpolation to compensate the nominal position. The industrial robot compensated is re-surveyed by measurement robot and evaluate the performance of the error compensation. The dissertation elaborated the FANUC_M_6iB robot kinematics analysis, introduces two kinds of robot work space solution method and solved the robot work space. The robot work space was meshed based on mapping method principle, and then discrete working space. Construct the model of space error grid. With the location outside the grid node calibrated using bilinear interpolation method. The dissertation introduced the working principle of FARO arm, set up the mathematical model of measuring arm, and laid foundation for numerical transform and error solving of the grid node measurements. At last, the dissertation adopts Matlab‘s strong math calculation functions and Access‘s adequate data storage functions, combined with industrial robot control software, adopts Visual C++ to compile the robot position calibration procedures.
引文
[1] RothZ, Benjamin W, Mooring, Bahram R. An overview of robot calibration [J]. IEEE Journal of Robotics and Automation, 1987, 03:377-385
[2]王东署.工业机器人标定技术研究.东北大学博士论文[J] . 2006.02
[3] Zhuang H Q and Roth Z S. Camera-aided Robot Calibration [M]. Florida: CRC Press, 1996.
[4] Hayati, S.A. Robot arm geometrical link Parameter estimation [C]. Proceedings of the 22nd IEEE conference and decision and control, 1983:1477-1483
[5] Judd R.P, Knasindki A.B. A technique to calibrate industrial robots with experimental verification [J]. IEEE Translation on robotics and automation, 1990, 6(1):20-30
[6] Henry W. Stone, Arthur C. Sanderson. Statistical Performance evaluation of the S- model arm signature identification technique [J]. IEEE Transactions on robotics and automation, 1988, 4:939-946
[7] Driels M.R, Pathre U.S. Robot manipulator kinematic compensation using a generalized Jacobian formulation [J]. Journal of robotic system, 1987, 4(2):259-280
[8] Hanqi Zhuang, Zvi S. Roth. A complete and parametrically continuous kinematic model for robot manipulators [J]. IEEE transaction on robotics and automation, 1992, 8(4):451-463
[9] Klaus Schroer, Stephen L. Albright, Michael Grethlein. Complete, minimal and model-continuous kinematic models of robot calibration [J]. Robotics & Computer integrated manufacturing, 1997, 13(1):73-85
[10] Sheth P.N, Uicker J.J. IMP (Integrated Mechanisms program), A computer aided design analysis system for mechanisms and linkages [J]. ASME journal of engineering for industry, 1992, 94:454-464
[11] K. Kazerounian, G. Z. Qian. Kinematic calibration of an industrial manipulator [J]. ASME journal of mechanisms, transmission and automation in design, 1989, 111:482-487
[12] Chen I M, Yang G L, Tan C T. Local POE model for robot kinematic calibration [J]. Mechanism and machine theory, 2001, 36:1215-1239
[13] Guilin Yang, I-Ming Chen, Wee Kiat Lim, Song Huat Yeo. Self-calibration of three-legged modular reconfigurable Parallel robots based on leg-end distance errors [J]. Robotic, 2001,19:187-198
[14] D.Payannet, M. J. Aldon, and A. Liegeois, Identification and Compensation of Mechanical Errors for Industrial Robots, in Proc. 15th ISIR (Tokyo), Sept. 1985:857-864
[15] G.Z. Qian and K. Kazerounian. Statistical error analysis and calibration of industrial robots for precision manufacturing, International Journal of Advanced Manufacturing Technology, Vol. II(1996):300-308
[16] Mahajan A and Figueroa F. An automatic self-installation and calibration method for a 3D position sensing system using ultrasonics [J]. Robotics and Autonomous System, 1999, 28:281-294
[17] Chou T N and Wykes C. An integrated ultrasonic system for detection, recognition and measurement [J]. Measurement, 1999. 26:179-190
[18] Zhang P, Larsson C N. An infrared target searching gyrator for robot calibration [A]. In: Proceedings, 8th International Conference on Advanced Robotics [C], 1997. ICAR '97., 1997:957-961
[19] Bernard F B, Johann P and Christian E. Efficient tracking of 3D-robot positions by dynamic triangulation [A]. In: IEEE Instrumentation and Measurement Technology Conference, IMTC98 Session on Instrumentation and Measurement in Robotics [C], St. Paul, Minnesota, May 18-21, 1998:446-449
[20] Tsai, R.Y.; Lenz, R.K. A new technique for fully autonomous and efficient 3D robotics hand/eye calibration, IEEE Transactions on Robotics and Automation, Volume: 5 Issue: 3 , June 1989,Page(s): 345-358
[21]盛昭瀚,曹忻.最优化方法基本教程.南京:东南大学出版社, 1992
[22] Renders J M, Rossignol E, et al. Kinemetic Calibration and Geometrical Parameter Identification for Robots [J]. IEEE Transactions on Robotics and Automation. 1991, 7(6):721-732
[23]王平均,张晓春.电子经纬仪检定探讨.中国计量,2008.08:109-110
[24]杨晓东,刘春太,申长雨等.内部带特征约束的任意平面域的三角形网格生成方法.计算物理,2000.3:293-298
[25] Driels M R and Pathre U S. Vision-based automatic theodolite for robot calibration [J]. IEEE Transactions on Robotics and Automation, 1991, 7(3):351-360
[26] Hanqi Zhuang, and Zvi S. Roth, Camera-aided calibration, 1996
[27] William K, VEITSCHEGGER and CHI-HAUR WU. Robot Calibration and Compensation, IEEE Journal of Robotics and Automation, 1988. Vol.4, No.6, pp.643-656
[28]王兴松.挠性机器人运动误差的集成傲光测量与补偿策略.中国机械工程,1997.Vol.8:15-18
[29]崔鲲,孙论强,吴林. V01弧焊机器人结构参数标定和变换矩阵的建立[J].焊接,1996(9):2-6
[30]宋月娥,吴林,张连新等.弧焊机器人离线编程系统标定模块的开发[J].机器人,2001.23(7):689-670
[31]蔡鹤皋,张超群,吴伟国.机器人实际几何参数识别与仿真[J].中国机械工程,1998.9(10):11-14
[32]朴用杰,邱涛,陈善本.弧焊机器人TCF参数的标定[J].机器人,2001.23(2):109-112
[33]宋月娥,吴林,田劲松等.用于机器人离线编程的工件标定算法研究[J].哈尔滨工业大学学报,2002, 34(6):735-738
[34]李金泉,陈善本,吴林.用于手眼立体视觉的弧焊机器人平面工件定位系统[J].焊接学报,2003, 24(4):9-14
[35]刘振宇,陈英林,曲道奎等.机器人标定技术研究[J].机器人,2002.24(5):447-450
[36]张建忠.机器人连杆参数的视觉标定[J].制造业自动化,2004.26(11):32-34
[37] Paul R P. Robot Manipulations: Mathematics, Programming, and Control [M]. Cambridge: The MIT Press, 1981
[38] Zhuang H Q and Roth Z S. Camera-aided Robot Calibration [M]. Florida: CRC Press, 1996
[39] Ziegert J, Datseris P. Basic consideration for robot calibration [A]. In: IEEE International Conference on Robotics and Automation [C], 1988(2): 932-938
[40]李发忠,赵德安,马从国. FANUC_M-6IB型机器人运动学逆解研究.机械设计与制造,2008.10:174-176
[41]孔凡斌,姜培刚,宋玲玲.基于UG Open C的FANUC_M-16iB/20工业机器人动态仿真.计算机应用与软件,2008.6:169-171
[42] A.Y. Elatta, Li Pei Gen, Fan Liang Zhi, Yu Daoyuan, Luo Fei. An overview of robot calibration techniques [J]. Information Technology Journal 2004.3(l):74-78
[43] I-Ming Chen, Guilin Yang. Kinematic calibration of modular reconfigurable robots using product of exponentials formula [J]. Journal of robotic systems, 1997.14(11):807-821
[44] T. Alban, H. Janocha. Dynamic calibration of industrial robots with inertial measurement systems [J]. www.google.com
[45] Ambarish Goswami, Arthur Quaid, Michael Peshkin. Complete parameter identifieationof a robot from partial pose information [C].1993 IEEE International Conference Robotic and Automation
[46] J. Hefele. Real-time photogrammetric algorithms of robot calibration [C]. The intenrational Archives of the photogrammetry, remote sensing and spatial information sciences, VoL 34, Part XXX
[47] Robert John Homing. A comparison of identification techniques for robot calibration [D]. Case Western Reserve University, Degree of Master of Science, August, 1998
[48]刘万里,曲兴华,闫永刚.便携式三坐标测量臂校准和误差补偿.仪器仪表学报,2006.04
[49]赵俊伟,代军.基于数据库查询的工业机器人误差补偿方法研究.基础与液压, 2008.11:5-17
[50]钟勇,朱建新.一种新的机器人工作空间求解方法.机床与液压,2004.No.4:66-67
[51]范守文,徐礼拒.机器人工作空间分析的解析法.电子科技大学,2006.7:194-197
[52]马香峰.机器人机构学.北京二机械工业出版社,1991.9
[53]段齐骏,黄德耕,李士楠.机器人工作空间与包容空间的图解法.南京理工大学学报,1996,20(4):318-322
[54]赵才军.机器人工作空间及关节运动可靠性规划.硕士学位论文,2003.3
[55] W A Cook, W R Oakes, Mapping Methods for Generating Three-Dimensional Meshes, Computers in Mechanical Engineering, 1982.8:67-72
[56]曲道奎,徐方.提高大型激光加工机器人精度的方法.机器人,2003.5:270-275
[57]吕恬生.工业机器人运动学校准的理论、方法及实验研究.硕士学位论文,2002.2
[58] William K.,VEITSCHEGGER and CHI-HAUR WURobot Calibration and Compensation, IEEE Journal of Robotics and Automation, Vol.4, No.6,pp.643-656
[59]唐蓉城,丁其志,郭玉申.装配机器人误差补偿的研究.机械设计,1999.7
[60]房勋. 3-PRS串并联机构位置正解的研究.河南理工大学硕士学位论文,2007.12
[61]杨建国,刘然.在Visual C++中不依赖MATLAB环境调用其函数的方法.计算机应用基础,2001.6:98-99
[62]万伟民,赵锡芳,张华.工业机器人校正技术及软件设计.南昌大学学报,2004.6:1-4
[63]孔凡斌,姜培刚,宋玲玲.基于UG Open C的FANUC_M-16iB/20工业机器人动态仿真.计算机应用与软件,2008.6:169-171
[64] Zhao Junwei, Dai Jun, Huang Junjie. 3-PRS Serial-Parallel Robot Error Modeling and Parameter Identification. 2008 Sino-European Workshop on Intelligent Robots and Systems. December 11-13, 2008 Chongqing University of Posts & Telecommunications Chongqing, China. (P241-245)
[65] Zhao Junwei, Dai Jun, Huang Junjie. 3-PRS Serial-Parallel Machine Tool Error Calibration and Parameter Identification. Int.重庆邮电大学学报,2009.2
[66] Zhao Jun-wei, Hu Yan-hui,Chen Guo-qiang. A new method for measuring the end error of the industrial robot. 2008 Sino-European Workshop on Intelligent Robots and Systems. December 11-13, 2008 Chongqing University of Posts & Telecommunications Chongqing, China. (P392-395)
[2]王东署.工业机器人标定技术研究.东北大学博士论文[J] . 2006.02
[3] Zhuang H Q and Roth Z S. Camera-aided Robot Calibration [M]. Florida: CRC Press, 1996.
[4] Hayati, S.A. Robot arm geometrical link Parameter estimation [C]. Proceedings of the 22nd IEEE conference and decision and control, 1983:1477-1483
[5] Judd R.P, Knasindki A.B. A technique to calibrate industrial robots with experimental verification [J]. IEEE Translation on robotics and automation, 1990, 6(1):20-30
[6] Henry W. Stone, Arthur C. Sanderson. Statistical Performance evaluation of the S- model arm signature identification technique [J]. IEEE Transactions on robotics and automation, 1988, 4:939-946
[7] Driels M.R, Pathre U.S. Robot manipulator kinematic compensation using a generalized Jacobian formulation [J]. Journal of robotic system, 1987, 4(2):259-280
[8] Hanqi Zhuang, Zvi S. Roth. A complete and parametrically continuous kinematic model for robot manipulators [J]. IEEE transaction on robotics and automation, 1992, 8(4):451-463
[9] Klaus Schroer, Stephen L. Albright, Michael Grethlein. Complete, minimal and model-continuous kinematic models of robot calibration [J]. Robotics & Computer integrated manufacturing, 1997, 13(1):73-85
[10] Sheth P.N, Uicker J.J. IMP (Integrated Mechanisms program), A computer aided design analysis system for mechanisms and linkages [J]. ASME journal of engineering for industry, 1992, 94:454-464
[11] K. Kazerounian, G. Z. Qian. Kinematic calibration of an industrial manipulator [J]. ASME journal of mechanisms, transmission and automation in design, 1989, 111:482-487
[12] Chen I M, Yang G L, Tan C T. Local POE model for robot kinematic calibration [J]. Mechanism and machine theory, 2001, 36:1215-1239
[13] Guilin Yang, I-Ming Chen, Wee Kiat Lim, Song Huat Yeo. Self-calibration of three-legged modular reconfigurable Parallel robots based on leg-end distance errors [J]. Robotic, 2001,19:187-198
[14] D.Payannet, M. J. Aldon, and A. Liegeois, Identification and Compensation of Mechanical Errors for Industrial Robots, in Proc. 15th ISIR (Tokyo), Sept. 1985:857-864
[15] G.Z. Qian and K. Kazerounian. Statistical error analysis and calibration of industrial robots for precision manufacturing, International Journal of Advanced Manufacturing Technology, Vol. II(1996):300-308
[16] Mahajan A and Figueroa F. An automatic self-installation and calibration method for a 3D position sensing system using ultrasonics [J]. Robotics and Autonomous System, 1999, 28:281-294
[17] Chou T N and Wykes C. An integrated ultrasonic system for detection, recognition and measurement [J]. Measurement, 1999. 26:179-190
[18] Zhang P, Larsson C N. An infrared target searching gyrator for robot calibration [A]. In: Proceedings, 8th International Conference on Advanced Robotics [C], 1997. ICAR '97., 1997:957-961
[19] Bernard F B, Johann P and Christian E. Efficient tracking of 3D-robot positions by dynamic triangulation [A]. In: IEEE Instrumentation and Measurement Technology Conference, IMTC98 Session on Instrumentation and Measurement in Robotics [C], St. Paul, Minnesota, May 18-21, 1998:446-449
[20] Tsai, R.Y.; Lenz, R.K. A new technique for fully autonomous and efficient 3D robotics hand/eye calibration, IEEE Transactions on Robotics and Automation, Volume: 5 Issue: 3 , June 1989,Page(s): 345-358
[21]盛昭瀚,曹忻.最优化方法基本教程.南京:东南大学出版社, 1992
[22] Renders J M, Rossignol E, et al. Kinemetic Calibration and Geometrical Parameter Identification for Robots [J]. IEEE Transactions on Robotics and Automation. 1991, 7(6):721-732
[23]王平均,张晓春.电子经纬仪检定探讨.中国计量,2008.08:109-110
[24]杨晓东,刘春太,申长雨等.内部带特征约束的任意平面域的三角形网格生成方法.计算物理,2000.3:293-298
[25] Driels M R and Pathre U S. Vision-based automatic theodolite for robot calibration [J]. IEEE Transactions on Robotics and Automation, 1991, 7(3):351-360
[26] Hanqi Zhuang, and Zvi S. Roth, Camera-aided calibration, 1996
[27] William K, VEITSCHEGGER and CHI-HAUR WU. Robot Calibration and Compensation, IEEE Journal of Robotics and Automation, 1988. Vol.4, No.6, pp.643-656
[28]王兴松.挠性机器人运动误差的集成傲光测量与补偿策略.中国机械工程,1997.Vol.8:15-18
[29]崔鲲,孙论强,吴林. V01弧焊机器人结构参数标定和变换矩阵的建立[J].焊接,1996(9):2-6
[30]宋月娥,吴林,张连新等.弧焊机器人离线编程系统标定模块的开发[J].机器人,2001.23(7):689-670
[31]蔡鹤皋,张超群,吴伟国.机器人实际几何参数识别与仿真[J].中国机械工程,1998.9(10):11-14
[32]朴用杰,邱涛,陈善本.弧焊机器人TCF参数的标定[J].机器人,2001.23(2):109-112
[33]宋月娥,吴林,田劲松等.用于机器人离线编程的工件标定算法研究[J].哈尔滨工业大学学报,2002, 34(6):735-738
[34]李金泉,陈善本,吴林.用于手眼立体视觉的弧焊机器人平面工件定位系统[J].焊接学报,2003, 24(4):9-14
[35]刘振宇,陈英林,曲道奎等.机器人标定技术研究[J].机器人,2002.24(5):447-450
[36]张建忠.机器人连杆参数的视觉标定[J].制造业自动化,2004.26(11):32-34
[37] Paul R P. Robot Manipulations: Mathematics, Programming, and Control [M]. Cambridge: The MIT Press, 1981
[38] Zhuang H Q and Roth Z S. Camera-aided Robot Calibration [M]. Florida: CRC Press, 1996
[39] Ziegert J, Datseris P. Basic consideration for robot calibration [A]. In: IEEE International Conference on Robotics and Automation [C], 1988(2): 932-938
[40]李发忠,赵德安,马从国. FANUC_M-6IB型机器人运动学逆解研究.机械设计与制造,2008.10:174-176
[41]孔凡斌,姜培刚,宋玲玲.基于UG Open C的FANUC_M-16iB/20工业机器人动态仿真.计算机应用与软件,2008.6:169-171
[42] A.Y. Elatta, Li Pei Gen, Fan Liang Zhi, Yu Daoyuan, Luo Fei. An overview of robot calibration techniques [J]. Information Technology Journal 2004.3(l):74-78
[43] I-Ming Chen, Guilin Yang. Kinematic calibration of modular reconfigurable robots using product of exponentials formula [J]. Journal of robotic systems, 1997.14(11):807-821
[44] T. Alban, H. Janocha. Dynamic calibration of industrial robots with inertial measurement systems [J]. www.google.com
[45] Ambarish Goswami, Arthur Quaid, Michael Peshkin. Complete parameter identifieationof a robot from partial pose information [C].1993 IEEE International Conference Robotic and Automation
[46] J. Hefele. Real-time photogrammetric algorithms of robot calibration [C]. The intenrational Archives of the photogrammetry, remote sensing and spatial information sciences, VoL 34, Part XXX
[47] Robert John Homing. A comparison of identification techniques for robot calibration [D]. Case Western Reserve University, Degree of Master of Science, August, 1998
[48]刘万里,曲兴华,闫永刚.便携式三坐标测量臂校准和误差补偿.仪器仪表学报,2006.04
[49]赵俊伟,代军.基于数据库查询的工业机器人误差补偿方法研究.基础与液压, 2008.11:5-17
[50]钟勇,朱建新.一种新的机器人工作空间求解方法.机床与液压,2004.No.4:66-67
[51]范守文,徐礼拒.机器人工作空间分析的解析法.电子科技大学,2006.7:194-197
[52]马香峰.机器人机构学.北京二机械工业出版社,1991.9
[53]段齐骏,黄德耕,李士楠.机器人工作空间与包容空间的图解法.南京理工大学学报,1996,20(4):318-322
[54]赵才军.机器人工作空间及关节运动可靠性规划.硕士学位论文,2003.3
[55] W A Cook, W R Oakes, Mapping Methods for Generating Three-Dimensional Meshes, Computers in Mechanical Engineering, 1982.8:67-72
[56]曲道奎,徐方.提高大型激光加工机器人精度的方法.机器人,2003.5:270-275
[57]吕恬生.工业机器人运动学校准的理论、方法及实验研究.硕士学位论文,2002.2
[58] William K.,VEITSCHEGGER and CHI-HAUR WURobot Calibration and Compensation, IEEE Journal of Robotics and Automation, Vol.4, No.6,pp.643-656
[59]唐蓉城,丁其志,郭玉申.装配机器人误差补偿的研究.机械设计,1999.7
[60]房勋. 3-PRS串并联机构位置正解的研究.河南理工大学硕士学位论文,2007.12
[61]杨建国,刘然.在Visual C++中不依赖MATLAB环境调用其函数的方法.计算机应用基础,2001.6:98-99
[62]万伟民,赵锡芳,张华.工业机器人校正技术及软件设计.南昌大学学报,2004.6:1-4
[63]孔凡斌,姜培刚,宋玲玲.基于UG Open C的FANUC_M-16iB/20工业机器人动态仿真.计算机应用与软件,2008.6:169-171
[64] Zhao Junwei, Dai Jun, Huang Junjie. 3-PRS Serial-Parallel Robot Error Modeling and Parameter Identification. 2008 Sino-European Workshop on Intelligent Robots and Systems. December 11-13, 2008 Chongqing University of Posts & Telecommunications Chongqing, China. (P241-245)
[65] Zhao Junwei, Dai Jun, Huang Junjie. 3-PRS Serial-Parallel Machine Tool Error Calibration and Parameter Identification. Int.重庆邮电大学学报,2009.2
[66] Zhao Jun-wei, Hu Yan-hui,Chen Guo-qiang. A new method for measuring the end error of the industrial robot. 2008 Sino-European Workshop on Intelligent Robots and Systems. December 11-13, 2008 Chongqing University of Posts & Telecommunications Chongqing, China. (P392-395)