臺灣博碩士論文加值系統

本文對多軸控制之點到點運動以及循跡運動進行詳細的探討。點到點運動包括單一三次多項式、梯形速度規劃、與S-curve速度規劃，以及直線與圓弧插值法。而循跡運動包括均勻式二次與三次雲形曲線以及PVT曲線。本文主要的重點在於提出具有速度及加速度限制之自動化機台運動軌跡的線上演算法則。理論的根據是針對各種不同軌跡在速度以及加速度的限制下對整個運動時間盡可能作最小化。所有提出的方法均在MATLAB工具軟體下模擬以及使用DSP運動控制器所控制的雙軸XY平台上測試，並得到成功的驗證。

A detailed study has been carried out for multi-axis motion control on point-to-point and contouring motions. In this thesis point-to-point motion includes a single cubic polynomial, trapezoidal velocity, and S-curve velocity profile, as well as its applications in linear and circular interpolation. Contour motion comprises uniform quadratic and cubic B-splines, and PVT(Position-Velocity-Timer or Hermite) curves. On-line algorithms are proposed to generate an automation machine’s motion trajectory under velocity and acceleration constraints. The theoretical result is based on optimizing the traveling time as small as possible while using different kind of curves and while under velocity and acceleration constraints. The proposed methods have been tested by MATLAB simulation and by a real dual-axis XY table. Both results have shown their efficiency.

中文摘要 -------------------------------------------------------------------- I
英文摘要 -------------------------------------------------------------------- II
致謝 -------------------------------------------------------------------------- III
目錄 -------------------------------------------------------------------------- IV
圖表索引 -------------------------------------------------------------------- VI
第一章 緒論 --------------------------------------------------------------- 1
1.1研究動機 ---------------------------------------------------------- 1
1.2發展現況 ---------------------------------------------------------- 5
1.3論文架構 ---------------------------------------------------------- 7
第二章 點到點運動軌跡規劃 ----------------------------------------- 8
2.1 單一三次多項式曲線 ----------------------------------------- 8
2.2 梯形速度規劃 --------------------------------------------------- 15
2.3 S-curve速度規劃 ---------------------------------------------- 21
2.4 直線插值法 ------------------------------------------------------ 36
2.5 圓弧插值法 ------------------------------------------------------ 38
第三章 PVT移動模式 -------------------------------------------------- 41
3.1 單軸PVT移動模式 -------------------------------------------- 42
3.2 具加速度限制之PVT移動模式 ---------------------------- 44
3.3 具速度限制之PVT移動模式 -------------------------------- 52
3.4 具急衝度限制之PVT移動模式 ----------------------------- 56
3.5 多軸PVT移動模式 -------------------------------------------- 62
第四章 雲形曲線插值法--------------------------------------------------- 65
4.1 二次雲形曲線 --------------------------------------------------- 65
4.2 三次雲形曲線 -------------------------------------------------- 72
4.3 即時曲線插值法 ------------------------------------------------ 81
第五章 測試系統架構 --------------------------------------------------- 92
5.1 DSP運動控制器硬體架構 ----------------------------------- 92
5.2 DSP運動控制器韌體架構 ----------------------------------- 95
5.3 人機界面軟體架構 --------------------------------------------- 101
5.4 軌跡實測 --------------------------------------------------------- 107
第六章 結論與展望 ------------------------------------------------------ 111
6.1 結論 --------------------------------------------------------------- 111
6.2 未來研究方向 -------------------------------------------------- 112
參考文獻 ------------------------------------------------------------------- 114

[1] 施慶隆，李文猶，”機電整合與運動控制：原理與單軸平台實
例”，高立圖書有限公司，1997。
[2] F. Imamura and H. Kaufman, “Time Optimal Contour Tracking forMachine Tool Controllers,” IEEE Control Systems, April 1991, pp. 11-17.
[3] J. J. Chou and D. C. H. Yang, “Command Generation for Three-Axis CNC Machine,” Journal of Engineering for Industry, Vol. 113, August 1991, pp. 305-310.
[4] C. C. Lo, “A New Approach to CNC Tool Generation,” Computer- Aided Design, Vol. 30, No. 8, 1998, pp. 649-655.
[5] D. Kiritsis, “High Precision Interpolation Algorithm for 3D
Parametric Curve Generation,” Computer Aided Design, Vol. 26,
November 1994, pp. 850-856.
[6] C. H. Yang and T. Kong, “Parametric Interpolator versus Linear Interpolator for Precision CNC Machining,” Computer Aided Design, Vol. 26, No. 3, March 1994, pp. 225-233.
[7] S. S. Yeh and P. L. Hsu, “The Speed-Controlled Interpolator for Machining Parametric Curves,” Computer Aided Design, 31, 1999, pp. 349-357.
[8] M. Shpitalni, Y. Koren and C.C. Lo, “Realtime Curve Interpolators,” Computer Aided Design, Vol. 26, No. 11, November 1994, pp.832-838.
[9] Q. G. Zhang and R. B. Greenway, “Development and
Implementation of a NURBS Curve Motion Interpolator,” Robotics
and Computer-Integrated Manufacturing,” 14, 1998, pp.27-36.
[10] C. Lewin, “Motion Control Gets Gradually Better,” Machine Design, Nov. 7, 1994, pp. 90-94.
[11] P. H. Meckl and P. B. Arestides, “Optimized S-Curve Motion Profiles for Minimum Residual Vibration,” Proceeding of American Control Conference, June 1998, pp. 2627-2631.
[12] P. H. Meckl and W. P. Seering, “Minimizing Residual Vibration for Point-to-Point Motion,” J. of Vib., Acous., Stress and Rel. in Des., Vol. 107, Oct. 1985, pp. 378-382.
[13] R. H. Castain and R. P. Paul, “On-line Dynamic Trajectory
Generation,” Int. j. of Robotics Research, Vol. 3, No. 1, 1984, pp. 68-72.
[14] IR L. Van Aken and H. V. Brussel, “On Line Robot Trajectory Control in Joint Coordinate by Mean of Imposed Acceleration Profile,” Robotica, Vol. 6, 1988, pp. 185-195.
[15] Tanaka Y, Tsuji T, Kaneko M., “Online Trajectory Generation of Robots Using Time Base Generator,” Transactions of the Institute of Electrical Engineers of Japan, Part C, Vol.119-C, No.10, Oct. 1999, pp.1262-7.
[16] J. Y. S. Luh, C. S. Lin and P. R. Chang, “Formulation and Optimization of Cubic Polynomial Joint Trajectories for Industrial Robots,” IEEE transactions on Automatic control, Vol. AC-28, No. 12, December, 1983, pp. 1066-1071.
[17] M. Y. Lee, A .J. Sturm, Jr.* and D. Lavalle, “New Approach for Robot Trajectory Generation with Velocity/Acceleration Clipping Constraints,” Advanced Robotics, Vol. 11, No. 7, 1998, pp. 713-723.
[18] P. Andre and M. C. Haddad, “Uniform B-Spline-Based Definition of Composite Contours for Machine Tool Control,” International Journal of Robotics and Automation, Vol. 10, No. 2, 1995, pp. 56-58.
[19] K. Choi and W. Kim, “Bounded Deviation Joint Path Algorithms For Piecewise Cubic Polynomial Trajectories,” IEEE Transactions on Systems, Man and Cybernetics. Vol. 20, No. 3, May/June, 1990, pp. 725-733.
[20] S. A. Bazaz and B. Tondu, “3-Cubic Spline for On-Line Cartesian Space Trajectory Planning of an Industrial Manipulator,” IEEE AMC ‘98-Coimbra, pp. 493498.
[21] Xiang-Rong Xu, Won-Jee Chung and Young-Hyu Choi, “A Method for On-Line Trajectory Planning of Robot Manipulators in Cartesian Space,” Computational Intelligence in Robotics and Automation, 1999. CIRA ''99. Proceedings. 1999 IEEE International Symposium on, 1999, pp. 41-46.
[22] Jeon, J.W., Park, S.-H, Kim, D.I, Kim, S., “An Efficient Trajectory Generation for Industrial Robots,” Industry Applications Society Annual Meeting, 1993., Conference Record of the 1993 IEEE , 1993 , pp. 2137 -2143 vol.3
[23] Kaihuai Qin, “General Matrix Representation for B-Splines,” IEEE,1998.
[24] C. G. Lim, “A Universal Parametrization in B-Spline Curve and Surface Interpolation,” Computer Aided Geometric Design, 16, 1999, pp. 407-422.
[25] B. Cao, G. I. Dodds and G. W. Irwin, “Constraints Time-Efficient and Smooth Cubic Spline Trajectory Generation for Industrial Robots,” IEE Proc-Control Theory Appl., Vol. 144, No. 5, Sept., 1997, pp. 467-475.
[26] C. H. Wang and J. G. Horng, “Constrained Minimum-Time Path Planning for Robot Manipulators via Virtual Knots of the Cubic B-Spline Function,” IEEE Tran., 1990 AC-35, pp.573-577.
[27] M. E. Kahn and B. Roth, “The Near-Minimum-time Control of Open-Loop Articulated Kinematic Chains,” ASME J. Dyn. Syst. Meas. Contr.,1971, pp. 164-172.
[28] Dong-Il Kim, Jin-Il Song, Sungkwun Kim, “Dependence of Machining Accuracy on Acceleration/Deceleration and Interpolation Methods in CNC Machine Tools,” Industry Applications Society Annual Meeting, 1994, Conference Record of the 1994 IEEE, 1994, pp. 1898 -1905 vol.3
[29] Jae Wook Jeon, “A Generalized Approach for the Acceleration and Deceleration of CNC Machine Tools,” Industrial Electronics, Control, and Instrumentation, 1996, Proceedings of the 1996 IEEE IECON 22nd International Conference on Vol. 2, 1996, pp. 1283 —1288.
[30] Jae Wook Jeon and Young Youl, “A Generalized Approach for the Acceleration and Deceleration of Industrial Robots and CNC Machine Tools,” Industrial Electronics, IEEE Transactions on
Vol. 47 1, Feb. 2000, pp. 133 —139.
[31] R. T. Farouki, Y-F. Tsai and C. S. Wilson, “Physical Constraints on Feedrates and Feed Accelerations along Curved Tool Paths,” Computer Aided Geometric Design, 17, 2000, pp. 337-359.
[32] P. Andre, M. C. Haddad, and C. Morelec, “Application of Uniform Cubic B-Splines to Machine Tools and Robots Numerical Control. Determination of Vertices under Various Constraints,” Advanced Robotics, 1991. ''Robots in Unstructured Environments'', 91 ICAR., Fifth International Conference on , 1991 , Page(s): 1602 -1605 vol.2
[33] F. Imamura and H. Kaufman, “Time Optimal Contour Tracking for Machine Tool Controllers,” IEEE Control Systems, April, 1991, pp. 11-17.
[34] C. C. Lo and C. Y. Hsiao, “CNC Machine Tool Interpolator with Path Ccompensation for Repeated Contour Machining,” Computer Aided Design, Vol. 30, No. 1, 1998, pp. 55-62.
[35] M. Sarfraz, Z. Habib and . Hussain, “Piecewise Interpolation for Designing of Parametric Curves,” Information Visualization, Proceedings. 1998 IEEE Conference on, 1998, pp. 307 -313
[36] C. Blanc and C. Schlick, “Accurate Parametrization of Conics by NURBS,” IEEE Computer Graphics and Applications, Vol. 16, No.6, Nov, 1996, pp. 64 —71.
[37] L. Piegl, “A Menageries of Rational B-Spline Circles,” IEEE Computer Graphics and Application, 1989, pp. 48-56.
[38] Hua Qiu, Kai Chenh and Yan Li, “Optimal Circular Arc Interpolation for NC Tool Path Generation in Curve Contour Manufacturing,” Computer Aided Design, Vol. 29, No 11, pp. 751-760.
[39] L. Piegl and W. Tiller, “Curve and Surface Constructions Using Rational B-Splines,” Computer Aided Design, Vol. 19, No. 9, November, 1987, pp.485-497.
[40] G. Farin, “From Conics to NURBS:A Tutorial and Survey,” IEEE Computer Graphics and Applications, September, 1992, pp. 78-86.
[41] L. Piegl, “On NURBS:A Survey,” IEEE Computer Graphics and Applications, January, 1991, pp. 55-71.
[42] L. Piegl and W. Tiller, “Computing Offsets of NURBS Curves and Surfaces,” Computer Aided Design, 31, 1999, pp. 147-156.
[43] Robert C. “An Introduction to the Curves and Surfaces of Computer-Aided Design”, 1991.
[44] 羅啟維，”以DSP為主體之運動控制器設計製作與應用”，國立
台灣科技大學電機工程研究所碩士論文，1998。
[45] 林勝雄，”DSP-Based 直流馬達數位運動控制器設計與製作”， 國立台灣科技大學電機工程研究所碩士論文，1999。
[46] 施慶隆，羅啟維，李建翔，”雙軸數位運動控制之設計與製作”，教育部八十八年度製造科技領域技術論文集，2000年6月。