本論文致力於分析六軸串連式機械手臂的路徑規劃。傳統的路徑規劃是以初始位置，末位置及軌跡長短來做計算。應用一個修正的滑動模型控制器取代傳統的PID控制器。修正的滑動模型控制是要解決傳統滑動模型控制器的顛震現象以及穩態誤差。為了解決這兩項問題，滑動模型控制器採用PID的滑順平面取代傳統的PD控制器設計來改善穩態誤差。此外，利用sigmoid函數取代傳統信號方程式來減少顛震現象。滑動模型控制器用來抑制干擾及參數不確定性。量測出在卡氏座標中的位置及節點角度，並比較這兩種路徑規畫。

This thesis is dedicated to analyze path planning of a 6-DOF serial manipulator. A conventional path planning is calculated using an initial point, a final point and a duration time of trajectory. However, during this motion, some non-smooth behaviors and singularities may appear, so a new path planning of joint angles with the same starting and ending positions are proposed. A sliding mode controller is a popular approach for systems containing unknown disturbances and parametric uncertainties. In this work, a modified sliding mode controller is applied instead of using a traditional PID controller. The sliding mode controller is developed to solve two main problems of a traditional sliding mode controller, chattering effect and steady state error. In order to solve these two problems, a sliding mode controller is designed with a PID controller as its sliding surface instead of using a conventional PD controller to solve the steady state error. In addition, to attenuate chattering effect, a traditional sign function is replaced by a sigmoid function. Cartesian positions and joint angles are measured, and a comparison is made between these two types of path planning

[1] A. Hourtash and M. Tarokh, "Manipulator Path Planning by Decomposition: Algorithm and Analysis," IEEE Transactions on Robotics and Automation, vol. 17, no. 6, pp. 842-856, Dec. 2001.
[2] K. H. Ang, G. Chong and Y. Lin, "PID Control System Analysis, Design, and Technology," IEEE Transactions on Control Systems Technology, vol. 13, no. 4, pp. 559-576, Jul. 2005.
[3] M. H. Moradi, "New Techniques for PID Controller Design," IEEE Proceedings Conference on Control Applications, vol. 2, pp. 903-908, Jun. 2003
[4] K. J. Astrom, C. C. Hang, P. Persson, and W. K. Ho, "Towards Intelligent PID Control," Automatica, vol. 28, no. 1, pp. 1-9, Jan. 1992.
[5] K. J. Astrom and T. Hagglund, "The Future of PID control," Control Engineering Practice, vol. 9, no. 11, pp. 1163-1175, Nov. 2001.
[6] K. J. Astrom, T. Hagglund, C. C. Hang, and W. K. Ho, "Automatic Tuning and Adaptation for PID Controllers - a Survey," Control Engineering Practice, vol. 1, no. 4, pp. 699-714, Aug. 1993.
[7] H. Shibata and N. Mitsukawa, "Comparison of Robustness between Adaptive Control and PID Control," IEEE Proceedings Conference on Computer, Communication, Control and Power Engineering, vol. 4, pp. 34-37, Oct. 1993.
[8] R. Ortega and M. W. Spong, "Adaptive Motion Control of Rigid Robots: A Tutorial," Automatica, vol. 25, no. 6, pp. 877-888, Nov. 1989
[9] J. J. E. Slotine and W. Li, "Composite Adaptive Control of Robot Manipulators," Automatica, vol. 25, no.4, pp. 509-519, Jul. 1989.
[10] B. K. Yoo and W. C. Ham, "Adaptive Control of Robot Manipulator using Fuzzy Compensator," IEEE Transactions on Fuzzy Systems, vol. 8, no. 2, pp. 186-199, Apr. 2000.
[11] J. J. E. Slotine and W. Li, "Adaptive Manipulator Control: A Case Study," IEEE Transactions on Automatic Control, vol. 33, no. 11, pp. 995-1003, Nov. 1988.
[12] D. J. Hoelzle, A. G. Alleyne and A. J. W. Johnson, "Basis Task Approach to Iterative Learning Control with Applications to Micro-Robotic Deposition," IEEE Transactions on Control Systems Technology, vol. 19, no. 5, pp. 1138-1148, Sep. 2011
[13] J. X. Xu, X. W. Wang and L. T. Heng, "Analysis of Continuous Iterative Learning Control Systems Using Current Cycle Feedback," IEEE Proceedings of the American Control Conference, vol. 6, pp. 4221-4225, Jun. 1995.
[14] C. K. Chen and K. S. Li, "Iterative Learning Control for Robotic Contouring," IEEE International Conference on Control and Automation, pp. 1092-1097, Dec. 2009.
[15] J. X. Xu, W. Wang and D. Huang, "Iterative Learning in Ballistic Control," IEEE Proceedings of the American Control Conference, pp.1293-1298, Jul. 2007
[16] T. Sugie and T. Ono, "An Iterative Learning Control Law for Dynamical Systems," Automatica, vol. 27, no. 4, pp. 729-732, July. 1991
[17] H. S. Ahn, Y. Chen and K. L. Moore, "Iterative Learning Control: Brief Survey and Categorization," IEEE Transactions on Systems Man and Cybernetics - Part C: Applications and Reviews, vol. 37, no. 6, pp. 1099-1121, Nov. 2007.
[18] P. Bondi, G. Casalino and L. Gambardella, "On the Iterative Learning Control Theory for Robotic Manipulators," IEEE Journal of Robotics and Automation, vol. 4, no. 1, pp. 14-22, Feb. 1988.
[19] Z. Qu, "Robust Control of Robots by the Computed Torque Law," Systems and Control Letters, vol. 16. no. 1, pp. 25-32, Jan. 1991.
[20] C. H. An, C. G. Atkeson, J. D. Griffiths, and J. M. Hollerbach, "Experimental Evaluation of Feedforward and Computed Torque Control," IEEE Transactions on Robotics and Automation, vol. 5, no. 3, pp. 368-373, Jun. 1989
[21] J. H. Park and K. D. Kim, "Biped Robot Walking Using Gravity-Compensated Inverted Pendulum Mode and Computed Torque Control," IEEE Proceedings Conference on Robotics and Automation, vol. 4, pp. 3528-3533, May 1998.
[22] R. H. Middleton and G. C. Goodwin, "Adaptive Computed Torque Control for Rigid Link Manipulations," Systems and Control Letters, vol. 10, no. 1, pp. 9-16, Jan. 1988.
[23] Y. Wang, "Robust Control of a Class of Uncertain Nonlinear Systems," Systems and Control Letters, vol. 19, no. 2, pp. 139-149, Aug. 1992
[24] M. W. Spong, "On the Robust Control of Robot Manipulators," IEEE Transactions on Automatic Control, vol. 37, no. 11, pp. 1782-1786, Nov. 1992
[25] W. Wroblewski, "Implementation of a Model Predictive Control Algorithm for a 6dof Manipulator - Simulation Results," IEEE Proceedings of the 4th International Workshop on Robot Motion and Control, pp. 209-212, Jun. 2004.
[26] C. E. Garcia, D. M. Prett and M. Morari, "Model Predictive Control: Theory and Practice - A Survey," Automatica, vol. 25, no. 3, pp. 335-348, May 1989
[27] S. J. Qin and T. A. Badgwell, "A Survey of Industrial Model Predictive Control Technology," Control Engineering Practice, vol. 11, no. 7, pp. 733-764, Jul. 2003.
[28] M. Morari and J. H. Lee, "Model Predictive Control: Past, Present and Future," Computers and Chemical Engineering, vol. 23, no. 4, pp. 667-682, May 1999.
[29] J. Richalet, "Industrial Applications of Model Based Predictive Control," Automatica, vol. 29, no. 5, pp. 1251-1274, Sep. 1993.
[30] P. Poignet and M. Gautier, "Nonlinear Model Predictive Control of a Robot Manipulator," IEEE Proceedings of 6th International Workshop on Advanced Motion Control, pp. 401-406, Apr. 2000.
[31] B. S. Chen, T. S. Lee and J. H. Feng, "A nonlinear H∞ Control Design in Robotic Systems under Parameter Perturbation and External Disturbance," International Journal of Control, vol. 59, no. 2, pp. 439-461, Oct. 1992.
[32] W. Feng and I. Postlethwaite, "Robust Non-Linear H∞/Adaptive Control of Robot Manipulator Motion," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 208, no. 4, pp. 221-230, Jun. 1994.
[33] G. N. Saridis and C. S. G. Lee, "An Approximation Theory of Optimal Control for Trainable Manipulators," IEEE Transactions on Systems Man and Cybernetics, vol. 9, no. 3, pp. 152-159, Mar. 1979.
[34] J. E. Bobrow, S. Dubowsky and J. S. Gibson, "On the Optimal Control of Robotic Manipulators with Actuator Constraints," IEEE American Control Conference, pp. 782-787, Jun. 1983
[35] F. Lin and R. D. Brandit, "An Optimal Control Approach to Robust Control of Robot Manipulators," IEEE Transactions on Robotics and Automation, vol. 14, no. 1, pp. 69-77, Feb. 1998.
[36] K. G. Shin and N. D. McKay, "Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints," IEEE Transactions on Automatic Control, vol. 30, no. 6, pp. 531-541, Jun. 1985
[37] C. K. Lin, "Nonsingular Terminal Sliding Mode Control of Robot Manipulators Using Fuzzy Wavelet Networks," IEEE Transactions on Fuzzy Systems, vol. 14, no. 6, pp. 849-859, Dec. 2006
[38] J. Wamg, A. B. Rad and P. T. Chan, "Indirect Adaptive Fuzzy Sliding Mode Control: Part I: Fuzzy Switching," Fuzzy Sets and Systems, vol. 122, no. 1, pp. 21-30, Aug. 2001.
[39] K. Koo, X. Jiang, A. Konno and M. Uchiyama, "End Effector Constrained Path Planning for 7DOF Manipulator," IEEE/SICE International Symposium on System Integration (SII), pp. 287-292, Dec. 2010.
[40] H. Seraji, M. K. Long and T. S. Lee, "Motion Control of 7-DOF Arms: The Configuration Control Approach," IEEE Transactions on Robotics and Automation, vol. 9, no. 2, pp. 125-139, Apr. 1993
[41] F. T. Cheng, J. S. Chen and F. C. Kung, "Study and Resolution of Singularities for a 7-DOF Redundant Manipulator," IEEE Transactions on Industrial Electronics, vol. 45, no. 3, pp. 469-480, Jun. 1998.
[42] K. Kreutz-Delgado, M. Long and H. Seraji, "Kinematic Analysis of 7DOF Anthropomorphic Arms," IEEE International Conference on Robotics and Automation, vol. 2, pp. 824-830, May 1990.
[43] J. Angeles, A. Morozov and O. Navarro, "A Novel Manipulator Architecture for the Production of SCARA Motions," IEEE International Conference on Robotics and Automation, vol. 3, pp. 2370-2375, Apr. 2000.
[44] A. Visioli and G. Legnani, "On the Trajectory Tracking Control of Industrial SCARA Robot Manipulators," IEEE Transactions on Industrial Electronics, vol. 49, no. 1, pp. 224-232. Feb. 2002
[45] F. T. Cheng, T. L. Hour, Y. Y. Sun, and T. H. Chen, "Study and Resolution of Singularities for a 6-DOF PUMA Manipulator," IEEE Transactions on Systems Man and Cybernetics, Part B: Cybernetics, vol. 27, no. 2, pp. 332-343, Apr. 1997.
[46] J. Burdick and O. Khatib, "Motion and Force Control of Robot Manipulators," IEEE International Conference on Robotics and Automation, vol. 3, pp. 1381-1386, Apr. 1986
[47] O. Khatib, "A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation," IEEE Journal of Robotics and Automation, vol. 3, no. 1, pp. 43-53. Feb. 1987.
[48] Z. Zhang, F. Ferry, Q. Fang and X. Gu, "Robotic Arm for Unsupervised Stroke Rehabilitation: A Pilot Study using PID Controller," IEEE International Conference on Orange Technologies, pp. 19-22, Mar. 2013
[49] A. Flores-Abad and A. Arpidez, "Embedded Control System for a 5-DOF Manipulator by Means of SPI Bus," IEEE Conference on Electronics, Robotics and Automotive Mechanics, pp. 151-156, Sep. 2009
[50] H. Chaudhary, R. Prasad and N. Sukavanum, "Position Analysis based Approach for Trajectory Tracking Control of Scorbot-ER-V Plus Robot Manipulator." International Journal of Advances in Engineering and Technology, vol. 3, no. 2, pp. 253-264, May 2012.
[51] H. Chaudhary, R. Prasad and N. Sukavanum, "Trajectory Tracking Control of Scorbot-ER-V Plus Robot Manipulator based on Kinematical Approach," International Journal of Engineering Science and Technology, vol. 4, no. 3, pp. 1174-1182, Mar. 2012
[52] D. Stewart, "A Platform with Six Degrees of Freedom," Proceedings of the institution of mechanical engineers, vol. 180, no. 1, pp. 371-386, May 1965.
[53] B. Dasgupta and T. S. Mruthyunjaya, "The Stewart Platform Manipulator: a Review," Mechanism and Machine Theory, vol. 35, no. 1, pp. 15-40, Jan. 2000.
[54] P. Nanua, K. J. Waldron and V. Murthy, "Direct Kinematic Solution of a Stewart Platform," IEEE Transactions on Robotics and Automation, vol. 6, no. 4, pp. 438-444, Aug. 1990.
[55] Y. Fang and L. W. Tsai, "Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators with Identical Limb Structures," The International Journal of Robotics Research, vol. 21, no. 9, pp. 799-810, Sep. 2002.
[56] F. Gao, W. Li, X. Zhao, Z. Jin and H. Zhao, "New Kinematic Structures for 2-, 3-, 4-, and 5-DOF Parallel Manipulator Design," Mechanism and Machine Theory, vol. 37, no. 11, pp. 1395-1411, Nov. 2002
[57] T. Huang, M. Li, M. Zhao, J. P. Mei, D. G. Chetwynd, and S. J. Hu, "Conceptual Design and Dimensional Synthesis for a 3-DOF Module of the TriVariant-a Novel 5-DOF Reconfigurable Hybrid Robot," IEEE Transactions on Robotics, vol. 21, no. 3, pp. 449-456, Jun. 2005
[58] S. B. Park, H. S. Kim, C. Song, and K. Kim, "Dynamics Modeling of a Delta-type Parallel Robot (ISR 2013)," IEEE 44th International Symposium on Robotics, pp. 1-5, Oct. 2013
[59] R. Clavel, "Delta, a Fast Robot with Parallel Geometry," 18th International Symposium on Industrial Robots, pp. 91-100, Jan. 1988
[60] L. W. Tsai, "Kinematics of a Three-DOF Platform Manipulator with Three Extensible Limbs," Recent Advances in Robot Kinematics, pp. 401-410, 1996
[61] X. J. Liu, "Optimal Kinematic Design of a Three Translational DOFs Parallel Manipulator," Robotica, vol. 24, no. 2, pp. 239-250, Mar. 2006.
[62] F. Pierrot, C. Reynaud and A. Fournier, "DELTA: a Simple and Efficient Parallel Robot," Robotica, vol .8, no. 2, pp. 105-109, Apr. 1990.
[63] M. Stock and K. Miller, "Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot," Journal of Mechanical Design, vol. 125, no. 2, pp. 292-301, Jun. 2003
[64] M. A. Laribi, L. Romdhane and S. Zeghloul, "Analysis and Dimensional Synthesis of the DELTA Robot for a Prescribed Workspace," Mechanism and Machine Theory, vol. 43, no. 7, pp. 859-870, Jul. 2007
[65] A. Codourey, "Dynamic Modelling and Mass Matrix Evaluation of the DELTA Parallel Robot for Axes Decoupling Control," IEEE/RSJ Conference on Intelligent Robots and Systems, vol. 3, pp. 1211-1218, Nov. 1996.
[66] K. Furuta, "Sliding Mode Control of a Discrete System," Systems and Control Letters, vol. 14, no. 2, pp. 145-152, Feb. 1990.
[67] K. D. Young, V. I. Utkin and U. Ozguner, "A Control Engineer’s Guide to Sliding Mode Control," IEEE Transactions on Control Systems and Technology, vol. 7, no. 3, pp. 328-342, May 1999.
[68] V. I. Uykin, "Sliding Mode Control Design Principles and Applications to Electric Drives," IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 23-36, Feb. 1993.
[69] O. Kaynak, K. Erbatur and M. Ertugnrl, "The Fusion of Computationally Intelligent Methodologies and Sliding Mode Control - A Survey," IEEE Transactions on Industrial Electronics, vol. 48, no. 1, pp. 4-17, Feb. 2001
[70] K. J. Kim, J. B. Park and Y. H. Choi, "Chattering Free Sliding Mode Control," IEEE International Joint Conference, pp. 732-735, Oct. 2006.
[71] A. Rhif, "Stabilizing Sliding Mode Control Design and Application for a DC Motor: Speed Control," International Journal of Instrumentation and Control Systems, vol. 2, no. 1, pp. 39-48, Jan. 2012
[72] V. S. C. Raviraj and P. C. Sen, "Comparative Study of Proportional – Integral, Sliding Mode, and Fuzzy Logic Controllers for Power Converters," IEEE Transactions on Industry Applications, vol. 33, no. 2, pp. 518-524, Mar. 1997.
[73] R. Shahnazi, H. M. Shanechi and N. Pariz, "Position Control of Induction and DC Servomotors: A Novel Adaptive Fuzzy PI Sliding Mode Control," IEEE Transactions on Energy Conversion, vol .23, no. 1, pp. 138-147, Mar. 2008.
[74] G. Bartolini, A. Pisano, E. Punta and E. Usai, "A Survey of Applications of Second-Order Sliding Mode Control to Mechanical Systems," International Journal of Control, vol. 46, no. 9-10, pp. 875-892, Nov. 2010.
[75] J. L. Chang, "On Chattering-Free Dynamic Sliding Mode Controller Design," Journal of Control Science and Engineering, vol. 2012, Aug. 2012
[76] G. Bartolini, A. Ferrara and E. Usani, "Chattering Avoidance by Second-Order Sliding Mode Control," IEEE Transactions on Automatic Control, vol. 43, no. 2, pp. 241-246, Feb. 1998.
[77] Y. B. Shtessel, I. A. Shkolnikov and M. D. J. Brown, "An Asymptotic Second-Order Smooth Sliding Mode Control," Asian Journal of Control, vol. 5, no. 4, pp. 498-504, Oct. 2008.
[78] A. Rhif, "A High Order Sliding Mode Control with PID Sliding Surface: Simulation on a Torpedo," International Journal of Information Technology, vol. 2, no. 1, Jan. 2012.
[79] Y. Li and Q. Xu, "Adaptive Sliding Mode Control With Perturbation Estimation and PID Sliding Surface for Motion Tracking of a Piezo-Driven Micromanipulator," IEEE Transactions on Control Systems Technology, vol. 18, no. 4, pp. 798-810, Jul. 2010.
[80] D. S. Negash and R. Mitra, "Integral Sliding Mode Controller for Trajectory Tracking Control of Stewart Platform Manipulator," International Conference on Industrial and Information Systems, pp. 650-654, Aug. 2010
[81] J. Shi, "Design of Sliding Mode Autopilot with Steady-State Error Elimination for Autonomous Underwater Vehicles," IEEE Region 10 Conference, pp. 1-4. Nov. 2006.
[82] H. Lee and V. I. Utkin, “Chattering suppression methods in sliding mode control systems,” Annual Reviews in Control, vol. 31, pp. 179-188, 2007
[83] P. I. Corke, “MATLAB Toolboxes: Robotics and for Students and Teachers,” IEEE Robotics and Automation Magazine, vol. 14, no. 4, pp. 16-17, Dec. 2007.
[84] P. I. Corke, “A Robotics Toolbox for MATLAB,” IEEE Robotics and Automation Magazine, vol. 3, no. 1, pp. 24-32, Mar. 1996.
[85] P. I. Corke, “A Computer Tool for Simulation and Analysis: The Robotics Toolbox for MATLAB,” Proceedings of the 1995 National Conference of the Australian Robot Association, pp. 319-330, Jul. 1995.
[86] P. I. Corke, “Robotics, Vision & Control.” Springer 2011, ISBN 978-3-642-20143-1.
[87] K. J. Astrom and T. Hagglund, “Revisiting the Ziegler-Nichols Step Response Method for PID Control,” Journal of Process Control, vol. 14, no. 6, pp. 635-650, Sep. 2004.
[88] M. D. O’Toole, K. Bouazza-Marouf and D. Kerr, “Performance Estimation of Two Sliding Mode Controllers for Chatter Reduction in Linear System,” IET Control Theory & Applications, vol. 7, no. 3, pp. 423-430, Feb. 2013.