在本篇論文中，我們提出了一個用來控制含有時變不確定參數的柔性關節機械臂的適應性控制器。該控制器不需要計算回饋矩陣，即不需要將機械臂數學模型線性參數化，從而極大地簡化了其實現的困難程度。同時，在不採用Slotine和Li的改進方法的前提下，該方法不需要回饋機器臂的加速度或者更高階的速度微分。以及，通過使用函數近似法，該方法下對未知參數的更新律的數量也極大地減少了，這進一步提升了該方法的應用性。該方法的閉環穩定性和內部信號的有界性是通過類李雅普諾夫理論來證明的。在最後，我們通過電腦模擬的方式確認了該方法的有效性。

In this thesis, an adaptive controller is proposed for controlling flexible joint robots containing time-varying uncertainties. The controller is free from the computation of the regressor matrix which largely simplifies its implementation. The feedback of link accelerations and their higher derivations are avoided without the support of Slotine and Li’s modification. The number of update laws in the estimation of uncertainties by using the function approximation technique is significantly reduced in this new design which further improves its applicability. The closed loop stability and boundedness of internal signals are proved by the Lyapunov-like theory. Computer simulations are performed to verify its effectiveness.

[1] M. W. Spong, K. Khorasani and P. V. Kokotovic, “An integral manifold approach to the feedback control of flexible joint robots,” IEEE Transactions on Robotics and Automation, vol. 3, no. 4, pp. 291-300, Aug. 1987.
[2] L. M. Sweet and M. C. Good, “Re-definition of the robot motion control problem: Effects of plant dynamics, drive system constraints, and user requirements,” Proceedings of the 23rd IEEE Conference Decision and Control, pp. 724-732, 12-14 Dec. 1984.
[3] E. I. Rivin, “Effective rigidity of robot structure: Analysis and enhancement,” American Control Conference, pp. 381-382, 19-21 Jun. 1985.
[4] C. M. Ou and J. S. Lin, “Nonlinear adaptive backstepping control design of flexible-joint robotic manipulator,” Proceedings of the 8th Asian Control Conference, pp. 1352-1357, 15-18, May 2011.
[5] M. Forrest-Barlach and S. Babcock, “Inverse dynamics position control of a compliant manipulator,” IEEE International Conference on Robotics and Automation, vol. 3, pp. 196-205, Apr. 1986.
[6] P. Tomei, “A simple PD controller for robots with elastic joints,” IEEE Transactions on Automatic Control, vol. 36, no. 10, pp. 1208-1213, Oct. 1991.
[7] G. Chen, “Exact closed-form optimal solutions for constrained trajectory control of single-link flexible-joint manipulators,” Proceedings of the 29th IEEE Conference on Decision and Control, vol. 4, pp. 2566-2567, 5-7 Dec. 1990.
[8] M. W. Spong, “Modeling and control of elastic joint manipulators,” Journal of Dynamics, Systems, Measurements and Control, vol. 109, no. 4, pp. 310-318, 1987.
[9] K. Khorasani and M. W. Spong, “Invariant manifolds and their application to robot manipulators with flexible joints,” Proceedings of the IEEE International Conference on Robotics and Automation, vol. 2, pp. 978-983, Mar. 1985.
[10] M. W. Spong, K. Khorasani, and P. V. Kokotovic, “An integral manifold approach to the feedback control of flexible joint robots,” IEEE Transactions on Robotics and Automation, vol. 3, no. 4, pp. 291-300, Aug. 1987.
[11] J. J. Slotine and S. Hong, “Two-time scale sliding control of manipulators with flexible joints,” American Control Conference, pp. 805-810, 18-20 Jun. 1986.
[12] J. Y. Lee, J. S. Yeon, J. H. Park and S. Lee, “Robust backstepping control for flexible-joint robot manipulators,” IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 183-188, Oct. 29 2007-Nov. 2 2007.
[13] F. Liang and H. ElMaraghy, “Robust control of flexible joint robots,” Canadian Conference on Electrical and Computer Engineering, vol. 1, pp. 127-130, 14-17 Sep. 1993.
[14] J. S. Yeon and J. H. Park, “Practical robust control for 旻xible joint robot manipulators,” IEEE International Conference on Robotics and Automation, pp. 3377-3382, 19-23 May 2008.
[15] S. C. Martindale, M. M. Bridges and D. M. Dawson, “Robust position tracking control for rigid-link flexible-joint robots,” Twenty-Fifth Southeastern Symposium on System Theory, pp. 358-362, 7-9 Mar. 1993.
[16] Y. Aoustin, “Robust controls for flexible joint robots: a single link case study with unknown joint stiffness parameter,” International Conference on Systems, Man and Cybernetics, vol. 4, pp. 45-50, 17-20 Oct. 1993.
[17] T. J. Ha, J. Lee and J. H Park, “Robust control by inverse optimal PID approach for flexible joint robot manipulator,” IEEE International Conference on Robotics and Biomimetics, pp. 336-341, 15-18 Dec. 2007.
[18] A. Patel, R. Neelgund, A. Wathore, J. P. Kolhe, M. M. Kuber, and S. E. Talole, “Robust control of 旻xible joint robot manipulator,” SICE-ICASE International Joint Conference, pp. 3963-3968, 18-21 Oct. 2006.
[19] F. Ghorbel, J. Y. Hung, and M. W. Spong, “Adaptive control of flexible joint manipulators,” IEEE International Conference on Robotics and Automation, vol. 2, pp. 1188-1193, 14-19 May 1989.
[20] R. A. Al-Ashoor, R. V. Patel, and K. Khorasani, “Robust adaptive controller design and stability analysis for flexible-joint manipulators,” IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 2, pp. 589-602, Mar/Apr 1993.
[21] K. Khorasani, “Adaptive control of flexible-joint robots,” IEEE Transactions on Robotics and Automation, vol. 8, no. 2, pp. 250-267, Apr. 1992.
[22] J. Yuan, and Y. Stepanenko, “Adaptive PD control of flexible joint robots without using the high-order regressor,” Proceedings of the 36th Midwest Symposium on Circuits and Systems, vol. 1, pp. 389-393, 16-18 Aug. 1993.
[23] L. Tian and A. Goldenberg, “Adaptive and sliding control of flexible joint robots in constrained motion,” IEEE International Conference on Systems, Man and Cybernetics, vol. 5, pp. 4161-4166, 22-25 Oct. 1995.
[24] I. Hassanzadeh, H. Kharrati and J. R. Bonab, “Model following adaptive control for a robot with flexible joints,” Canadian Conference on Electrical and Computer Engineering, pp. 001467-001472, 4-7 May 2008.
[25] J. M. Huang and Z. G. Liu , “A simple adaptive control approach for flexible joint robots,” 33rd Chinese Control Conference, pp. 8741-8746, 28-30 July 2014.
[26] A. C. Huang and Y. C. Chen, “Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties,” IEEE Transactions on Control Systems Technology, vol. 12, no. 5, pp. 770-775, Sept. 2004.
[27] M. C. Chien and A. C. Huang, “Adaptive impedance control of robot manipulators based on function approximation technique,” Robotica, vol. 22, no. 04, pp.395-403, Aug. 2004.
[28] A. C. Huang, S. C. Wu and W. F. Ting, “An FAT-based adaptive controller for robot manipulators without regressor matrix: Theory and Experiments,” Robotica, vol. 24, no. 02, pp. 205-210, Mar. 2006.
[29] A. C. Huang and K. K. Liao, “FAT-based adaptive sliding control for flexible arms, theory and experiments,” Journal of Sound and Vibration, vol. 298, no. 1-2, pp. 194-205, 22 Nov. 2006.
[30] C. Y. Kai and A. C. Huang, “A regressor-free adaptive controller for robot manipulators without Slotine and Li’s modication,” Robotica, vol. 31, no. 07, pp.1051-1058, Oct. 2013.
[31] A. C. Huang and M. C. Chien, Adaptive Control of Robot Manipulators, A Unified Regressor-Free Approach, World Scientific, 2010.