無回歸矩陣機械臂適應性控制法改善了傳統方法，使其能夠有效地處理未知時變參數，並且簡化了控制器設計的複雜度。跟許多的控制法相同，大部分的無回歸矩陣機械臂適應性控制都需要回授機械臂關節的速度與位置。本文提出無需速度回授的無回歸矩陣機械臂適應性控制器，其中使用線性濾波器產生估測速度來取代真實速度回授，同時利用Lyapunov穩定法則證明閉迴路的穩定性。本文以電腦模擬和實驗來證明此控制法的可行性。

The regressor-free approach for robot manipulators provides a feasible adaptive design to deal with time-varying uncertainties without knowing their variation bounds. Similar to most other strategies, the adaptive controllers based on the regressor-free approach need the feedback of both the joint positions and velocities. In this paper, we would like to propose a regressor-free adaptive controller without using the velocity measurements. A linear filter is constructed to generate a pseudo velocity signal. The closed loop stability is proved by Lyapunov-like method. Both the simulation and experimental studies show effectiveness of the proposed design.

F. Alonge, F. D’Ippolito and F. M. Raimondi, “An adaptive control law for robotic manipulator without velocity feedback,” Control Engineering Practice, vol. 11, pp 999-1005, 2003.

M. A. Arteaga and R. Kelly, “Robot control without velocity measurements: New theory and experimental results,” IEEE Trans. on Robotics and Automation, vol. 20, no. 2, pp. 297–308, Apr. 2004.

M. A. Arteaga, “Robot control and parameter estimation with only joint position measurements,” Automatica, vol. 39, pp 67-73, 2003.

T. Burg, J. Hu and D. Dawson, “A redesigned DCAL controller without velocity measurements: Theory and experimentation,” in Proc. IEEE Conf. Decis. Contr., Lake Buena Vista, FL, Dec. 1994, pp. 824-828.

F. Caccavale, C. Natale, and L. Villani, “Task-space control without velocity measurements,” in Proc. IEEE Int. Conf. Robotics and Automation, Detroit, MI, pp. 512–517, 1999.

M. C. Chien and An-Chyau Huang, “Adaptive control for flexible-joint electrically driven robot with time-varying uncertainties,” IEEE Transactions on Industrial Electronics, vol. 54, no. 2, pp 1032-1038, April 2007.

J. J. Craig, Adaptive Control of Robot Manipulators. Reading, MA: Addison-Wesley, 1988.

W. E. Dixon, M. S. de Queiroz, D. M. Dawson, and F. Zhang, “Tracking control of robot manipulators with bounded torque inputs,” Robotica, vol. 17, pp. 121–129, 1999.

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems. Upper Saddle River, NJ, USA: Prentice-Hall, 2002.

R. M. Guerra, A. Poznyak, E. Gortcheva, and V. Diaz de Leon, “Robot angular link velocity estimation in the presence of high-level mixed uncertainties,” Proc. IEE—Contr. Theory Appl., vol. 147, no. 5, pp. 515–522, 2000.

A. C. Huang and M. C. Chien, Adaptive Control of Robot Manipulators: A Unified Regressor-Free Approach, World Scientific, 2010.

A. C. Huang and Y. S. Kuo, “Sliding control of nonlinear systems containing time-varying uncertainties with unknown bounds,” Int. J. Control, vol. 74, no. 3, pp. 252–264, 2001.

A. C. Huang, S. C. Wu, and W. F. Ting, “A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments,” Robotica, vol. 24, pp. 205–210, 2006.

A. C. Huang, Y. F. Chen and C. Y. Kai, Adaptive Control of Underactuated Mechanical Systems, World Scientific, 2015.

C. Y. Kai and A. C. Huang, “A regressor-free adaptive controller for robot manipulators without Slotine and Li’s modification,” Robotica, vol. 31, Issue 7, pp.1051-1058, Oct. 2013.

K. Kaneko and R. Horowitz, “Repetitive and Adaptive Control of Robot Manipulators with Velocity Estimation,” IEEE Trans. on Robotics and Automation, vol. 13, no. 2, pp 204-217, April 1997.

R. C. Kavanagh, “Probabilistic learning technique for improved accuracy of sinusoidal encoders,” IEEE Trans. Ind. Electron., vol. 48, no. 3, pp. 673–681, Jun. 2001.

R. Kelly, V. Santibanez and A. Loria, Control of Robot Manipulators in Joint Space, Springer-Verlag, London Limited, 2005.

B. C. Kuo and F. Golnaraghi, Automatic Control Systems, 8th ed. New York, NY, USA: Wiley, 2002.

Laib, “Adaptive Output Regulation of Robot Manipulators Under Actuator Constraints, “ IEEE Trans. on Robotics and Automation, vol. 16, no. 1. pp 29-35, Feb. 2000.

J. G. Lau, M. A. Arteaga, L. A. Munoz and V. P. Vega, “On the control of cooperative robots without velocity measurements,” IEEE Trans. Contr. Syst. Technol., vol. 12, no. 4, pp 600-608, July 2004.

F. L. Lewis, D. M. Dawson and C. T. Abdallah, Robot Manipulator Control: Theory and Practice, Second Ed., Marcel Dekker, Inc., 2004.
Y. Li, S. Tong and T. Li, “Adaptive fuzzy output feedback control for a single-link flexible robot manipulator driven DC motor via backstepping, “Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp 483-494, 2013.

S. Nicosia and P. Tomei, “Robot control by using only joint position measurements,” IEEE Trans. Automat. Contr., vol. 35, pp. 1058- 1061, Sep. 1990.

N. S. Nise, Control Systems Engineering, John-Wiley Sons, 4th edition, 2004.

K. Ogata, Modern Control Engineering, 5th ed. New Jersey: Prentice Hall, 2009.

T. Ohmae, T. Matsuda, and K. Kamiyama, “A microprocessor-controlled high-accuracy wide-range speed regulator for motor drives,” IEEE Trans. Ind. Electron., vol. 29, no. 4, pp. 207–211, Aug. 1982.

S. Purwar, I. N. Kar and A. N. Jha, “Adaptive output feedback tracking control of robot manipulators using position measurements only,” Expert Systems with Applications, vol. 34, no. 4, pp 2789-2798, 2008.

F. J. Sharifi, V. Hayward, and C.-S. J. Chen, “Discrete-time adaptive windowing for velocity estimation,” IEEE Trans. Contr. Syst. Technol., vol. 8, no. 6, pp. 1003–1009, Nov. 2000.

M. W. Spong, S. Hutchinson and M. Vidyasaga, Robot Modelling and Control, John Wiley & Sons, Inc., 2006.

Y. X. Su, C. H. Zheng, D. Sun and B. Y. Duan, “A simple nonlinear velocity estimator for high-performance motion control,” IEEE Trans. Ind. Electron, vol. 52, no. 4, pp. 1161-1169, Aug. 2005.

P. Tomei, “Design of nonlinear observers for elastic joint robots,” IFAC Symp. Nonlinear Contr. Syst. Design, Capri, Italy, June 1989.

R. J. Wai, Y. C. Huang, Z. W. Yang and C. Y. Shih, “Adaptive fuzzy-neural-network velocity sensorless control for robot manipulator position tracking, “ IET Control Theory and Applications, vol. 4, no. 6, pp 1079-1093, 2010.

E. Zergeroglu, W. E. Dixon, D. Haste, and D. M. Dawson, “A composite adaptive output feedback tracking controller for robotic manipulators,” Robotica, vol. 17, pp. 591–600, 1999.

F. Zhang, D. M. Dawson, M. S. de Queiroz, and W. E. Dixon, “Global adaptive output feedback tracking control of robot manipulators,” IEEE Trans. Automat. Contr., vol. 45, no. 6, pp. 1203–1208, Jun. 2000.