本研究是以影像為基礎的視覺伺服系統為架構，並且藉由論文中所閳述的影像轉換矩陣(即物件之影像速度與其空間速度之關係矩陣)為基礎來設計此控制器，使用的理論基礎為最小方根誤差運用遞迴運算求出每個取樣時間內系統的影像轉換矩陣，藉由影像轉換矩陣的收斂使得系統穩定且估算正確的控制命令。
接下來我們將提出一里阿普諾函式(Lyapunov function)證明此視覺伺服系統的穩定性，並且討論系統包含不確定因素(uncertainties)時的穩定性極限，經由更完整的攝影機模型推導出更接近於真實的影像轉換矩陣，由模擬的結果得知系統穩定性極限的數據並且比較在收斂性實驗的經驗數據，來提供架設此適應性控制系統的依據。
本文所提的視覺伺服系統主要的優點為避開繁雜的攝影機校正與推導機械臂的動態方程式，並且由即時的影像的回授與控制法則計算出此時的機械臂控制命令(Robot Command)正確追蹤到目標物。

In recent years, the application of robot is extensive. In order to recognize the relative position between robot and working space, CCD is applied to get the image information to orientate . The focus of our work is to achieve real-time tracking object using visual sensory feedback under non-calibrated environment. The image Jacobian, relating robot velocity commands to image feature’s velocity, is derived based on the scheme of three cameras and shown to be a function of camera focal lengths, fiducial’s depths, fiducial’s positions relative to robot reference frame and pose between camera reference frames and object reference frames. We proposed an on-line adaptive control algorithm to recursively estimate the image Jacobian for robot control. If the image jacobian matrix is convergence, the visual system will be stable. Then we will prove the stability of this visual system by Lyapunov function and discuss robust stability bounds of this linear discrete-time system with time-varying uncertainties. From the result of simulation and experimentation, we can get experience dates in mounting cameras.
The main advantages of our system is avoiding tedious camera calibration, pose estimation, and ignoring the robot dynamics. Experiment results are presented to demonstrate the effectiveness of the proposed algorithm. Experiments on MITSUBISHI RV-1 robot are presents to demonstrate the effectiveness of the image-based visual servo with our algorithm.

[1] A. C. Saderson and L. E. Weiss, ’’ Image-based visual servo control
using relational graph error singals,’’ Proc. IEEE, pp. 1074-1077,1980.
[2] B. K. P. Horn, Robot Vision. MIT Press, Cambridge, MA, 1986.
[3] T. Hamel and R. Mahony, ’’ Visual servoing of an under-actuated dynamic rigid-body system: an image-based approach,’’ IEEE Transactions on , Volume: 18 Issue: 2 , Apr 2002 ,Page(s): 187 –198
[4] J.S.Cho , H.W.Kim and I.S.Kweon, ’’ Image-based visual servoing using position and angle of image features,’’ Electronics Letters , Volume: 37 Issue: 13 , 21 Jun 2001 ,Page(s): 862 –864
[5] P.I.Corke and S.A.Hutchinson, ’’ A new partitioned approach to image-based visual servo control,’’ Robotics and Automation, IEEE Transactions on , Volume: 17 Issue: 4 , Aug 2001 ,Page(s): 507 –515
[6] J.S Park and M.J. Chung, ’’ Path planning with uncalibrated stereo rig for image-based visual servoing under large pose discrepancy,’’ Robotics and Automation, IEEE Transactions on , Volume: 19 Issue: 2 , Apr 2003 ,Page(s): 250 –258
[7] C.Collewet, F.Chaumette and P.Loisel, ’’ Image-based visual servoing on planar objects of unknown shape,’’ Volume: 1 , 2001 ,Page(s): 247 -252 vol.1
[8] Y.T.Kim, S.C.Fan, S.H.Han and H.S.Go,’’ Image-based visual feedback control of a dual-arm robot,’’ Industrial Electronics, 2001. Proceedings. ISIE 2001. IEEE International Symposium on , Volume: 3 , 2001 ,Page(s): 1603 -1608 vol.3
[9] J.Feedema and O.Mitchell,’’Vision-guided servoing with feature based trajectory generation,’’ IEEE Trans. Robot. Autom, vol.5, pp.691-700, Oct. 1989.
[10] B.Espian, F.Chaumette, and P.Rives, ’’ A New Approach to Visual Servoing in Robotics,’’ IEEE Transactions on Robotics and Automation,
vol.8, pp. 313-326, 1991.
[11] K.Hashimoto, T.Kimoto, T.Ebine, and H.Kimura, ’’Manipulator control with image-based visual servo,’’ in Proc. IEEE Int. Coni. Robotics and Automation, pp.2267-2272, 1991.
[12]N.P.Papanikolopoulos and P.K.Khosla, ’’ Adaptive Robot Visual Tracking: Theory and Experiments,’’ IEEE Transactions on Automatic Control, vol.38, no.3,pp.429-445, 1993.
[13] N.P.Papanikolopoulos and P.K.Khosla, ’’Visual Tracking of a Moving Target by a Camera Mounted on a Robot: A Combination of Vision and Control,’’ IEEE Transactions on Robotics and Automation, vol.9, no.1, pp.14-36-5, 1993.
[14] R.J.Schilling, ’’Fundamentals of robotics: analysis and control,’’ Prentice-Hall,Inc., 1990.
[15]R.Jain,R.Kasturi,B.G.Schunck,’’MachineVision,’’McGraw-Hall,Inc.,1995
[16] J.A.Piepmeier,’’ Experimental results for uncalibrated eye-in-hand visual servoing’’, System Theory, 2003. Proceedings of the 35th Southeastern Symposium on , 2003 ,Page(s): 335 –339
[17] R.Kelly, R.Carelli, O.Nasisi, B.Kuchen,and F.Reyes,’’Stable visual servoing of camera-in-hand robotic systems’’ Mechatronics, IEEE/ASME Transactions on , Volume: 5 Issue: 1 , Mar 2000 Page(s): 39 –48
[18] C.C.Cheah, S.Kawamura,and S.Arimoto, ’’Visual servoing of robot manipulator without camera calibration’’ Advanced Motion Control, 1998. AMC ''98-Coimbra., 1998 5th International Workshop on , 29 Jun-1 Jul 1998 Page(s): 688 –693
[19] E.Zergeroglu, D.M.Dawson, M.S. Queiroz, S.Nagarkatti, ’’Robust visual-servo control of robot manipulators in the presence of uncertainty’’ Decision and Control, 1999. Proceedings of the 38th IEEE Conference on , Volume: 4 , 1999 Page(s): 4137 -4142 vol.4
[20] A.Astolfi,Liu Hsu, M.Netto, R.Ortega,’’A solution to the adaptive visual servoing problem’’ Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on , Volume: 1 , 2001 Page(s): 743 -748 vol.1
[21] J.H. SU and I.K.FONG ; ’’New robust stability bounds of linear discrete-time systems with time-invarying uncertainties’’ INT.J.CONTR-
OL.1993.VOL.58. NO.6.1461-1467
[22] Katsuhiko Ogata,Discrete-Time Control Systems,1995 by Prentice-
Hall, Inc.
[23] D.Y. Landau , Adaptive Control-The Mode Reference Approach
[24] Hsin ,Color Image Registration Using Wavelet-Based Motion Model and Its Application to New View Synthesis,2001