An adaptive output feedback motion tracking controller for robot manipulators: Uniform global asymptotic stability and experimentation

Yarza, A. ; Santibanez, V. ; Moreno-Valenzuela, J.

International Journal of Applied Mathematics and Computer Science, Tome 23 (2013) no. 3, pp. 599-611.

Résumé

This paper deals with two important practical problems in motion control of robot manipulators: the measurement of joint velocities, which often results in noisy signals, and the uncertainty of parameters of the dynamic model. Adaptive output feedback controllers have been proposed in the literature in order to deal with these problems. In this paper, we prove for the first time that Uniform Global Asymptotic Stability (UGAS) can be obtained from an adaptive output feedback tracking controller, if the reference trajectory is selected in such a way that the regression matrix is persistently exciting. The new scheme has been experimentally implemented with the aim of confirming the theoretical results.

Détail

Keywords: adaptive control, robot control, nonlinear control, output feedback, Lyapunov UGAS stability
Mots-clés : sterowanie adaptacyjne, sterowanie robotem, sterowanie nieliniowe, sprzężenie zwrotne, stabilność Lyapunova

Bibliographie

[1] Abdessameud, A. and Khelfi, M.F. (2006). A variable structure observer for the control of robot manipulators, International Journal of Applied Mathematics and Computer Science 16(2):189–196.

[2] Arimoto, S., Parra-Vega, V. and Naniwa, T. (1994). A class of linear velocity observers for nonlinear mechanical systems, Asian Control Conference, Tokyo, Japan, pp. 633–636.

[3] Arimoto, S. (1995a). Fundamental problems of robot control, Part I: Innovation in the realm of robot servo-loops, Robotica 13(1): 19–27.

[4] Arimoto, S. (1995b). Fundamental problems of robot control, Part II: A nonlinear circuit theory towards an understanding of dexterous motions, Robotica 13(2): 111–122.

[5] Bańka, S., Dworak, P. and Jaroszewski, K. (2013). Linear adaptive structure for control of a nonlinear MIMO dynamic plant, International Journal of Applied Mathematics and Computer Science 23(1): 47–63, DOI: 10.2478/amcs-2013-0005.

[6] Berghuis, H. and Nijmeijer, H. (1993). A passivity approach to controller-observer design for robots, IEEE Transactions on Robotics and Automation 9(6): 740–754.

[7] Burkov, I. (1993). Asymptotic stabilization of nonlinear Lagrangian systems without measuring velocities, International Symposium on Active Control in Mechanical Engineering, Lyon, France, pp. 37–41.

[8] Craig, J., Hsu, P. and Sastry, S. (1987). Adaptive control of mechanical manipulators, International Journal of Robotics Research 6(2): 16–28.

[9] Daly, J. and Schwarz, H. (2006). Experimental results for adaptive output feedback control, Robotica 24(6): 727–738.

[10] Kelly, R. (1993). A simple set-point robot controller by using only position measurements, International Federation of Automatic Control World Congress, Sydney, Australia, pp. 173–176.

[11] Kelly, R., Carelli, R. and Ortega, R. (1989). Adaptive motion control design to robot manipulators: An input-output approach, International Journal of Control 50(6): 2563–2581.

[12] Kelly, R., Santibanez, V. and Loria, A. (2005). Control of Robot Manipulators in Joint Space, Springer-Verlag, Berlin.

[13] Khalil, H. (2002). Nonlinear Systems, Prentice-Hall, Englewood Cliffs, NJ.

[14] Koditschek, D. (1984). Natural motion for robot arms, Conference on Decision and Control, Las Vegas, NV, USA, pp. 733–735.

[15] Lim, S., Dawson, D. and Anderson, K. (1996). Re-examining the Nicosia–Tomei robot observer-controller from a backstepping perspective, IEEE Transactions on Control Systems Technology 4(3): 304–310.

[16] Lopez-Araujo, D., Zavala-Rio, A., Santibanez, V. and Reyes, F. (2012). Output-feedback adaptive control for the global regulation of robot manipulators with bounded inputs, International Journal of Control, Automation and Systems 11(1): 105–115.

[17] Loria, A., Kelly, R. and Teel, A. (2005). Uniform parametric convergence in the adaptive control of mechanical systems, European Journal of Control 11(2): 87–100.

[18] Loria, A.E., Panteley, Popovic D. and Teel A. (2002). δ-Persistency of excitation: A necessary and sufficient condition for uniform attractivity. IEEE Conference on Decision and Control, Las Vegas, NV, USA, pp. 3506–3511.

[19] Loria, A. and Nijmeijer, H. (1998). Bounded output feedback tracking control of fully-actuated Euler–Lagrange systems, Systems Control Letters 33(3): 151–161.

[20] Middleton, R. and Goodwin, G. (1998). Adaptive computed torque control for rigid link manipulators, Systems Control Letters 10(1): 9–16.

[21] Moreno-Valenzuela, J., Santibanez, V., Orozco-Manriquez, E. and Gonzalez-Hernandez, L. (2010). Theory and experiments of global adaptive output feedback tracking control of manipulators, IET Control Theory and Applications 4(9): 1639–1654.

[22] Moreno-Valenzuela, J., Santibanez, V., Campa, R. (2008a). A class of OFT controllers for torque-saturated robot manipulators: Lyapunov stability and experimental evaluation, Journal of Intelligent Robotic Systems 51(1): 65–88.

[23] Moreno-Valenzuela, J., Santibanez, V., Campa, R. (2008b). On output feedback tracking control of robots manipulators with bounded torque input, International Journal of Control, Automation, and Systems 6(1): 76–85.

[24] Nicosia, S. and Tomei, P. (1990). Robot control by using only position measurements, IEEE Transactions on Automatic Control 35(9): 1058–1061.

[25] Ortega, R., Loria, A. and Kelly, R. (1995). A semiglobally stable output feedback PI2D regulator for robot manipulators, IEEE Transactions on Automatic Control 40(8): 1432–1436.

[26] Ortega, R. and Spong, M. (1989). Adaptive motion control of rigid robots: A tutorial, Automatica 25(6): 877–888.

[27] Reyes, F. and Kelly, R. (2001). Experimental evaluation of model-based controllers on a direct-drive robot arm, Mechatronics 11(3): 267–282.

[28] Sadegh, N. and Horowitz, R. (1987). Stability analysis of an adaptive controller for robotic manipulators, International Conference on Robotics and Automation, Raleigh, NC, USA, pp. 1223–1229.

[29] Santibanez, V. and Kelly, R. (2001). Global asymptotical stability of bounded output feedback tracking control for robot manipulators, IEEE Conference on Decision and Control, Orlando, FL, USA, pp. 1378–1379.

[30] Santibanez, V. and Kelly, R. (1999). Global convergence of the adaptive PD controller with computed feedforward for robot manipulators, IEEE International Conference on Robotics and Automation, Detroit, MI, USA, pp. 1831–1836.

[31] Slotine, J. and Li, W. (1987). On the adaptive control of robot manipulators, International Journal of Robotics Research 6(3): 49–59.

[32] Spong, M., Hutchinson, S. and Vidyasagar, M. (2005). Robot Modeling and Control, John Wiley and Sons, New York, NY.

[33] Witkowska, A. and Śmierzchalski, R. (2012). Designing a ship course controller by applying the adaptive backstepping method, International Journal of Applied Mathematics and Computer Science 22(4): 985–997, DOI: 10.2478/v10006-012-0073-y.

[34] Yarza, A., Santibanez, V. and Moreno-Valenzuela, J. (2011). Uniform global asymptotic stability of an adaptive output feedback tracking controller for robot manipulators, International Federation of Automatic Control World Congress, Milan, Italy, pp. 14590–14595.

[35] Zavala-Rio, A., Aguinaga-Ruiz, E. and Santibanez, V. (2011). Global trajectory tracking through output feedback for robot manipulators with bounded inputs, Asian Journal of Control 13(3): 430–438.

[36] Zergeroglu, E., Dawson, D.M., de Queiroz, M.S. and Krstic, M. (2000). On global output feedback tracking control of robot manipulators, Proceedings of the IEEE Conference on Decision and Control, Sydney, Australia, pp. 5073–5077.

[37] Zhang, F., Dawson, D.M., de Queiroz, M.S. and Dixon, W.E. (2000). Global adaptive output feedback tracking control of robot manipulators, IEEE Transactions on Automatic Control 45(6): 1203–1208.