Abstract
In this paper, two nonlinear control methods including adaptive learning control and adaptive robust control are designed for a robotic manipulator with time-varying uncertainties. We first present an adaptive learning control by incorporated learning control approaches into an adaptive control system to handle periodic uncertainties with known periods. We explore Lyapunov functional method to design the controller such that the convergence of tracking errors can be ensured. If the periods of uncertaines are unknown or uncertainties are non-periodic, an adaptive robust control is further designed to guarantee that the solution trajectory is finite and arbitrarily close to the desired trajectory by choosing design parameters in the controller. The efficacy of the proposed nonlinear controllers has been demonstrated in a two-link robot manipulator.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arimoto, S.: Control Theory of Nonlinear Mechanical Systems-A Passivity-Based and Circuit-Theoretic Approach. Clarendon Press, Oxford (1996)
Buss, S., Kim, J.S.: Selectively damped least squares for inverse kinematics. Journal of Graphics tools 10(3), 37–49 (2005)
Choi, J.Y., Lee, J.S.: Adaptive iterative learning control of uncertain robotic systems. Inst. Elect. Eng. Proc. 147(2), 217–223 (2000)
Sun, M.X., Ge, S.S., Mareels, M.Y.: Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning. IEEE Trans. Robot. 22(3), 563–568 (2006)
Ge, S.S., Lee, T.H., Hang, C.C.: Structure network modeling and control of rigid body robots. IEEE Trans. Robot. Autom. 14(5), 823–826 (1998)
Ge, S.S., Lee, T.H., Harris, C.J.: Adaptive Neural Network Control of Robotic Manipulators. World Scientific, London (1998)
Lewis, F.L., Abdallah, C.T., Dawson, D.M.: Control of Robot Manipulators. Macmillan, New York (1993)
Lewis, F.L., Jagannathan, S., Yesildirek, A.: Neural Network Control of robot Manipulators and Nonlinear Systems. Taylor & Francis, London (1999)
Maciejewski, A.A., Klein, C.K.: Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments. International Journal of Robotics Research 4, 109–117 (1985)
Norrlof, M.: An adaptive iterative learning control algorithm with experiments on an industrial robot. IEEE Trans. Robot. Autom. 18(2), 245–251 (2002)
Qu, Z.H., Dawson, D.: Robust Tracking Control of Robot Manipulators. IEEE Press, New York (1996)
Sadegh, N., Horowitz, R.: Stability and robustness analysis of a class of adaptive controller for robotic manipulators. Int. J. Robot. Res. 9(3), 74–92 (1990)
Slotine, J.J.E., Li, W.: Adaptive manipulator control: a case study. IEEE Trans. Autom. Control 33(11), 995–1003 (1988)
Spong, M.W., Midyasagar, M.: Robot Dynamics and Control. Wiley, New York (1989)
Tomei, P.: Robust adaptive friction compensation for tracking control of robot manipulators. IEEE Trans. Autom. Control 45(11), 2164–2169 (2000)
Xu, J.X., Viswanathan, B., Qu, Z.H.: Robust learning control for robotic manipulators with an extension to a class of non-linear system. Int. J. Control 73(10), 858–870 (2000)
Xu, J.X., Yan, R.: Synchronization of chaotic systems via learning control. International journal of bifurcation and Chaos 15(12), 4035–4041 (2005)
Xu, J.X., Yan, R.: On repetitive learning control for periodic tracking tasks. IEEE Trans. on Automatic Control 51(11), 1842–1848 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yan, R., Tee, K.P., Li, H. (2010). Nonlinear Control of a Robot Manipulator with Time-Varying Uncertainties. In: Ge, S.S., Li, H., Cabibihan, JJ., Tan, Y.K. (eds) Social Robotics. ICSR 2010. Lecture Notes in Computer Science(), vol 6414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17248-9_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-17248-9_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17247-2
Online ISBN: 978-3-642-17248-9
eBook Packages: Computer ScienceComputer Science (R0)