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Robust Practical Point Stabilization of a Nonholonomic Mobile Robot Using Neural Networks

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Abstract

A control structure that makes possible the integration of a kinematiccontroller and a neural network (NN) computed-torque controller fornonholonomic mobile robots is presented. A combined kinematic/torque controllaw is developed and stability is guaranteed by Lyapunov theory. Thiscontrol algorithm is applied to the practical point stabilization problemi.e., stabilization to a small neighborhood of the origin. The NN controllercan deal with unmodeled bounded disturbances and/or unstructured unmodeleddynamics in the vehicle. On-line NN weight tuning algorithms that do notrequire off-line learning yet guarantee small tracking errors and boundedcontrol signals are utilized.

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References

  • Barraquand, J. and Latombe, J.-C.: 1991, Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles, in: Proc. IEEE Int. Conf. Robot. Autom., Sacramento, CA, 1991, pp. 2328–2335.

  • Berns, K., Dillman, R., and Hofstetter, R.: 1991, An application of a backpropagation network for the control of a tracking behavior, in: Proc. IEEE Int. Conf. on Robotics and Automation, Vol. 3, pp. 2426–2431, Sacramento, CA, April 1991.

    Google Scholar 

  • Bloch, A. M., Reyhanoglu, M., and McClamroch, N. H.: 1992, Control and stabilization of nonholonomic dynamic systems, IEEE Trans. Autom. Control 37(11), 1746–1757.

    Google Scholar 

  • Brockett, R. W.: 1983, Asymptotic stability and feedback stabilization, in: R. W. Brockett, R. S. Millman, and H. J. Sussmann (eds.), Differential Geometric Control Theory, Boston, Birkhäuser, pp. 181–191.

    Google Scholar 

  • Campion, G., d’Andrréa-Novel, B., and Bastin, G.: 1991, Controllability and state feedback stabilizability of nonholonomic mechanical systems, in: C. Canudas de Wit (ed.), Lecture Notes in Control and Information Science, Springer-Verlag, Berlin, pp. 106–124.

    Google Scholar 

  • Canudas de Wit, C., Khennouf, H., Samson, C., and Sordalen, O. J.: 1993, Nonlinear control design for mobile robots, in: Y. F. Zheng (ed.), Recent Trends in Mobile Robots, World Scientific, Singapore, pp. 121–156.

    Google Scholar 

  • Canudas de Wit, C. and Khennouf, H.: 1995, quasi-continuous stabilizing controllers for nonholonomic systems: design and robustness considerations, in: Proc. Eur. Control Conf., Rome, 1995, pp. 2630–2635.

  • Chen, F. C. and Liu, C. C.: 1994, Adaptively controlling nonlinear continuous-time systems using multilayer neural network, IEEE Trans. Autom. Control 39(6), 1306–1310.

    Google Scholar 

  • Cybenko, G.: 1989, Approximation by superposition of a sigmoidal function, Math. Controls Sig. Syst. 2(4), pp. 303–314.

    Google Scholar 

  • Fierro, R. and Lewis, F. L.: 1995, Control of nonholonomic mobile robot: Backstepping kinematics into dynamics, in: Proc. IEEE Conf. Dec. Control, New Orleans, LA, 1995, pp. 3805–3810.

  • Hornik, K., Stinchcombe, M., and White, H.: 1989, Multilayer feedforward networks are universal approximators, Neural Network 2, 359–366.

    Google Scholar 

  • Jiang, Z. P. and Pomet, J.-B.: 1994, Combining backstepping and time-varying techniques for a new set of adaptive controllers, in: Proc. IEEE Conf. Dec. Control, Lake Buena Vista, FL, 1994, pp. 2207–2212.

  • Kanayama, Y., Kimura, Y., Miyazaki, F., and Noguchi, T.: 1990, A stable tracking control method for an autonomous mobile robot, in: Proc. IEEE Int. Conf. Robot. Autom., 1990, pp. 384–389.

  • Kolmanovsky, I. and McClamroch, N. H.: 1995, Developments in nonholonomic control problems, in: IEEE Control Systems, Dec. 1995, pp. 20–36.

  • Lewis, F. L., Abdallah, C. T., and Dawson, D. M.: 1993, Control of Robot Manipulators, MacMillan, New York.

    Google Scholar 

  • Lewis, F. L.: 1996, Neural network control of robot manipulators, in: 1996 June, IEEE Expert, pp. 64–75.

  • Lewis, F. L., Yesildirek, A., and Liu, K.: 1996, Multi-layer neural-net roobot controller with guaranteed tracking performance, IEEE Trans. Neural Netw. 7(2), 1–20.

    Google Scholar 

  • M’Closkey, R. T. and Murray, R. M.: 1994, Extending exponential stabilizers for nonholonomic systems from kinematic controlllers to dynamic controllers, in: Proc. IFAC Symp. Robot Control, Capri, Italy, 1994, pp. 211–216.

  • Murray, R. M., Li, Z., and Sastry, S. S.: 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.

    Google Scholar 

  • Nagata, S., Sekiguchi, M., and Asakawa, K.: 1990, Mobile robot control by a structured hierarchical neural network, IEEE Control Systems, 69–76.

  • Narendra, K. S.: 1991, Adaptive control using neural networks, in: W. T. Miller, R. S. Sutton, and P. W. Werbos (eds), Neural Networks for Control, MIT Press, Cambridge, pp. 115–142.

    Google Scholar 

  • Oelen, W., Berghuis, H., Nijmeijer, H., and Canudas de Wit, C.: 1995, Hybrid stabilizing control on a real mobile robot, IEEE Robot. automat. Magazine, 16–23.

  • Polycarpou, M. M. and Ioannu, P. O.: 1992, Neural networks as on-line approximators of nonlinear systems, in: Proc. IEEE Conf. Dec. Control, Tucson, AZ, 1992, pp. 7–12.

  • Rovithakis, G. A. and Christodoulou, M. A.: 1994, Adaptive control of unknown plants using dynamical neural networks, IEEE Trans. Syst. Man Cyber. 24(3), 400–412.

    Google Scholar 

  • Sadegh, N.: 1993, A perceptron network for functional identification and control of nonlinear systems, IEEE Trans. Neural Netw. 4(6), 982–988.

    Google Scholar 

  • Samson, C.: 1991, Velocity and torque feedback control of a nonholonomic cart, in: C. Canudas de Wit (ed.), Lecture Notes in Control and Information Science, Springer-Verlag, Berlin, pp. 125–151.

    Google Scholar 

  • Sarkar, N. Yun, X., and Kumar, V.: 1994, Control of mechanical systems with rolling constraints: Application to dynamic control of mobile robots, Int. J. Robot. Res. 13(1), 55–69.

    Google Scholar 

  • Werbos, P. J.: 1989, Backpropagation: past and future, in: Proc. 1988 Int. Conf. Neural Netw., Vol. 1, 1989, pp. 1343–1353.

    Google Scholar 

  • Yamamoto, Y. and Yun, X.: 1993, Coordinating locomotion and manipulation of a mobile manipulator, in: Y. F. Zheng (ed.), Recent Trends in Mobile Robots, World Scientific, Singapore, pp. 157–181.

    Google Scholar 

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Fierro, R., Lewis, F.L. Robust Practical Point Stabilization of a Nonholonomic Mobile Robot Using Neural Networks. Journal of Intelligent and Robotic Systems 20, 295–317 (1997). https://doi.org/10.1023/A:1007916529436

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