Adaptive output feedback tracking control of a nonholonomic mobile robot. (English) Zbl 1298.93239

Summary: An adaptive output feedback tracking controller for nonholonomic mobile robots is proposed to guarantee that the tracking errors are confined to an arbitrarily small ball. The major difficulties are caused by simultaneous existence of nonholonomic constraints, unknown system parameters and a quadratic term of unmeasurable states in the mobile robot dynamic system as well as their couplings. To overcome these difficulties, we propose a new adaptive control scheme including the design of a new adaptive state feedback controller and two high-gain observers to estimate the unknown linear and angular velocities respectively. It is shown that the closed loop adaptive system is stable and the tracking errors are guaranteed to be within the pre-specified bounds which can be arbitrarily small. Simulation results also verify the effectiveness of the proposed scheme.


93C85 Automated systems (robots, etc.) in control theory
93C40 Adaptive control/observation systems
93B52 Feedback control
93D21 Adaptive or robust stabilization
Full Text: DOI


[1] Brockett, R. W., Asymptotic stability and feedback stabilization, (Differential geometric control theory (1983), Birkhauser: Birkhauser Boston), 181-191 · Zbl 0528.93051
[2] Do, K. D.; Jiang, Z. P.; Pan, J., Simultaneous tracking and stabilization of mobile robots: an adaptive approach, IEEE Transactions on Automatic Control, 49, 7, 1147-1152 (2004) · Zbl 1365.93321
[3] Do, K. D.; Jiang, Z.-P.; Pan, J., A global output-feedback controller for simultaneous tracking and stabilization of unicycle-type mobile robots, IEEE Transactions on Robotics and Automation, 20, 589-594 (2004)
[4] Dong, W.; Huo, W.; Tso, S. K.; Xu, W. L., Tracking control of uncertain dynamic nonholonomic system and its application to wheeled mobile robots, IEEE Transactions on Robotics and Automation, 16, 6, 870-874 (2000)
[5] Egerstedt, M.; Hu, X.; Stotsky, A., Control of mobile platforms using a virtual vehicle approach, IEEE Transactions on Automatic Control, 46, 1777-1782 (2001) · Zbl 1015.93040
[6] Fierro, R.; Lewis, F., Control of a nonholonomic mobile robot: backstepping kinematics into dynamics, Journal of Robotic Systems, 14, 3, 149-163 (1997) · Zbl 0897.70019
[7] Fukao, T.; Nakagawa, H.; Adachi, N., Adaptive tracking control of a nonholonomic mobile robot, IEEE Transactions on Robotics and Automation, 16, 609-615 (2000)
[8] Ge, S. S.; Wang, Z.; Lee, T. H., Adaptive stabilization of uncertain nonholonomic systems by state and output feedback, Automatica, 39, 8, 1451-1460 (2003) · Zbl 1038.93079
[10] Jiang, Z.-P., Lyapunov design of global state and output feedback tracker for nonholonomic control systems, International Journal of Control, 73, 9, 744-761 (2000) · Zbl 1006.93537
[11] Jiang, Z.-P.; Lefeber, E.; Nijmeijer, H., Saturated stablization and tracking of a nonholonomic mobile robot, Systems & Control Letters, 42, 327-332 (2001) · Zbl 0974.93040
[12] Jiang, Z.-P.; Nijmeijer, H., Tracking control of mobile robots: a case study in backstepping, Automatica, 1393-1399 (1997) · Zbl 0882.93057
[13] Khalil, H. K., Adaptive output feedback control of nonlinear systems represented by input-output models, IEEE Transactions on Automatic Control, 41, 177-188 (1996) · Zbl 0842.93033
[14] Kolmanovsky, I.; McClamroch, N., Development in nonholonomic control problems, IEEE Control System Magazine, 15, 20-36 (1995)
[15] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P., Nonlinear and adaptive control design (1995), John Wiley and Sons · Zbl 0763.93043
[16] Lee, K. W.; Khalil, H. K., Adaptive output feedback control of robot manipulators using high-gain observer, International Journal of Control, 67, 6, 869-886 (1997) · Zbl 0881.93049
[17] Lee, T. C.; Song, K. T.; Lee, C. H.; Teng, C. C., Tracking control of unicycle-modeled mobile robots using a saturation feedback controller, IEEE Transactions on Control Systems Technology, 9, 305-318 (2001)
[18] Loria, A., Global tracking control of one-degree-of-freedom Euler-Lagrange systems without velocity measurement, European Journal of Control, 144-151 (1996) · Zbl 0875.93156
[19] Luo, J.; Tsiotras, P., Exponentially convergent control laws for nonholonomic systems in power form, Systems & Control Letters, 35, 87-95 (1998) · Zbl 0909.93029
[20] (Nijmeijer, H.; Fossen, T. I., New directions in nonlinear observer design (1999), Springer-Verlag: Springer-Verlag London, U.K) · Zbl 0915.00063
[21] Samson, C., Velocity and torque feedback control of a nonholonomic cart, Advanced Robotics Control, 125-151 (1991) · Zbl 0800.93910
[22] Samson, C., Time-varying feedback stabilization of car-like wheeled mobile robots, International Journal of Robotics Research, 12, 1, 55-64 (1993)
[23] Sarkar, N.; Yun, X.; Kumar, V., Control of mechanical systems with rolling constraints: application to dynamic control of mobile robots, International Journal of Robotics Research, 13, 1, 55-69 (1994)
[24] Sordalen, O. J.; Egeland, O., Exponential stabilization of nonholonomic chained systems, IEEE Transactions on Automatic Control, 40, 35-49 (1995) · Zbl 0828.93055
[25] Tikhonov, A. N., Systems of differential equations containing small parameters in the derivatives, Matematicheski˘ Sbornik, 31, 73):3, 575-586 (1952) · Zbl 0048.07101
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