Abstract
In this paper, a nonlinear controller based on sliding mode control is applied to a two-wheeled Welding Mobile Robot (WMR) to track a smooth curved welding path at a constant velocity of the welding point. The mobile robot is considered in terms of dynamics model in Cartesian coordinates under the presence of external disturbance, and its parameters are exactly known. It is assumed that the disturbance satisfies the matching condition with a known boundary. To obtain the controller, the tracking errors are defined, and the two sliding surfaces are chosen to guarantee that the errors converge to zero asymptotically. Two cases are to be considered : fixed torch and controllable torch. In addition, a simple way of measuring the errors is introduced using two potentiometers. The simulation and experiment on a two-wheeled welding mobile robot are provided to show the effectiveness of the proposed controller.
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Abbreviations
- (x, y):
-
Coordinates of the WMR’s center [m]
- ø:
-
Heading angle of the WMR [rad]
- v:
-
Linear velocity of the WMR’s center [m/s]
- ω:
-
Angular velocity of the WMR’s center [rad/s]
- ωrw, ωlw :
-
Angular velocities of the right and the left wheels [rad/s]
- (xw, yw):
-
Coordinates of the welding point [m]
- øw:
-
Heading angle of the welding point [rad]
- Vw:
-
Linear velocity of the welding point [m/s]
- ωw:
-
Angular velocity of the welding point [rad/s]
- Xr, yr:
-
Coordinates of the reference point [m]
- ør:
-
Angle between\(\vec \nu \) and x axis [rad]
- vr:
-
Welding velocity [m/s]
- ωr:
-
Angular velocity of the reference point (the rate of change of\(\vec \nu _r \)) [rad/s]
- b:
-
Distance between driving wheel and the symmetric axis [m]
- r:
-
Radius of driving wheel [m]
- d:
-
Distance between geometric center and mass center of the WMR [m]
- l:
-
Torch length [m]
- M (q):
-
Symmetric, positive definite inertia matrix
- V(q,\(\dot q\)):
-
Centripetal and coriolis matrix
- B(q):
-
Input transformation matrix
- A(q):
-
Matrix related with the nonholonomic constraints
- τ:
-
Control input vector [kgm]
- τrw, τlw:
-
Torques of the motors which act on the
- right and the left wheels [kgm] λ:
-
Constraint force vector
- u:
-
Control law which determines error
- dynamics mc :
-
Mass of the body without the driving
- wheels [kg] mw :
-
Mass of each driving wheel with its
- motor [kg] Iw :
-
Moment of inertia of each wheel with
- its motor about the wheel axis [kgm2] Im :
-
Moment of inertia of each wheel with its motor about the wheel diameter [kgm2]
- Ic :
-
Moment of inertia of the body about the vertical axis through the mass center of the WMR [kgm2]
References
Bui, T. H., Chung, T. L., Nguyen, T. T. and Kim, S. B., 2003, “Adaptive Tracking Control of Two-Wheeled Welding Mobile Robot with Smooth Curved Welding Path,”KSME International Journal, Vol. 17. No. 11. pp. 1684–1694.
Bui, T. H., Nguyen, T. T., Chung, T. L. and Kim, S. B., 2003, “A Simple Nonlinear Control of a Two-Wheeled Welding Mobile Robot,”International Journal of Control, Automation, and System (IJCAS), Vol. 1, No. I, pp. 35–42.
Chwa, D. K., Seo J. H., Kim, P. J. and Choi, J. Y., 2002, “Sliding Mode Tracking Control of Nonholonomic Wheeled Mobile Robots,”Proc. of the American Control Conference, pp. 3991–996.
Fierro. R. and Lewis, F. L., 1997, “Control of a Nonholonomic Mobile Robot : Backstepping Kinematics into Dynamics.”Journal of Robotic Systems, John Wiley & Sons, Inc., pp. 149–163.
Fukao, T., Nakagawa, H. and Adachi, N., 2000, “Adaptive Tracking Control of a Nonholonomic Mobile Robot,”IEEE Trans, on Robotics and Automation, Vol. 16, No. 5, pp. 609–615.
Jeon, Y. B., Park, S. S. and Kim, S. B., 2002, “Modeling and Motion Control of Mobile Robot for Lattice Type of Welding,”KSME Inter national Journal, Vol. 16, No. 1, pp. 83–93.
Jean-Jacques E. Slotine and Weiping Li. 1991,Applied Nonlinear Control, Prentice-Hall International, Inc., pp. 122–125.
Kam, B. O., Jeon, Y. B. and Kim, S. B., 2001, “Motion Control of Two-Wheeled Welding Mobile Robot with Seam Tracking Sensor,”Proc. IEEE Industrial Electronics, Vol. 2, pp. 851–856.
Kanayama, Y., Kimura, Y., Miyazaki, F. and Noguchi, T., 1991, “A Stable Tracking Control Method for a Nonholonomic Mobile Robot,”Proc. IEEE Intelligent Robots and Systems Workshop, Japan, Vol. 3. pp. 1236–1241.
Kim, M. Y., Ko, K. W., Cho, H. S. and Kim, J. H., 2000, “Visual Sensing and Recognition of Welding Environment for Intelligent Shipyard Welding Robots,”Proc. IEEE Intelligent Robots and Systems, Vol. 3, pp. 2159–2165.
Lee. T. C., Lee, C. H. and Teng, C. C., 1999, “Adaptive Tracking Control of Nonholonomic Mobile Robot by Computed Torque,”Proc. IEEE Decision and Control, pp. 1254–1259.
Yang, J. M. and Kim, J. H., 1999, “Sliding Mode Control for Trajectory Tracking of Nonholonomic Wheeled Mobile Robots,”IEEE Trans. Robotics and Automation, Vol. 15, No. 3, pp. 578–587.
Yun, X. and Yamamoto, Y., 1993, “Internal Dynamics of a Wheeled Mobile Robot,”Proc. IEEE Intelligent Robots and Systems, pp. 1288–1294.
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Chung, T.L., Bui, T.H., Nguyen, T.T. et al. Sliding mode control of two-wheeled welding mobile robot for tracking smooth curved welding path. KSME International Journal 18, 1094–1106 (2004). https://doi.org/10.1007/BF02983284
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DOI: https://doi.org/10.1007/BF02983284