Abstract
Considered is the control design problem for planar motion of a wheeled robot. The mathematical model of the robot accounts for kinematic relationships between the velocity of a given point of chassis referred to as the reference point, orientation of the chassis, and control. Among the kinematic relations is the requirement that each of the four wheels perform a slip-free motion. The rear wheels are assumed to be driving while the front wheels are responsible for the rotation of the chassis. The control objective is to place the reference point in the prespecified trajectory and to stabilize the motion of the reference point along the prespecified trajectory. The trajectory consists of line segments and circular arcs. In the mathematical model under consideration, the current curvature of the trajectory of the reference point is taken as control; it is related to the steering angle of the front wheels by a simple algebraic expression. The control is subject to two-sided constraints due to limitations on the steering angle of the front wheels. For the control law proposed, the attraction domain in the space “distance to the trajectory—orientation” is analyzed. For the initial conditions from this domain, the system is guaranteed to hit a trajectory with given index of exponential stability.
Similar content being viewed by others
References
Samson, C., Control of Chained Systems Application to Path Following and Time-Varying Point-Stabilization of Mobile Robots, IEEE Trans. Automat. Control, 1995, vol. 40, no. 1, pp. 64–77.
Kolmanovsky, I. and McClamroch, N.H., Developments in Nonholonomic Control Problems, IEEE Control Syst., 1995, no. 12, pp. 20–36.
Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemani (Nonlinear and Adaptive Control of Complex Dynamical Systems), St. Petersburg: Nauka, 2000.
Thuilot, B., Cariou, C., Martinet, P., and Berducat, M., Automatic Guidance of a Farm Tractor Relying on a Single CP-DGPS, Autonomous Robots, 2002, no. 13, pp. 53–61.
Cordesses, L., Cariou, C., and Berducat M., Combine Harvester Control Using Real Time Kinematic GPS, Precision Agriculture, 2000, no. 2, pp. 147–161.
Guldner, J. and Utkin, V.I., Stabilization of Nonholonomic Mobile Robots Using Lyapunov Functions for Navigation and Sliding Mode Control, Proc. 33rd IEEE Conf. Decision Control, Florida, 1994, pp. 2967–2972.
Pyatnitskii, E.S., Absolute Stability of Nonstationary Nonlinear Systems, Avtom. Telemekh., 1970, no. 1, pp. 5–15.
Gelig, A.H., Leonov, G.A., and Yakubovich, V.A., Ustoichivost’ nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with Non-Unique Equilibrium State), Moscow: Nauka, 1978.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994.
Formal’skii, A.M., Upravlyaemost’ i ustoichivost’ sistem s ogranichennymi resursami (Controllability and Stability of Systems with Limited Resource), Moscow: Nauka, 1974.
Rapoport, L.B., Estimation of an Attraction Domain for Multivariable Lur’e Systems Using Looseless Extension of the S-Procedure, Proc. Am. Control Conf., San-Diego, 1999, pp. 2395–2396.
Rapoport, L.B. et al., OCTOPUS: Multi Antennae GPS/GLONASS RTK System, Proc. ION GPS’99 Technical Meeting, Nashville, 1999, pp. 797–804.
Zotov, Yu.K., Controllability and Stabilization of the Programmed Motions of a Transport Robot, Prikl. Mat. Mekh., 2000, vol. 64, no. 6, pp. 909–928.
Author information
Authors and Affiliations
Additional information
Original Russian Text © L.B. Rapoport, 2006, published in Avtomatika i Telemekhanika, 2006, No. 9, pp. 69–89.
This work was supported by the Russian Foundation for Basic Research, project no. 04-01-00391a, and Integrated Research Program no. 19–1.5 of the Presidium of the Russian Academy of Sciences.
Rights and permissions
About this article
Cite this article
Rapoport, L.B. Estimation of attraction domains in wheeled robot control. Autom Remote Control 67, 1416–1435 (2006). https://doi.org/10.1134/S0005117906090062
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0005117906090062