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Finite-time tracking control of multiple nonholonomic mobile robots with external disturbances. (English) Zbl 1363.93009
Summary: This paper investigates finite-time tracking control problem of multiple nonholonomic mobile robots in dynamic model with external disturbances, where a kind of Finite-Time Disturbance Observer (FTDO) is introduced to estimate the external disturbances for each mobile robot. First of all, the resulting tracking error dynamic is transformed into two subsystems, i.e., a third-order subsystem and a second-order subsystem for each mobile robot. Then, the two subsystem are discussed respectively, continuous finite-time disturbance observers and finite-time tracking control laws are designed for each mobile robot. Rigorous proof shows that each mobile robot can track the desired trajectory in finite time. Simulation example illustrates the effectiveness of our method.

MSC:
93A14 Decentralized systems
93D15 Stabilization of systems by feedback
93D21 Adaptive or robust stabilization
93C85 Automated systems (robots, etc.) in control theory
93C73 Perturbations in control/observation systems
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[1] Bhat, S., Bernstein, D.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 (2000), 751-766. · Zbl 0945.34039
[2] Chen, W.: Disturbance observer based control for nonlinear systems. IEEE/ASME Trans. Mechatronics 9 (2004), 706-710.
[3] Chen, W., Ballance, D., Gawthrop, P., O’Reilly, J.: A nonlinear disturbance observer for robotic manipulators. IEEE Trans. Ind. Electron. 47 (2000), 932-938.
[4] Ding, S., Wang, J., Zheng, W.: Second-order sliding mode control for nonlinear uncertain systems bounded by positive functions. IEEE Trans. Ind. Electron. 62 (2015), 5899-5909.
[5] Desai, J., Ostrowski, J., Kumar, V.: Modeling and control of formations of nonholonomic mobile robots. IEEE Trans. Robot. Automat. Control 17 (2001), 905-908.
[6] Dong, W.: Robust formation control of multiple wheeled mobile robots. J. Intel. Robot. Syst.: Theory and Appl. 62 (2011), 547-565. · Zbl 1245.93085
[7] Dong, W., Farrell, J.: Cooperative control of multiple nonholonomic mobile agents. IEEE Trans. Automat. Control 53 (2008), 1434-1448. · Zbl 1367.93226
[8] Dong, W., Farrell, J.: Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty. Automatica 45 (2009), 706-710. · Zbl 1166.93302
[9] Du, H., He, Y., Cheng, Y.: Finite-time cooperative tracking control for a class of second-order nonlinear multi-agent systems. Kybernetika 49 (2013), 507-523. · Zbl 1274.93008
[10] Guo, L., Chen, W.: Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. Int. J. Robust Nonlin. Control 15 (2005), 109-125. · Zbl 1078.93030
[11] Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge University Press, Cambridge 1952. · Zbl 0634.26008
[12] Ou, M., Du, H., Li, S.: Finite-time formation control of multiple nonholonomic mobile robots. Int. J. Robust Nonlin. Control 24 (2014), 140-165. · Zbl 1278.93173
[13] Jiang, Z., Nijmeijer, H.: Tracking control of mobile robots: a case study in backstepping. Automatica 33 (1997), 1393-1399. · Zbl 0882.93057
[14] Justh, E., Krishnaprasad, P.: Equilibrium and steering laws for planar formations. Syst. Control Lett. 52 (2004), 25-38. · Zbl 1157.93406
[15] Li, S., Du, H., Lin, X.: Finite time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47 (2011), 1706-1712. · Zbl 1226.93014
[16] Lin, Z., Francis, B., Maggiore, M.: Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans. Automat. Control 50 (2005), 121-127. · Zbl 1365.93324
[17] Jadbabaie, A., Lin, J., Morse, A.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003), 988-1001. · Zbl 1364.93514
[18] Kanayama, Y., Kimura, Y., Miyazaki, F., Noguchi, T.: A stable tracking control method for an autonomous mobile robot. Proc. IEEE Int. Conf. Rob. Autom. (1990), pp. 384-389.
[19] Levant, A.: Higher-order sliding modes, differentiation and output-feedback control. Int. J. Control 76 (2003), 924-941. · Zbl 1049.93014
[20] Li, S., Ding, S., Li, Q.: Global set stabilisation of the spacecraft attitude using finite-time control technique. Int. J. Control 82 (2009), 822-836. · Zbl 1165.93328
[21] Murray, R.: Recent research in cooperative control of multivehicle systems. ASME J. Dyn. Syst. Meas. Control 129 (2007), 571-583.
[22] Ni, W., Wang, X., Xiong, C.: Leader-following consensus of multiple linear systems under switching topologies: an averaging method. Kybernetika 48 (2012), 1194-1210. · Zbl 1255.93069
[23] Ou, M., Du, H., Li, S.: Finite-time tracking control of multiple nonholonomic mobile robots. J. Franklin Inst. 49 (2012), 2834-2860. · Zbl 1264.93158
[24] Ou, M., Li, S., Wang, C.: Finite-time tracking control for a nonholonomic mobile robot based on visual servoing. Asian J. Control 16 (2014), 679-691. · Zbl 1301.93121
[25] Ou, M., Sun, H., Li, S.: Finite time tracking control of a nonholonomic mobile robot with external disturbances. Proc. 31th Chinese Control Conference, Hefei 2012, pp. 853-858. · Zbl 1265.68291
[26] Ren, W., Beard, R.: Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. Automat. Control 50 (2005), 655-661. · Zbl 1365.93302
[27] Saber, R., Murray, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004), 1520-1533. · Zbl 1365.93301
[28] Shtessel, Y., Shkolnikov, I., Levant, A.: Smooth second-order sliding modes: missile guidance application. Automatica 43 (2007), 1470-1476. · Zbl 1130.93392
[29] Vicsek, T., Czirok, A., Jacob, E., Cohen, I., Schochet, O.: Novel type of phase transitions in a system of self-driven particles. Phys. Rev. Lett. 75 (1995), 1226-1229.
[30] Wang, J., Qiu, Z., Zhang, G.: Finite-time consensus problem for multiple non-holonomic mobile agents. Kybernetika 48 (2012),1180-1193. · Zbl 1255.93118
[31] Wu, Y., Wang, B., Zong, G.: Finite time tracking controller design for nonholonomic systems with extended chained form. IEEE Trans. Circuits Sys. II: Express Briefs 52 (2005), 798-802.
[32] Yang, J., Li, S., Chen, X., Li, Q.: Disturbance rejection of ball mill grinding circuits using DOB and MPC. Powder Technol. 198 (2010), 219-228.
[33] Yu, S., Long, X.: Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode. Automatica 54 (2015), 158-165. · Zbl 1318.93009
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