Finite-time tracking control of multiple nonholonomic mobile robots with external disturbances
Kybernetika, Tome 51 (2015) no. 6, pp. 1049-1067
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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.
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.
DOI : 10.14736/kyb-2015-6-1049
Classification : 93A14, 93D15, 93D21
Keywords: finite-time tracking control; finite-time disturbance observer; external disturbances; nonholonomic mobile robot; dynamic model
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Ou, Meiying; Gu, Shengwei; Wang, Xianbing; Dong, Kexiu. Finite-time tracking control of multiple nonholonomic mobile robots with external disturbances. Kybernetika, Tome 51 (2015) no. 6, pp. 1049-1067. doi: 10.14736/kyb-2015-6-1049

[1] Bhat, S., Bernstein, D.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 (2000), 751-766. | DOI | MR | Zbl

[2] Chen, W.: Disturbance observer based control for nonlinear systems. IEEE/ASME Trans. Mechatronics 9 (2004), 706-710. | DOI

[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. | DOI

[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. | DOI

[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. | DOI

[6] Dong, W.: Robust formation control of multiple wheeled mobile robots. J. Intel. Robot. Syst.: Theory and Appl. 62 (2011), 547-565. | DOI | Zbl

[7] Dong, W., Farrell, J.: Cooperative control of multiple nonholonomic mobile agents. IEEE Trans. Automat. Control 53 (2008), 1434-1448. | DOI | MR

[8] Dong, W., Farrell, J.: Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty. Automatica 45 (2009), 706-710. | DOI | MR | Zbl

[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. | MR | Zbl

[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. | DOI | MR | Zbl

[11] Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge University Press, Cambridge 1952. | MR | Zbl

[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. | DOI | MR | Zbl

[13] Jiang, Z., Nijmeijer, H.: Tracking control of mobile robots: a case study in backstepping. Automatica 33 (1997), 1393-1399. | MR | Zbl

[14] Justh, E., Krishnaprasad, P.: Equilibrium and steering laws for planar formations. Syst. Control Lett. 52 (2004), 25-38. | DOI | MR

[15] Li, S., Du, H., Lin, X.: Finite time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47 (2011), 1706-1712. | DOI | MR | Zbl

[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. | DOI | MR

[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. | DOI | MR

[18] Kanayama, Y., Kimura, Y., Miyazaki, F., Noguchi, T.: A stable tracking control method for an autonomous mobile robot. In: 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. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[21] Murray, R.: Recent research in cooperative control of multivehicle systems. ASME J. Dyn. Syst. Meas. Control 129 (2007), 571-583. | DOI

[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. | MR | Zbl

[23] Ou, M., Du, H., Li, S.: Finite-time tracking control of multiple nonholonomic mobile robots. J. Franklin Inst. 49 (2012), 2834-2860. | DOI | MR | Zbl

[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. | DOI | MR

[25] Ou, M., Sun, H., Li, S.: Finite time tracking control of a nonholonomic mobile robot with external disturbances. In: Proc. 31th Chinese Control Conference, Hefei 2012, pp. 853-858. | MR | Zbl

[26] Ren, W., Beard, R.: Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. Automat. Control 50 (2005), 655-661. | DOI | MR

[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. | DOI | MR

[28] Shtessel, Y., Shkolnikov, I., Levant, A.: Smooth second-order sliding modes: missile guidance application. Automatica 43 (2007), 1470-1476. | DOI | MR | Zbl

[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. | DOI

[30] Wang, J., Qiu, Z., Zhang, G.: Finite-time consensus problem for multiple non-holonomic mobile agents. Kybernetika 48 (2012),1180-1193. | MR | Zbl

[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. | DOI

[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. | DOI

[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. | DOI | MR | Zbl

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