Abstract
This paper investigates the distributed formation control problem for multiple nonholonomic wheeled mobile robots. A variable transformation is first proposed to convert the formation control problem into a state consensus problem. Then, when the dynamics of the mobile robots are considered, the distributed kinematic controllers and neural network torque controllers are derived for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern along the specified reference trajectory. The specified reference trajectory is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers. Also the followers are assumed to have only local interaction. Moreover, the neural network torque controllers proposed in this work can tackle the dynamics of robots with unmodeled bounded disturbances and unstructured unmodeled dynamics. Some sufficient conditions are derived for accomplish the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples illustrate the effectiveness of the proposed controllers.
Similar content being viewed by others
References
Das, A.K., Fierro, R., Kumar, V., Ostrowski, J.P., Spletzer, J., Taylor, C.J.: A vision-based formation control framework. IEEE Trans. Rob. Autom. 18(5), 813–825 (2002)
Desai, J.P., Ostrowski, J.P., Kumar, V.: Modeling and control of formations of nonholonomic mobile robots. IEEE Trans. Rob. Autom. 17(6), 905–908 (2001). doi:10.1109/70.976023
Balch, T., Arkin, R.C.: Behavior-based formation control for multi-robot teams. IEEE Trans. Rob. Autom. 14(6), 1–15 (1998)
Egerstedt, M., Hu, X.: Formation constrained multi-agent control. IEEE Trans. Rob. Autom. 17(6), 947–951 (2001). doi:10.1109/70.976029
Lewis, M.A., Tan, K.: High precision formation control of mobile robots using virtual structures. Auton. Rob. 4(4), 387–403 (1997)
Chen, J., Sun, D., Yang, J., Chen, H.: Leader–follower formation control of multiple nonholonomic mobile robots incorporating a receding-horizon scheme. Int. J. Rob. Res. 29(6), 727–747 (2010). doi:10.1177/0278364909104290
Dong, W.: Tracking control of multiple-wheeled mobile robots with limited information of a desired trajectory. IEEE Trans. Rob. 28(1), 262–268 (2012). doi:10.1109/TRO.2011.2166436
Peng, Z., Wen, G., Rahmani, A., Yu, Y.: Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory. Int. J. Syst. Sci. 46(8), 1447–1457 (2015). doi:10.1080/00207721.2013.822609
Fierro, R., Lewis, F.: Control of a nonholonomic mobile robot using neural networks. IEEE Trans. Neural Netw. 9(4), 589–600 (1998). doi:10.1109/72.701173
Fukao, T., Nakagawa, H., Adachi, N.: Adaptive tracking control of a nonholonomic mobile robot. IEEE Trans. Rob. Autom. 16(5), 609–615 (2000)
Dong, W.: Robust formation control of multiple wheeled mobile robots. J. Intell. Rob. Syst. 62(3–4), 547–565 (2011)
Peng, Z., Yang, S., Wen, G., Rahmani, A.: Distributed consensus-based robust adaptive formation control for nonholonomic mobile robots with partial known dynamics. Math. Probl. Eng. 2014, 1–11 (2014). doi:10.1155/2014/670497
Liu, J., Ji, J., Zhou, J., Xiang, L., Zhao, L.: Adaptive group consensus in uncertain networked Euler–Lagrange systems under directed topology. Nonlinear Dyn. 82(3), 1145–1157 (2015)
Kwan, C., Lewis, F., Dawson, D.: Robust neural-network control of rigid-link electrically driven robots. IEEE Trans. Neural Netw. 9(4), 581–588 (1998). doi:10.1109/72.701172
Wang, X., Liu, Z., Cai, Y.: Adaptive single neural network control for a class of uncertain discrete-time nonlinear strict-feedback systems with input saturation. Nonlinear Dyn. 82(4), 2021–2030 (2015)
Consolini, L., Morbidi, F., Prattichizzo, D., Tosques, M.: Leader–follower formation control of nonholonomic mobile robots with input constraints. Automatica 44(5), 1343–1349 (2008). doi:10.1016/j.automatica.2007.09.019
Peng, Z., Wen, G., Rahmani, A., Yu, Y.: Leader–follower formation control of nonholonomic mobile robots based on a bioinspired neurodynamic based approach. Rob. Auton. Syst. 61(9), 988–996 (2013)
Dierks, T., Jagannathan, S.: Neural network control of mobile robot formations using RISE feedback. IEEE Trans. Syst. Man Cybern. B Cybern. 39(2), 332–347 (2009). doi:10.1109/TSMCB.2008.2005122
Dong, W., Farrell, J.A.: Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty. Automatica 45(3), 706–710 (2009). doi:10.1016/j.automatica.2008.09.015
Dong, W.: Flocking of multiple mobile robots based on backstepping. IEEE Trans. Syst. Man Cybern. B Cybern. 41(2), 414–424 (2011). doi:10.1109/TSMCB.2010.2056917
Zhao, L., Ji, J., Liu, J., Wu, Q., Zhou, J.: Tracking task-space synchronization of networked Lagrangian systems with switching topology. Nonlinear Dyn. 83(3), 1673–1685 (2016)
Li, X., Su, H., M.C.: Flocking of networked Euler–Lagrange systems with uncertain parameters and time-delays under directed graphs. Nonlinear Dyn. (2016)
Peng, Z., Yang, S., Wen, G., Rahmani, A., Yu, Y.: Adaptive distributed formation control for multiple nonholonomic wheeled mobile robots. Neurocomputing 173(3), 1485–1494 (2016). doi:10.1016/j.neucom.2015.09.022. http://www.sciencedirect.com/science/article/pii/S0925231215013302
Meyer, C.D. (ed.): Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia (2000)
Lewis, F.L., Abdallah, C.T., Dawson, D.M.: Control of Robot Manipulators, vol. 92. MacMillan, New York (1993)
Chung, F.R.K.: Spectral Graph Theory, vol. 92. American Mathematical Society, Providence, RI (1997)
Cortes, J.: Discontinuous dynamical systems. IEEE Control Syst. 28(3), 36–73 (2008). doi:10.1109/MCS.2008.919306
Ji, M., Egerstedt, M.: Connectedness preserving distributed coordination control over dynamic graphs. In: Proceedings of the 2005 American Control Conference, pp. 93–98 (2005). doi:10.1109/ACC.2005.1469914
Paden, B.E., Sastry, S.S.: A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulators. IEEE Trans. Circuits Syst. 34(1), 73–82 (1987). doi:10.1109/TCS.1987.1086038
Shevitz, D., Paden, B.: Lyapunov stability theory of nonsmooth systems. IEEE Trans. Autom. Control 39(5), 1910–1914 (1994)
Dong, W., Farrell, J.: Cooperative control of multiple nonholonomic mobile agents. IEEE Trans. Autom. Control 53(6), 1434–1448 (2008). doi:10.1109/TAC.2008.925852
Kwan, C., Dawson, D., Lewis, F.: Robust adaptive control of robots using neural network: global tracking stability. In: Proceedings of the 34th IEEE Conference on Decision and Control, vol. 2, pp. 1846 –1851 (1995). doi:10.1109/CDC.1995.480610
Park, B.S., Park, J.B., Choi, Y.H.: Adaptive formation control of electrically driven nonholonomic mobile robots with limited information. IEEE Trans. Syst. Man Cybern. B Cybern. 41(4), 1061–1075 (2011). doi:10.1109/TSMCB.2011.2105475
Wen, G., Peng, Z., Rahmani, A., Yu, Y.: Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics. Int. J. Syst. Sci. 45(9), 1892–1901 (2014). doi:10.1080/00207721.2012.757386
Dierks, T., Jagannathan, S.: Neural network output feedback control of robot formations. IEEE Trans. Syst. Man Cybern. B Cybern. 40(2), 383–399 (2010). doi:10.1109/TSMCB.2009.2025508
Lewis, F.L., Dawson, D., Abdallah, C. (eds.): Robot Manipulator Control: Theory and Practice, 2nd edn. CRC Press, Boca Raton (2003)
Acknowledgments
This work is supported by the Fundamental Research Funds for the Central Universities (Nos. YWF-14-RSC-032, YWF-15-SYS-JTXY-007, YWF-16-BJ-Y-21), by the Laboratoire international associé, and by the National Natural Science Foundation of China under Grants 61403019, 61503016.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Peng, Z., Wen, G., Yang, S. et al. Distributed consensus-based formation control for nonholonomic wheeled mobile robots using adaptive neural network. Nonlinear Dyn 86, 605–622 (2016). https://doi.org/10.1007/s11071-016-2910-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-016-2910-2