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Formation control of multiple wheeled mobile robots based on model predictive control

Published online by Cambridge University Press:  18 February 2022

Najla Nfaileh ,
Khalil Alipour Open the ORCID record for Khalil Alipour [Opens in a new window] ,
Bahram Tarvirdizadeh  and
Alireza Hadi Open the ORCID record for Alireza Hadi [Opens in a new window]
Najla Nfaileh
Affiliation:
Advanced Service Robots (ASR) Laboratory, Department of Mechatronics Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran
Khalil Alipour*
Affiliation:
Advanced Service Robots (ASR) Laboratory, Department of Mechatronics Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran
Bahram Tarvirdizadeh
Affiliation:
Advanced Service Robots (ASR) Laboratory, Department of Mechatronics Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran
Alireza Hadi
Affiliation:
Advanced Service Robots (ASR) Laboratory, Department of Mechatronics Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran
*
*Corresponding author. E-mail: k.alipour@ut.ac.ir
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Abstract

This paper considers the problem of formation control for a team of nonholonomic wheeled mobile robots considering obstacle avoidance. A new control algorithm based on the model predictive control (MPC) and the nonlinear dynamics of the system is presented here. The control algorithm is applied to the nonlinear system using two different controllers including linear MPC and nonlinear MPC. The virtual structure formation approach and artificial potential field method are employed to determine the reference trajectories of the robots and to solve the problem of obstacle avoidance. A control algorithm consisting of two parts is proposed to track the trajectories and maintain the team’s formation. Two advantages of using MPC techniques are the ability to consider control and state constraints which are of high importance in practical applications. The main contribution of this paper is the design of two robust control systems to disturbance with respect to actuator saturation limits. Simulation results demonstrate the effectiveness and robustness of the proposed control algorithm in trajectory tracking and formation maintenance in the presence of disturbance and actuator limits.

Keywords

formation controlvirtual structurenonholonomic WMRlinear model predictive controlnonlinear model predictive controlobstacle avoidance
Type
Research Article
Information
Robotica , Volume 40 , Issue 9 , September 2022 , pp. 3178 - 3213
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Lewis, M. A. and Tan, K.-H., “High precision formation control of mobile robots using virtual structures,” Auton. Robots 4(4), 387–403 (1997).10.1023/A:1008814708459CrossRefGoogle Scholar
Das, A. K., Fierro, R., Kumar, V., Ostrowski, J. P., Spletzer, J. and Taylor, C. J., “A vision-based formation control framework,” IEEE Trans. Robot. Autom. 18(5), 813–825 (2002).CrossRefGoogle Scholar
Yamchi, M. H. and Esfanjani, R. M., “Formation control of networked mobile robots with guaranteed obstacle and collision avoidance,” Robotica 35(6), 1365 (2017).CrossRefGoogle Scholar
Oh, K.-K., Park, M.-C. and Ahn, H.-S., “A survey of multi-agent formation control,” Automatica 53, 424–440 (2015).CrossRefGoogle Scholar
Chen, F. and Ren, W., “On the control of multi-agent systems: A survey,” Foundations and Trends® in Systems and Control, 6(4), 339–499 (2019).CrossRefGoogle Scholar
Zhao, Y., Park, D., Moon, J. and Lee, J., “Leader-follower formation control for multiple mobile robots by a designed sliding mode controller based on kinematic control method,” 2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE) (2017) IEEE.CrossRefGoogle Scholar
Chung, S.-J., Paranjape, A. A., Dames, P., Shen, S. and Kumar, V., “A survey on aerial swarm robotics,” IEEE Trans. Robot. 34(4), 837–855 (2018).CrossRefGoogle Scholar
Desai, J. P., Kumar, V. and Ostrowski, J. P., “Control of changes in formation for a team of mobile robots,” Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No. 99CH36288C) (1999) IEEE.Google Scholar
Li, X., Xiao, J. and Cai, Z., “Backstepping based multiple mobile robots formation control,” 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (2005) IEEE.Google Scholar
Shi-Cai, L., Da-Long, T. and Guang-Jun, L., “Robust leader-follower formation control of mobile robots based on a second order kinematics model,” Acta Automat. Sin. 33(9), 947–955 (2007).Google Scholar
Jin, J., Ramirez, J.-P., Wee, S., Lee, D., Kim, Y. and Gans, N., “A switched-system approach to formation control and heading consensus for multi-robot systems,” Intell. Serv. Robot. 11(2), 207–224 (2018).CrossRefGoogle Scholar
Kamel, M. A., Yu, X. and Zhang, Y., “Real-time fault-tolerant formation control of multiple WMRs based on hybrid GA-PSO algorithm,” IEEE Trans. Autom. Sci. Eng. 18(3), 1263–1276 (2020).CrossRefGoogle Scholar
Miao, Z., Liu, Y.-H., Wang, Y., Yi, G. and Fierro, R., “Distributed estimation and control for leader-following formations of nonholonomic mobile robots,” IEEE Trans. Autom. Sci. Eng. 15(4), 1946–1954 (2018).CrossRefGoogle Scholar
Han, Q., Sun, S. and Lang, H., “Leader-follower formation control of multi-robots based on bearing-only observations,” Int. J. Robot. Autom. 34(2) (2019).Google Scholar
Hou, R., Cui, L., Bu, X. and Yang, J., “Distributed formation control for multiple non-holonomic wheeled mobile robots with velocity constraint by using improved data-driven iterative learning,” Appl. Math. Comput. 395, 125829 (2021).Google Scholar
Abbaspour, A., Moosavian, S. A. A. and Alipour, K., “A virtual structure-based approach to formation control of cooperative wheeled mobile robots,” Proceeding of the 2013 RSI/ISM International Conference on Robotics and Mechatronics, February 13–15, Tehran, Iran (2013).Google Scholar
Rezaee, H. and Abdollahi, F., “A decentralized cooperative control scheme with obstacle avoidance for a team of mobile robots,” IEEE Trans. Ind. Electron. 61(1), 347–354 (2014).10.1109/TIE.2013.2245612CrossRefGoogle Scholar
Young, B. J., Beard, R. W. and Kelsey, J. M., “A control scheme for improving multi-vehicle formation maneuvers,” Proceedings of the 2001 American Control Conference (Cat. No. 01CH37148) (2001) IEEE.CrossRefGoogle Scholar
Varghese, B. and McKee, G., “A mathematical model, implementation and study of a swarm system,” Robot. Auton. Syst. 58(3), 287–294 (2010).CrossRefGoogle Scholar
Abbaspour, A., Moosavian, S. and Alipour, K., “Formation control and obstacle avoidance of cooperative wheeled mobile robots,” Int. J. Robot. Autom. 30(5), 418–428 (2015).Google Scholar
Monteiro, S. and Bicho, E., “Attractor dynamics approach to formation control: Theory and application,” Auton. Robot. 29(3–4), 331–355 (2010).CrossRefGoogle Scholar
Antonelli, G., Arrichiello, F. and Chiaverini, S., “Flocking for multi-robot systems via the null-space-based behavioral control,” Swarm Intell. 4(1), 37 (2010).CrossRefGoogle Scholar
Balch, T. and Arkin, R. C., “Behavior-based formation control for multirobot teams,” IEEE Trans. Robot. Autom. 14(6), 926–939 (1998).CrossRefGoogle Scholar
Balch, T. and Hybinette, M., “Social potentials for scalable multi-robot formations,” Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No. 00CH37065) (2000) IEEE.Google Scholar
Lee, G. and Chwa, D., “Decentralized behavior-based formation control of multiple robots considering obstacle avoidance,” Intell. Serv. Robot. 11(1), 127–138 (2018).CrossRefGoogle Scholar
El-Ferik, S., Siddiqui, B. A. and Lewis, F. L., “Distributed nonlinear MPC of multi-agent systems with data compression and random delays,” IEEE Trans. Automat. Control 61(3), 817–822 (2016).CrossRefGoogle Scholar
Ettefagh, M. H., Naraghi, M., Towhidkhah, F. and Izi, H., “Laguerre based model predictive control for trajectory tracking of nonholonomic mobile robots,” 2018 6th RSI International Conference on Robotics and Mechatronics (IcRoM) (2018) IEEE.CrossRefGoogle Scholar
Kassaeiyan, P., Tarvirdizadeh, B. and Alipour, K., “Control of tractor-trailer wheeled robots considering self-collision effect and actuator saturation limitations,” Mech. Syst. Signal Process. 127, 388–411 (2019).CrossRefGoogle Scholar
Kamel, M. A. and Zhang, Y., “Linear model predictive control via feedback linearization for formation control of multiple wheeled mobile robots,” 2015 IEEE International Conference on Information and Automation (2015) IEEE.CrossRefGoogle Scholar
Kuwata, Y., Richards, A., Schouwenaars, T. and How, J. P., “Distributed robust receding horizon control for multivehicle guidance,” IEEE Trans. Control Syst. Technol. 15(4), 627–641 (2007).CrossRefGoogle Scholar
Dunbar, W. B. and Caveney, D. S., “Distributed receding horizon control of vehicle platoons: Stability and string stability,” IEEE Trans. Automat. Control 57(3), 620–633 (2012).CrossRefGoogle Scholar
Franco, E., Magni, L., Parisini, T., Polycarpou, M. M. and Raimondo, D. M., “Cooperative constrained control of distributed agents with nonlinear dynamics and delayed information exchange: A stabilizing receding-horizon approach,” IEEE Trans. Automat. Control 53(1), 324–338 (2008).CrossRefGoogle Scholar
Baca, T., Loianno, G. and Saska, M., “Embedded model predictive control of unmanned micro aerial vehicles,” 2016 21st International Conference on Methods and Models in Automation and Robotics (MMAR) (2016) IEEE.CrossRefGoogle Scholar
Siciliano, B. and Khatib, O., Springer Handbook of Robotics (Springer-Verlag, Berlin Heidelberg, 2016).CrossRefGoogle Scholar
Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control (John Wiley & Sons, USA, 2006).Google Scholar
Ge, S. S. and Cui, Y. J., “New potential functions for mobile robot path planning,” IEEE Trans. Robot. Automat. 16(5), 615–620 (2000).CrossRefGoogle Scholar
Wang, L., Model Predictive Control System Design and Implementation Using MATLAB® (Springer-Verlag, London, 2009).Google Scholar
Camacho, E. F. and Bordons, C., Model predictive control (Springer-Verlag, London, 2004).Google Scholar
Loehning, M., Reble, M., Hasenauer, J., Yu, S. and Allgoewer, F., “Model predictive control using reduced order models: Guaranteed stability for constrained linear systems,” J. Process Control 24(11), 1647–1659 (2014).CrossRefGoogle Scholar
Mayne, D. Q., “Optimization in Model Predictive Control,” In: Methods of Model Based Process Control. NATO ASI Series (Series E: Applied Sciences) (R. Berber, ed.), vol. 293 (Springer, Dordrecht, 1995) pp. 367–396.CrossRefGoogle Scholar
Magni, L., De Nicolao, G., Scattolini, R. and Allgöwer, F., “Robust model predictive control for nonlinear discrete-time systems,” Int. J. Robust Nonlin. Control IFAC-Aff. J. 13(3–4), 229–246 (2003).CrossRefGoogle Scholar
Mayne, D. Q., “Model predictive control: Recent developments and future promise,” Automatica 50(12), 2967–2986 (2014).CrossRefGoogle Scholar
Farrell, J. A. and Polycarpou, M. M., Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches. Vol. 48 (John Wiley & Sons, Hoboken, NJ, 2006).CrossRefGoogle Scholar
Lars, G. and Jürgen, P., Nonlinear Model Predictive Control Theory and Algorithms (Springer-Verlag, London, 2011).Google Scholar
Maciejowski, J. M., Predictive Control: With Constraints (Pearson Education Limited, Prentice Hall, London, 2002).Google Scholar
Wang, L., “Discrete model predictive controller design using Laguerre functions,” J. Process Control 14(2), 131–142 (2004).CrossRefGoogle Scholar
Mayne, D. Q., Rawlings, J. B., Rao, C. V. and Scokaert, P. O., “Constrained model predictive control: Stability and optimality,” Automatica 36(6), 789–814 (2000).CrossRefGoogle Scholar
Chen, H. and Allgöwer, F., “A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability,” Automatica 34(10), 1205–1217 (1998).CrossRefGoogle Scholar