Finite-time formation control of multiple nonholonomic mobile robots.

*(English)*Zbl 1278.93173Summary: This paper considers finite-time formation control problem for a group of nonholonomic mobile robots. The desired formation trajectory is represented by a virtual dynamic leader whose states are available to only a subset of the followers and the followers have only local interaction. First of all, a continuous distributed finite-time observer is proposed for each follower to estimate the leader’s states in a finite time. Then, a continuous distributed cooperative finite-time tracking control law is designed for each mobile robot. Rigorous proof shows that the group of mobile robots converge to the desired geometric formation pattern in finite time. At the same time, all the robots can track the desired formation trajectory in finite time. A simulation example illustrates the effectiveness of our method.

##### Keywords:

finite-time formation control; nonholonomic mobile robot; cooperative control; distributed control
PDF
BibTeX
XML
Cite

\textit{M. Ou} et al., Int. J. Robust Nonlinear Control 24, No. 1, 140--165 (2014; Zbl 1278.93173)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Balch, Behavior-based formation control for multirobot teams, IEEE Transactions on Robotics and Automation 14 (6) pp 926– (1998) |

[2] | Jonathan, A decentralized approach to formation maneuvers, IEEE Transactions on Robotics and Automation 19 (6) pp 933– (2003) |

[3] | Sugihara, Distributed algorithms for formation of geometric patterns with many mobile robots, Journal of Robotic Systems 13 (3) pp 127– (1996) · Zbl 0875.70032 |

[4] | Lewis, High precision formation control of mobile robots using virtual structures, Autonomous Robots 4 (4) pp 387– (1997) |

[5] | Beard, A coordination architecture for spacecraft formation control, IEEE Transactions on Control Systems Technology 9 (6) pp 777– (2001) |

[6] | Ren, Formation feedback control for multiple spacecraft via virtual structures, IEE Proceedings: Control Theory and Applications 151 (3) pp 357– (2004) |

[7] | Tanner, Leader-to-formation stability, IEEE Transactions on Robotics and Automation 20 (3) pp 443– (2004) |

[8] | Desai, Modeling and control of formations of nonholonomic mobile robots, IEEE Transactions on Robotics and Automation 17 (6) pp 905– (2001) |

[9] | Chen, An internal model approach to autonomous leader follower trailing for non-holonomic vehicles, International Journal of Robust and Nonlinear Control 16 (14) pp 641– (2006) · Zbl 1134.93335 |

[10] | Hassan GM Yahya KM Haq IU Leader-follower approach using full-state linearization via dynamic feedback Proceedings of the 2nd International Conference on Emerging Technologies 2006 297 305 |

[11] | Saber RO Murray RM Distributed structural stabilization and tracking for formations of dynamic multi-agents Proceedings of the IEEE Conference on Decision and Control 2002 209 215 |

[12] | Fax, Information flow and cooperative control of vehicle formations, IEEE Transaction on Automatic Control 49 (9) pp 1465– (2004) · Zbl 1365.90056 |

[13] | Lafferriere, Decentralized control of vehicle formations, Systems and Control Letters 54 (9) pp 899– (2005) · Zbl 1129.93303 |

[14] | Liu, Controllability of switching networks of multi-agent systems, International Journal of Robust and Nonlinear Control 22 (6) pp 630– (2012) · Zbl 1273.93027 |

[15] | Ren, Consensus strategies for cooperative control of vehicle formations, IET Control Theory and Applications 1 (2) pp 505– (2007) |

[16] | Ren, Distributed multi-vehicle coordinated control via local information exchange, International Journal of Robust and Nonlinear Control 17 (10-11) pp 1002– (2007) · Zbl 1266.93010 |

[17] | Liu, Formation control of multi-agent systems with heterogeneous communication delays, International Journal of Systems Science 40 (6) pp 627– (2009) · Zbl 1291.93013 |

[18] | Hong, Lyapunov-based approach to multiagent systems with switching jointly connected interconnection, IEEE Transactions on Automatic Control 52 (5) pp 943– (2007) · Zbl 1366.93437 |

[19] | Hong, Tracking control for multi-agent consensus with an active leader and variable topology, Automatica 4 (7) pp 1177– (2006) · Zbl 1117.93300 |

[20] | Hong, Distributed observers design for leader-following control of multi-agent networks, Automatica 44 (3) pp 846– (2008) · Zbl 1283.93019 |

[21] | Ren, Multi-vehicle consensus with a time-varying reference state, System and Control Letters 56 (7-8) pp 474– (2007) · Zbl 1157.90459 |

[22] | Ren, On consensus algorithms for double-integrator dynamics, IEEE Transactions on Automatic Control 53 (6) pp 1503– (2008) · Zbl 1367.93567 |

[23] | Dong, Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty, Automatica 45 (3) pp 706– (2009) · Zbl 1166.93302 |

[24] | Dong, Cooperative control of multiple nonholonomic mobile agents, IEEE Transaction on Automatic Control 53 (6) pp 1434– (2008) · Zbl 1367.93226 |

[25] | Cao KC Formation control of multiple nonholonomic mobile robots based on cascade design Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference 2009 8340 8344 |

[26] | Bhat, Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization 38 (3) pp 751– (2000) · Zbl 0945.34039 |

[27] | Li, Global set stabilisation of the spacecraft attitude using finite-time control technique, International Journal of Control 82 (5) pp 822– (2009) · Zbl 1165.93328 |

[28] | Du, Finite-time attitude tracking control of spacecraft with application to attitude synchronization, IEEE Transactions on Automatic Control 56 (11) pp 2711– (2011) · Zbl 1368.70036 |

[29] | Zhao, Robust finite-time control approach for robotic manipulators, IET Control Theory and Applications 4 (1) pp 1– (2010) |

[30] | Huang, Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica 41 (5) pp 881– (2005) · Zbl 1098.93032 |

[31] | Ding, Stabilization of the attitude of a rigid spacecraft with external disturbances using finite-time control techniques, Aerospace Science and Technology 13 (4-5) pp 256– (2009) |

[32] | Zhao, Finite time position synchronised control for parallel manipulators using fast terminal sliding mode, International Journal of Systems Science 40 (8) pp 829– (2009) · Zbl 1291.93092 |

[33] | Zhu, Attitude stabilization of rigid spacecraft with finite-time convergence, International Journal of Robust and Nonlinear Control 21 (6) pp 686– (2011) · Zbl 1214.93100 |

[34] | Li, Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems, IEEE Transaction on Automatic Control 51 (5) pp 879– (2006) · Zbl 1366.93507 |

[35] | Qian, Global finite-time stabilization by output feedback for planar systems without observable linearization, IEEE Transaction on Automatic Control 50 (6) pp 885– (2005) · Zbl 1365.93415 |

[36] | Hong, On an output feedback finite-time stabilization problem, Proceedings of the IEEE Conference on Decision and Control 2 pp 1302– (1999) |

[37] | Xiao, Finite-time formation control for multi-agent systems, Automatica 45 (11) pp 2605– (2009) · Zbl 1180.93006 |

[38] | Cao, Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking, Systems and Control Letters 59 (9) pp 522– (2010) · Zbl 1207.93103 |

[39] | Li, Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics, Automatica 47 (8) pp 1706– (2011) · Zbl 1226.93014 |

[40] | Bhat SP Bernstein DS Finite-time stability of homogeneous systems Proceedings of the American Control Conference 4 1997 2513 2514 |

[41] | Hong, Finite-time control for robot manipulators, Systems and Control Letters 46 (4) pp 243– (2002) · Zbl 0994.93041 |

[42] | Khalil, Nonlinear, Systems (2002) |

[43] | Dixon, Nonlinear Control of Wheeled Mobile Robots 262 (2001) · Zbl 0994.93500 |

[44] | Hardy, Inequalities[M] (1952) |

[45] | Kanayama Y Kimura Y Miyazaki F Noguchi T A stable tracking control method for an autonomous mobile robot Proceedings of the IEEE International Conference on Robotics and Automation 1990 384 389 |

[46] | Li, Finite-time stability of cascade time-varying systems, International Journal of Control 80 (4) pp 646– (2007) · Zbl 1117.93004 |

[47] | Xia, Attitude tracking of rigid spacecraft with bounded disturbances, IEEE Transactions on Industrial Electronics 58 (2) pp 647– (2011) |

[48] | Xia, Back-stepping sliding mode control for missile systems based on extended state observer, IET Control Theory and Applications 5 (1) pp 93– (2011) |

[49] | Xia, Active disturbance rejection control for uncertain multivariable systems with time-delay, IET Control Theory and Applications 1 (1) pp 75– (2007) |

[50] | Li, Generalized extended state observer based control for systems with mismathched uncertaintied, IEEE Transactions on Industrial Electronics 59 (12) pp 4792– (2012) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.