Robust finite-time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback
Yingying Cheng
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China
Search for more papers by this authorRuting Jia
Department of Electrical and Computer Engineering, California State University at Northridge, Northridge, CA, USA
Search for more papers by this authorCorresponding Author
Haibo Du
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China
Correspondence
Haibo Du, School of Electrical Engineering and Automation, Hefei University of Technology, 230009 Hefei, China.
Email: [email protected]
Search for more papers by this authorGuanghui Wen
Department of Mathematics, Southeast University, Nanjing, China
Search for more papers by this authorWenwu Zhu
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China
Search for more papers by this authorYingying Cheng
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China
Search for more papers by this authorRuting Jia
Department of Electrical and Computer Engineering, California State University at Northridge, Northridge, CA, USA
Search for more papers by this authorCorresponding Author
Haibo Du
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China
Correspondence
Haibo Du, School of Electrical Engineering and Automation, Hefei University of Technology, 230009 Hefei, China.
Email: [email protected]
Search for more papers by this authorGuanghui Wen
Department of Mathematics, Southeast University, Nanjing, China
Search for more papers by this authorWenwu Zhu
School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China
Search for more papers by this authorSummary
The finite-time formation control for multiple nonholonomic wheeled mobile robots with a leader-following structure is studied. Different from the existing results, the considered mobile robot has the following features: (i) a higher-order dynamic model, (ii) the robot's velocities cannot be measured, and (iii) there are external disturbances. To solve the problem, a finite-time consensus formation control algorithm via output feedback is explicitly given. At the first step, some finite-time convergent observers are skillfully constructed to estimate both the unknown velocity information and the disturbance in finite time by imposing certain assumptions on the disturbances. Then, on the basis of the integral sliding-mode control method, a disturbance observer-based finite-time output feedback controller is developed. Rigorous proof shows that the finite-time formation can be achieved in finite time. An example is finally given to verify the efficiency of the proposed method.
REFERENCES
- 1Ren W, Beard RW. Distributed Consensus in Multivehicle Cooperative Control: Theory and Applications. Berlin: Springer; 2007.
- 2Fax A, Murray R. Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control. 2004; 49(9): 1453-1464.
- 3Dong W, Farrell A. Cooperative control of multiple nonholonomic mobile agents. IEEE Trans Autom Control. 2008; 53(6): 1434-1448.
- 4Chen Y, Tian Y. A backstepping design for directed formation control of three-coleader agents in the plane. Int J Robust Nonlinear Control. 2009; 19(7): 729-745.
- 5Lin Z, Bruce F, Maggiore M. Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans Autom Control. 2005; 50(1): 121-127.
- 6Zhu J, Lu J, Yu X. Flocking of multi-agent non-holonomic systems with proximity graphs. IEEE Trans Circ Syst I: Regular Pap. 2013; 60(1): 199-210.
- 7Dimarogonas D, Kyriakopoulos K. On the rendezvous problem for multiple nonholonomic agents. IEEE Trans Autom Control. 2007; 52(5): 916-922.
- 8Dong W, Farrell A. Cooperative control of multiple nonholonomic mobile agents. IEEE Trans Autom Control. 2008; 53(6): 1434-1448.
- 9Liu T, Jiang Z. Distributed formation control of nonholonomic mobile robots without global position measurements. Automatica. 2013; 49(2): 592-600.
- 10Bhat SP, Bernstein DS. Finite-time stability of continuous autonomous systems. SIAM J Control Optim. 2000; 38(3): 751-766.
- 11Ou M, Du H, Li S. Finite-time formation control of multiple nonholonomic mobile robots. Int J Robust Nonlinear Control. 2014; 24(1): 140-165.
- 12Wang J, Qiu Z, Zhang G. Finite-time consensus problem for multiple non-holonomic mobile agents. Kybernetika. 2012; 48(6): 1180-1193.
- 13Du H, Wen G, Yu X, Li S, Chen MZQ. Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer. Automatica. 2015; 62: 236-242.
- 14Shen Y, Xia X. Semi-global finite-time observers for nonlinear systems. IEEE Trans Autom Control. 2008; 44(12): 3152-3156.
- 15Shen Y, Huang Y. Uniformly observable and globally Lipschitzian nonlinear systems admit global finite-time observers. IEEE Trans Autom Control. 2009; 54(11): 2621-2625.
- 16Qian C, Li J. Global finite-time stabilization by output feedback for planar systems without observable linearization. IEEE Trans Autom Control. 2005; 50(6): 885-890.
- 17Hong Y, Huang J, Xu Y. On an output feedback finite-time stabilization problem. IEEE Trans Autom Control. 2001; 46(2): 305-309.
- 18Frye M, Ding S, Qian C, Li S. Fast convergent observer design for output feedback stabilization of a planar vertical takeoff and landing aircraft. IET Control Theory Appl. 2010; 4(4): 690-700.
- 19Jin X, He Y, He Y. Finite-time robust fault-tolerant control against actuator faults and saturations. IET Control Theory Appl. 2017; 11(4): 550-556.
- 20Du H, Li S, Lin X. Finite-time formation control of multi-agent systems via dynamic output feedback. Int J Robust Nonlinear Control. 2013; 23(14): 1609-1628.
- 21Zheng Y, Wang L. Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements. Syst Control Lett. 2012; 61(8): 871-878.
- 22Du H, He Y, Cheng Y. Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans Circ Syst I: Regular Pap. 2014; 61(6): 1778-1788.
- 23Wang X, Li S, Lam J. Distributed active anti-disturbance output consensus algorithms for higher-order multi-agent systems with mismatched disturbances. Automatica. 2016; 74: 30-37.
- 24Wang X, Li S, Yu X, Yang J. Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances. IEEE Trans Autom Control. 2017; 62(11): 5795-5801.
- 25Sun N, Wu Y, Fang Y, Chen H, Lu B. Nonlinear continuous global stabilization control for underactuated RTAC systems: design, analysis, and experimentation. IEEE/ASME Trans Mechatron. 2017; 22(2): 1104-1115.
- 26Xu B, Zhang P. Composite learning sliding mode control of flexible-link manipulator. Complexity. 2017; 2017:9430259, 6 pages. https://doi.org/10.1155/2017/9430259
- 27Ren W, Atkins E. Distributed multi-vehicle coordinated control via local information exchange. Int J Robust Nonlinear Control. 2007; 17(10-11): 1002-1033.
- 28Yang J, Li S, Yu X. Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans Ind Electron. 2013; 60(1): 160-169.
- 29Yang J, Li S, Sun C, Guo L. Nonlinear-disturbance-observer-based robust flight control for airbreathing hypersonic vehicles. IEEE Trans Aerosp Electron Syst. 2013; 49(2): 1263-1275.
- 30Hong Y, Hu J, Gao L. Tracking control for multi-agent consensus with an active leader and variable topology. Automatica. 2006; 42(7): 1177-1182.
- 31Bhat S, Bernstein D. Finite-time stability of homogeneous systems. Paper presented at: American Control Conference; 1997; Albuquerque, USA.
- 32Hong Y, Xu Y, Huang J. Finite-time control for robot manipulators. Syst Control Lett. 2002; 46(4): 243-253.
- 33Levant A. Higher-order sliding modes, differentiation and output-feedback control. Int J Control. 2003; 76(9-10): 924-941.
- 34Khalil HK. Nonlinear systems. 3rd ed. Upper Saddle River, NJ: Prentice Hall; 2002.
