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This study studies robust synchronisation for networked Lagrangian systems under dynamic uncertainties and communication delays. Using weighted storage functions, the authors propose a robust control scheme to guarantee that networked Lagrangian systems achieve ultimately bounded solutions over strongly connected communication graphs. Since the developed control system can ensure synchronous action in the absence of a common trajectory, the robust control algorithm is applied for bilateral teleoperations with multiple remote robots. The ultimate boundedness of the solutions can enable the teleoperation system to account for the presence of uncertain dynamics when a human operator intermittently intervenes on local robots. Numerical examples of a group of two-link non-linear robotic systems are presented to validate the efficacy of the developed control algorithms.
References
-
-
1)
-
13. Slotine, J., Wang, W.: ‘A study of synchronization and group cooperation using partial contraction theory’. in , Kumar, V., Leonard, N. E., Morse, A. S., Eds., vol. 309, Berlin, Springer-Verlag, 2005, pp. 207–228.
-
2)
-
5. Liu, Y.-C., Chopra, N.: ‘Synchronization of networked robotic systems on strongly connected graphs’. in IEEE Conf. Decision and Control, December 2010, pp. 3194–3199.
-
3)
-
S.-J. Chung ,
J.-J. Slotine
.
Cooperative robot control and concurrent synchronization of lagrangian systems.
IEEE Trans. Robot.
,
3 ,
1 -
15
-
4)
-
L. Scardavi ,
S. Sepulchre
.
Synchronization in networks of identical linear systems.
Automatica
,
11 ,
2557 -
2562
-
5)
-
34. Hokayem, P.F., Stipanović, D.M., Spong, M.W.: ‘Semiautonomous control of multiple networked Lagrangian systems’, Int. J. Robust Nonlinear Control, 2009, 19, (18), pp. 2040–2055 (doi: 10.1002/rnc.1391).
-
6)
-
13. Slotine, J., Wang, W.: ‘A study of synchronization and group cooperation using partial contraction theory’. in Cooperative Control, ser. Lecture Notes in Control and Information Sciences, Kumar, V., Leonard, N. E., Morse, A. S., Eds., vol. 309, Berlin, Springer-Verlag, 2005, pp. 207–228.
-
7)
-
Y. Tian ,
C. Liu
.
Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations.
Automatica
,
5 ,
1347 -
1353
-
8)
-
28. Spong, M.W., Hutchinson, S., Vidyasagar, M.: ‘Robot modeling and control’ (John Wiley & Sons, Inc., New York, 2006).
-
9)
-
Y. Kang ,
Z. Li ,
W. Shang ,
H. Xi
.
Motion synchronisation of bilateral teleoperation systems with mode-dependent time-varying communication delays.
IET Control Theory Appl.
,
10 ,
2129 -
2140
-
10)
-
15. Chen, G., Lewis, F.L.: ‘Distributed adaptive tracking control for synchronization of unknown networked Lagrangian systems’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2011, 41, (3), pp. 805–816 (doi: 10.1109/TSMCB.2010.2095497).
-
11)
-
20. Wang, H.: ‘Passivity based synchronization for networked robotic systems with uncertain kinematics and dynamics’, Automatica, 2013, 49, (3), pp. 755–761 (doi: 10.1016/j.automatica.2012.11.003).
-
12)
-
24. Franchi, A., Secchi, C., Son, H.I., Bülthoff, H.H., Giordano, P.R.: ‘Bilateral teleoperation of groups of mobile robots with time-varying topology’, IEEE Trans. Robotics, 2012, 28, (5), pp. 1019–1033 (doi: 10.1109/TRO.2012.2196304).
-
13)
-
W. Ren
.
On consensus algorithms for double-integrator dynamics.
IEEE Trans. Autom. Control
,
6 ,
1503 -
1509
-
14)
-
10. Liu, Y.C., Chopra, N.: ‘Controlled synchronization of hetergeneous robotic manipulators in the task space’, IEEE Trans. Robot., 2012, 28, (1), pp. 268–275 (doi: 10.1109/TRO.2011.2168690).
-
15)
-
27. Liu, Y.-C., Chopra, N.: ‘Control of semi-autonomous teleoperation system with time delays’, Automatica, 2013, 49, (6), pp. 1553–1565 (doi: 10.1016/j.automatica.2013.02.009).
-
16)
-
30. Igarashi, Y., Hatanaka, T., Fujita, M., Spong, M.W.: ‘Passivity-based attitude synchronziation in SE(3)’, IEEE Trans. Control Syst. Technol., 2009, 17, (5), pp. 1119–1134 (doi: 10.1109/TCST.2009.2014357).
-
17)
-
31. Steur, E., Nijmeijer, H.: ‘Synchronization in networks of diffusively time-delay coupled (semi-)passive systems’, IEEE Trans. Circuits Syst. I, Regul. Pap., 2011, 58, (6), pp. 1358–1371 (doi: 10.1109/TCSI.2010.2097670).
-
18)
-
D. Zhao ,
S. Li ,
F. Gao ,
Q. Zhu
.
Robust adaptive terminal sliding mode-based synchronized position control for multiple motion axed systems.
IET Control Theory Appl.
,
1 ,
136 -
150
-
19)
-
A. Rodriguez-Angeles ,
H. Nijmeijer
.
Mutual synchronization of robots via estimated state feedback: a cooperative approach.
IEEE Trans. Control Syst. Technol
,
4 ,
542 -
554
-
20)
-
32. Hale, J.K., Lunel, S.M.V.: ‘Introduction to functional differential equations’ (Springer-Verlag, New York, 1993).
-
21)
-
22. Liu, Y.-C., Chopra, N.: ‘Robust controlled synchronization of interconnected robotic systems’. in American Control Conf., June 2010, pp. 1434–1439.
-
22)
-
R. Olfati-Saber ,
J.A. Fax ,
R.M. Murray
.
Consensus and cooperation in networked multi-agent systems.
Proc. IEEE.
,
1 ,
215 -
233
-
23)
-
29. Godsil, C., Royle, G.: ‘Algebraic graph theory’ (Springer, 2001).
-
24)
-
W. Ren
.
Distributed leaderless consensus algorithms for networked Euler–Lagrange systems.
Int. J. Control
,
11 ,
2137 -
2149
-
25)
-
19. Rohrs, C., Valavani, L., Athans, M., Stein, G.: ‘Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics’, IEEE Trans. Autom. Control, 1985, 30, (9), pp. 881–889 (doi: 10.1109/TAC.1985.1104070).
-
26)
-
E. Jin ,
Z. Sun
.
Robust attitude synchronisation controllers design for spacecraft formation.
IET Control Theory Appl.
,
3 ,
325 -
339
-
27)
-
14. Kyrkjebø, E., Pettersen, K.Y., Wondergem, M., Nijmeijer, H.: ‘Output synchronization control of ship replenishment operations: theory and experiments’, Control Eng. Practice, 2007, 15, pp. 741–755 (doi: 10.1016/j.conengprac.2006.07.001).
-
28)
-
43. Trentelman, H.L., Takaba, K., Monshizadeh, N.: ‘Robust synchronization of uncertain linear multi-agent systems’, IEEE Trans. Autom. Control, 2013, 58, (6), pp. 1511–1523 (doi: 10.1109/TAC.2013.2239011).
-
29)
-
2. Zhou, J., Hu, Q., Zhang, Y., Ma, G.: ‘Decentralised adaptive output feedback synchronisation tracking control of spacecraft formation flying with time-varying delay’, IET Control Theory Appl., 2012, 6, (13), pp. 2009–2020 (doi: 10.1049/iet-cta.2011.0031).
-
30)
-
11. Chopra, N., Spong, M.: ‘Synchronization of networked lagrangian systems’, in Lagrangian and Hamiltonian Methods for Nonlinear Control, Bullo, F., Fujimoto, K., Eds. Springer Verlag, 2007, pp. 47–57.
-
31)
-
12. Liu, Y.-C., Chopra, N.: ‘Synchronization of networked mechanical systems with communication delays and human input’, ASME J. Dyn. Syst. Meas. Control, 2013, 135, (4), (doi: 10.1115/1.4023398).
-
32)
-
N. Chopra ,
M.W. Spong ,
R. Lozano
.
Adaptive coordination control of bilateral teleoperators with time delay.
Automatica
,
8 ,
2142 -
2148
-
33)
-
23. Rodriguez-Seda, E.J., Tory, J.J., Erignac, C.A., Murray, P., Stipanović, D.M., Spong, M.W.: ‘Bilateral teleoperation of multiple mobile agents: coordinated motion and collision avoidance’, IEEE Trans. Control Syst. Technol., 2010, 18, (4), pp. 984–992 (doi: 10.1109/TCST.2009.2030176).
-
34)
-
33. Niculescu, S.-I., Taoutaou, D., Lozano, R.: ‘Bilateral teleoperation with communication delays’, Int. J. Robust Nonlinear Control, 2003, 13, (9), pp. 873–883 (doi: 10.1002/rnc.851).
-
35)
-
35. Khalil, H.K.: ‘Nonlinear systems’ (Prentice-Hall, New Jersey, 2002).
-
36)
-
18. Spong, M.W.: ‘On the robust control of robot manipulators’, IEEE Trans. Autom. Control, 1992, 37, (11), pp. 1782–1786 (doi: 10.1109/9.173151).
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