The problem of controlling a group of networked mechanical systems to synchronize and follow a common trajectory is studied in this paper. We first address the results for networked mechanical systems to achieve synchronization when the interagent communication graph is balanced and strongly connected with communication delays. Subsequently, a control law is developed to guarantee synchronization and trajectory tracking for networked mechanical systems communicating on regular graphs when there are constant time delays in communication and the interconnection topology is time-varying. The case when a human operator input is introduced in the closed-loop system is also considered. It is demonstrated that a bounded human operator input results in bounded tracking and synchronization errors, even when there are constant time delays in communication. The simulation and experimental results are presented by utilizing the kinematic and dynamic models of PHANToM Omni derived in this paper.

References

References
1.
Spong
,
M. W.
,
Hutchinson
,
S.
, and
Vidyasagar
,
M.
,
2006
,
Robot Modeling and Control
,
John Wiley and Sons, Inc.
,
New York
.
2.
Rodriguez-Angeles
,
A.
, and
Nijmeijer
,
H.
,
2004
, “
Mutual Synchronization of Robots via Estimated State Feedback: A Cooperative Approach
,”
IEEE Trans. Control Syst. Technol.
,
12
(
4
), pp.
542
554
.10.1109/TCST.2004.825065
3.
Chopra
,
N.
, and
Liu
,
Y.-C.
,
2008
, “
Controlled Synchronization of Mechanical Systems
,”
ASME
Dynamic Systems and Control Conference, pp.
1221
1228
.10.1115/DSCC2008-2267
4.
Chung
,
S.-J.
, and
Slotine
,
J.-J. E.
,
2009
, “
Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems
,”
IEEE Trans. Rob.
,
25
(
3
), pp.
686
700
.10.1109/TRO.2009.2014125
5.
Liu
,
Y.-C.
, and
Chopra
,
N.
,
2012
, “
Controlled Synchronization of Heterogeneous Robotic Manipulators in the Task Space
,”
IEEE Trans. Rob.
,
28
(
1
), pp.
268
275
.10.1109/TRO.2011.2168690
6.
Liu
,
Y.-C.
, and
Chopra
,
N.
,
2009
, “
Controlled Synchronization of Robotic Manipulators in the Task Space
,”
ASME
Dynamic Systems and Control Conference, pp.
443
450
.10.1115/DSCC2009-2684
7.
Kyrkjebø
,
E.
,
Pettersen
,
K. Y.
,
Wondergem
,
M.
, and
Nijmeijer
,
H.
,
2007
, “
Output Synchronization Control of Ship Replenishment Operations: Theory and Experiments
,”
Control Eng. Pract.
,
15
(
6
), pp.
741
755
.10.1016/j.conengprac.2006.07.001
8.
Bondhus
,
A. K.
,
Pettersen
,
K. Y.
, and
Gravdahl
,
J. T.
,
2005
, “
Leader/Follower Synchronization of Satellite Attitude Without Angular Velocity Measurements
,”
IEEE
Conference on Decision and Control, pp.
7270
7277
.10.1109/CDC.2005.1583334
9.
Kristiansen
,
R.
,
Loría
,
A.
,
Chaillet
,
A.
, and
Nicklasson
,
P. J.
,
2009
, “
Spacecraft Relative Rotation Tracking Without Angular Velocity Measurements
,”
Automatica
,
45
(
3
), pp.
750
756
.10.1016/j.automatica.2008.10.012
10.
Sun
,
D.
,
Wang
,
C.
,
Shang
,
W.
, and
Feng
,
G.
,
2009
, “
A Synchronization Approach to Trajectory Tracking of Multiple Mobile Robots While Maintaining Time-Varying Formations
,”
IEEE Trans. Rob.
,
25
(
5
), pp.
1074
1086
.10.1109/TRO.2009.2027384
11.
Mehrabian
,
A. R.
,
Tafazoli
,
S.
, and
Khorasani
,
K.
,
2010
, “
Cooperative Tracking Control of Euler-Lagrange Systems With Switching Communication Network Topologies
,”
IEEE
/ASME International Conference on Advanced Intelligent Mechatronics, pp.
756
761
.10.1109/AIM.2010.5695803
12.
Chen
,
G.
,
and Lewis
,
F. L.
,
2011
, “
Distributed Adaptive Tracking Control for Synchronization of Unknown Networked Lagrangian Systems
,”
IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
,
41
(
3
), pp.
805
816
.10.1109/TSMCB.2010.2095497
13.
Nuño,
E.
,
Ortega
,
R.
,
Basañez
,
L.
, and
Hill
,
D.
,
2011
, “
Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays
,”
IEEE Trans. Automat.Control
,
56
(
4
), pp.
935
941
.10.1109/TAC.2010.2103415
14.
Mei
,
J.
,
Ren
,
W.
, and
Ma
,
G.
,
2011
, “
Distributed Coordinated Tracking With a Dynamic Leader for Multiple Euler-Lagrange Systems
,”
IEEE Trans. Automat. Control
,
56
(
6
), pp.
1415
1421
.10.1109/TAC.2011.2109437
15.
Miller
,
P.
,
Lee
,
L.-F.
, and
Krov
i,
V. N.
,
2009
, “
Output Synchronization for Teleoperation of Wheel Mobile Robot
,”
ASME
Dynamic Systems and Control Conference, pp.
707
714
.10.1115/DSCC2009-2637
16.
Vilchis
,
A.
,
Troccaz
,
J.
,
Cinquin
,
P.
,
Masuda
,
K.
, and
Pellissier
,
F.
,
2003
, “
A New Robot Architecture for Tele-Echography
,”
IEEE Trans. Rob.
,
19
(
5
), pp.
922
926
.10.1109/TRA.2003.817509
17.
Hribar
,
A.
, and
Munih
,
M.
,
2010
, “
Development and Testing of fMRI-Compatible Haptic Interface
,”
Robotica
,
28
(
2
), pp.
259
265
.10.1017/S0263574709990646
18.
Cavusoglu
,
M. C.
,
Feygin
,
D.
, and
Tendick
,
F.
,
2002
, “
A Critical Study of the Mechanical and Electrical Properties of the Phantom Haptic Interface and Improvements for High-Performance Control
,”
Presence: Teleoperators Virtual Environ.
,
11
(
6
), pp.
555
568
.10.1162/105474602321050695
19.
Taati
,
B.
,
Tahmasebi
,
A. M.
, and
Hashtrudi-Zaad
,
K.
,
2008
, “
Experimental Identification and Analysis of the Dynamics of a Phantom Premium 1.5A Haptic Device
,”
Presence: Teleoperators Virtual Environ.
,
17
(
4
), pp.
327
343
.10.1162/pres.17.4.327
20.
Godsil
,
C.
, and
Royle
,
G.
,
2001
,
Algebraic Graph Theory
,
Springer
,
New York
.
21.
Slotine
,
J.-J.
, and
Li
,
W. P.
,
1988
, “
Adaptive Manipulator Control: A Case Study
,”
IEEE Trans. Automat. Control
,
33
(
11
), pp.
995
1003
.10.1109/9.14411
22.
Chopra
,
N.
, and
Spong
,
M. W.
,
2006
, “
Passivity-Based Control of Multi-Agent Systems
,”
Advances in Robot Control: From Everyday Physics to Human-Like Movements
,
S.
Kawamura
, and
M.
Svinin
, eds.,
Springer Verlag
,
New York
, pp.
107
134
.
23.
Sontag
,
E. D.
,
2003
, “
A Remark on the Converging-Input Converging-State Property
,”
IEEE Trans. Automat. Control
,
48
(
2
), pp.
313
314
.10.1109/TAC.2002.808490
24.
Richard
,
J. P.
,
2003
, “
Time-Delay Systems: An Overview of Some Recent Advances and Open Problems
,”
Automatica
,
39
(
10
), pp.
1667
1694
.10.1016/S0005-1098(03)00167-5
25.
Hespanha
,
J.
,
Liberzon
,
D.
,
Angeli
,
D.
, and
Sontag
,
E.
,
2005
, “
Nonlinear Norm-Observability Notions and Stability of Switched Systems
,”
IEEE Trans. Automat. Control
,
50
(
2
), pp.
154
168
.10.1109/TAC.2004.841937
26.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems
,
Prentice Hall
,
Englewood Cliffs, NJ
.
27.
Chopra
,
N.
, and
Spong
,
M. W.
,
2008
, “
Output Synchronization on Strongly Connected Graphs
,”
International Symposium on Mathematical Theory of Networks and Systems
.
28.
Chopra
,
N.
,
2012
, “
Output Synchronization on Strongly Connected Graphs
,”
IEEE Trans. Automat. Control
,
57
(
11
), pp.
2896
2901
.10.1109/TAC.2012.2193704
29.
Liu
,
Y.-C.
, and
Chopra
,
N.
,
2010
, “
Synchronization of Networked Robotic Systems on Strongly Connected Graphs
,”
IEEE
Conference on Decision and Control, pp.
3194
3199
.10.1109/CDC.2010.5718176
30.
Naerum
,
E.
,
Cornellà
,
J.
, and
Elle
,
O. J.
,
2008
, “
Contact Force Estimation for Backdrivable Robotic Manipulators With Coupled Friction
,”
IEEE
/RSJ International Conference on Intelligent Robots and Systems, pp.
3021
3027
.10.1109/IROS.2008.4651192
You do not currently have access to this content.