Uncertainty and disturbance are common in a planar snake robot model due to its structural complexity and variation in system parameters. To achieve efficient head angle and velocity tracking with least computational complexity and unknown uncertainty bounds, a time-delayed control (TDC) scheme has been presented in this paper. A Serpenoid gait function is being tracked by the joint angles utilizing virtual holonomic constraints (VHCs) method. The first layer of TDC has been proposed for stabilizing the VHC dynamics to the origin. Once the VHCs are satisfied, the system is said to be on the constraint manifold. The second layer of TDC has been applied to an output system defined over the reduced order dynamics on the constrained manifold. To establish the robustness of the control approach through simulation, uncertainty in the friction coefficients is considered to be time-varying emulating change in the ground conditions. Simulation results and Lyapunov stability analysis affirm the uniformly ultimately bounded stability of the robot employing the proposed approach.

References

1.
Hirose
,
S.
, and
Morishima
,
A.
,
1990
, “
Design and Control of a Mobile Robot With an Articulated Body
,”
Int. J. Rob. Res.
,
9
(
2
), pp.
99
114
.
2.
Liljeback
,
P.
,
Pettersen
,
K. Y.
,
Stavdahl
,
Ø.
, and
Gravdahl
,
J. T.
,
2011
, “
Controllability and Stability Analysis of Planar Snake Robot Locomotion
,”
IEEE Trans. Autom. Control
,
56
(
6
), pp.
1365
1380
.
3.
Liljebäck
,
P.
,
Pettersen
,
K. Y.
,
Stavdahl
,
Ø.
, and
Gravdahl
,
J. T.
,
2012
,
Snake Robots: Modelling, mechatronics, and Control
,
Springer Science & Business Media
,
London
.
4.
Mohammadi
,
A.
,
Rezapour
,
E.
,
Maggiore
,
M.
, and
Pettersen
,
K. Y.
,
2016
, “
Maneuvering Control of Planar Snake Robots Using Virtual Holonomic Constraints
,”
IEEE Trans. Control Syst. Technol.
,
24
(
3
), pp.
884
899
.
5.
Kohl
,
A. M.
,
Kelasidi
,
E.
,
Mohammadi
,
A.
,
Maggiore
,
M.
, and
Pettersen
,
K. Y.
,
2016
, “
Planar Maneuvering Control of Underwater Snake Robots Using Virtual Holonomic Constraints
,”
Bioinspiration Biomimetics
,
11
(
6
), p.
065005
.
6.
Zhang
,
A.
,
Ma
,
S.
,
Li
,
B.
,
Wang
,
M.
,
Guo
,
X.
, and
Wang
,
Y.
,
2016
, “
Adaptive Controller Design for Underwater Snake Robot With Unmatched Uncertainties
,”
Sci. China Inf. Sci.
,
59
(
5
), p.
052205
.
7.
Mukherjee
,
J.
,
Mukherjee
,
S.
, and
Kar
,
I. N.
,
2017
, “
Sliding Mode Control of Planar Snake Robot With Uncertainty Using Virtual Holonomic Constraints
,”
IEEE Rob. Autom. Lett.
,
2
(
2
), pp.
1077
1084
.
8.
Mukherjee
,
J.
,
Kar
,
I. N.
, and
Mukherjee
,
S.
,
2017
, “
Adaptive Sliding Mode Control for Head-Angle and Velocity Tracking of Planar Snake Robot
,”
11th Asian Control Conference
(
ASCC
),
Gold Coast, Australia
,
Dec. 17–20
, pp.
537
542
.
9.
Hsia
,
T. C.
, and
Gao
,
L. S.
,
1990
, “
Robot Manipulator Control Using Decentralized Linear Time-Invariant Time-Delayed Joint Controllers
,”
IEEE
International Conference on Robotics and Automation
,
Cincinnati, OH
,
May 13–18
, pp.
2070
2075
.
10.
Youcef-Toumi
,
K.
, and
Ito
,
O.
,
1988
, “
A Time Delay Controller for Systems With Unknown Dynamics
,”
American Control Conference
(
ACC
),
Atlanta, GA
,
June 15–17
, pp.
904
913
.
11.
Jin
,
M.
,
Lee
,
J.
,
Chang
,
P. H.
, and
Choi
,
C.
,
2009
, “
Practical Nonsingular Terminal Sliding-Mode Control of Robot Manipulators for High-Accuracy Tracking Control
,”
IEEE Trans. Ind. Electron.
,
56
(
9
), pp.
3593
3601
.
12.
Lee
,
J.
,
Yoo
,
C.
,
Park
,
Y.-S.
,
Park
,
B.
,
Lee
,
S.-J.
,
Gweon
,
D.-G.
, and
Chang
,
P.-H.
,
2012
, “
An Experimental Study on Time Delay Control of Actuation System of Tilt Rotor Unmanned Aerial Vehicle
,”
Mechatronics
,
22
(
2
), pp.
184
194
.
13.
Roy
,
S.
,
Kar
,
I. N.
, and
Lee
,
J.
,
2017
, “
Toward Position-Only Time-Delayed Control for Uncertain Euler–Lagrange Systems: Experiments on Wheeled Mobile Robots
,”
IEEE Rob. Autom. Lett.
,
2
(
4
), pp.
1925
1932
.
14.
Roy
,
S.
,
Kar
,
I. N.
,
Lee
,
J.
, and
Jin
,
M.
,
2017
, “
Adaptive-Robust Time-Delay Control for a Class of Uncertain Euler–Lagrange Systems
,”
IEEE Trans. Ind. Electron.
,
64
(
9
), pp.
7109
7119
.
You do not currently have access to this content.