Article
Transactions of the Institute of
Measurement and Control
2018, Vol. 40(1) 269–278
Ó The Author(s) 2018
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DOI: 10.1177/0142331216654534
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Adaptive and sliding mode tracking
control for wheeled mobile robots with
unknown visual parameters
Fang Yang
1,2
, Hongye Su
1
, Chaoli Wang
3
and Zhenxing Li
3
Abstract
The trajectory tracking control problem of dynamic nonholonomic wheeled mobile robots is considered via visual servoing feedback. A novel visual
feedback tracking error model is proposed. Its tracking controller is independent of uncalibrated visual parameters by using new methods. This control-
ler consists of two units: one is an adaptive control for compensation of the uncertainties of dynamic parameters, the other is a variable structure con-
trol for the interference suppression. In addition, the torque tracking controller is global and smooth, and the chattering phenomenon is eliminated.
The asymptotic convergence of tracking errors to equilibrium point is rigorously proved by the Lyapunov method. Simulation and experiment results
are provided to illustrate the performance of the control law.
Keywords
Wheeled mobile robots, dynamic, tracking, visual servoing
Introduction
The control of wheeled mobile robots with nonholonomic
constraints has attracted much attention due to the inherent
nonlinearity in robot dynamics and the usefulness in many
applications. By the theorem of Brockett (1983), a nonholo-
nomic system cannot be stabilized at a single equilibrium
point by any continuous, time-invariant, state-feedback con-
troller. However, several other approaches have been pro-
posed (Astolfi, 1996; Tian and Li, 2002; Hu et al., 2004;
Samson, 2005; Wang et al., 2015).
In the control of nonholonomic mobile robots, it is usually
assumed that the robot states are available and exactly recon-
structed using proprioceptive and exteroceptive sensor mea-
surements. Unfortunately, in real-world applications, these
assumptions often do not hold due to uncertainties in the
kinematic and dynamic models, mechanical limitations and
measurement noise. As a consequence, the estimation of the
robot states from sensor measurements can be affected by
these perturbations. An interesting approach to overcome this
position measurement problem is to utilize a vision system to
directly obtain the Cartesian position information required
by the controller. Since the late 1980s, much effort has been
devoted to visual servoing and vision-based manipulations
(Fang et al., 2012; Wang et al., 2010). To implement a visual
servo controller, an important step is to calibrate the intrinsic
and extrinsic parameters of cameras. It is well known that the
camera calibration is costly and tedious. To avoid camera
calibration, a lot of effort has been made to achieve uncali-
brated visual servoing (Chen et al., 2014; Liang et al., 2015).
Recently, the visual tracking control problem of nonholo-
nomic mobile robots has been proposed. In Chen et al.
(2006), a visual servoing tracking controller was developed
for a monocular camera system mounted on an underactu-
ated wheeled mobile robot subject to nonholonomic motion
constraints. The reference (Wang et al., 2010) presented a
dynamic feedback tracking controller for a nonholonomic
wheeled mobile robot (WMR) kinematic system under the
assumption that the unknown visual parameters a
1
= a
2
= a.
The methods mentioned above are based on kinematics
only and the nonlinear forces in robot dynamics are neglected.
However, in practice, it is more realistic to formulate the non-
holonomic system control problem at dynamic level, where
the torque and force are taken as the control inputs. Liu et al.
(2006) presented a new adaptive controller for image-based
dynamic control of a robot manipulator using a fixed camera
whose intrinsic and extrinsic parameters are not known. Yang
et al. (2013) used feedback from an uncalibrated, fixed (ceil-
ing-mounted) camera to develop an adaptive tracking control-
ler for a type (1,1) nonholonomic mobile robot, a novel
trajectory tracking torque controller was designed based on
Lyapunov’s direct method and backstepping technique. But
the method proposed in Yang et al. (2013) cannot be used to
1
National Laboratory of Industrial Control Technology, Institute of
Cyber-Systems and Control, PRC
2
School of Science, Ningbo University of Technology, PRC
3
Control Science and Engineering Department, University of Shanghai
for Science and Technology, PRC
Corresponding author:
Fang Yang, School of Science, Ningbo University of Technology, No.201
Fenghua Road, Ningbo City, Zhejiang, Ningbo 315211, PRC.
Email: liusha_02@163.com
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