IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 24, NO. 6, NOVEMBER 2016 2125
Brief Papers
Formation Control of Mobile Robots Using Distributed Controller
With Sampled-Data and Communication Delays
Zhe Liu, Weidong Chen, Member, IEEE, Junguo Lu, Hesheng Wang, Senior Member, IEEE,
and Jingchuan Wang
Abstract—This brief presents a synchronous formation control
approach using distributed controller with sampled-data and
communication delay. The local information of each robot is
sampled first, and then transmitted to its coupling robots through
a network with communication delays, i.e., the information
exchanged between coupling robots is the sampled-data with
communication delays. The distributed formation controller is
designed by using the synchronization approach, which enables
mobile robots to maintain time-varying formations while per-
forming a group task in a synchronous manner. A sufficient con-
dition for formation control that can guarantee the exponential
convergence of both the position errors and the synchronization
errors is obtained by using the Lyapunov approach. Based
on the proposed sufficient condition, an upper bound of the
sampling period and the communication delay that guarantees
mobile robots to converge to the desired formations can be easily
obtained. Finally, the effectiveness of the proposed method is
demonstrated by simulations and real experiments.
Index Terms—Communication delay, formation control,
multiple mobile robots, sampled-data, synchronization.
I. INTRODUCTION
I
N RECENT years, formation control has been received an
increasing research interest due to its practical applications
such as target tracking [1], persistent surveillance [2], and
transportation [3]. In these tasks, mobile robots are usually
required to maintain time-varying formations while performing
a group task in a synchronous manner [4]. Furthermore, in
real applications, the computer control system is sampled-
data based and the communication delays in information
exchange channels are inevitable. In this brief, we focus on
the synchronous formation control problem of mobile robots
with sampled-data and communication delays.
Classical formation approaches can be classified into
three categories: 1) behavior-based control [5], [6];
2) virtual structure approach [7]–[9]; and 3) leader-follower
approach [10]–[12]. Interested readers should refer to [4] for
Manuscript received May 25, 2015; revised October 20, 2015 and
December 23, 2015; accepted December 31, 2015. Date of publication
February 3, 2016; date of current version October 14, 2016. Manuscript
received in final form January 13, 2016. This work was supported by
the National Natural Science Foundation of China under Grant 61221003,
Grant 61374030, Grant 61533012, and Grant 61573243. Recommended by
Associate Editor C. N. Hadjicostis. (Corresponding author: Weidong Chen.)
The authors are with the Key Laboratory of System Control and Infor-
mation Processing, Department of Automation, Ministry of Education of
China, Shanghai Jiao Tong University, Shanghai 200240, China, and also
with the Shanghai Key Laboratory of Navigation and Location Services,
Shanghai 200240, China (e-mail: liuzhesjtu@sjtu.edu.cn; wdchen@sjtu.
edu.cn; jglu@sjtu.edu.cn; wanghesheng@sjtu.edu.cn; jchwang@sjtu.edu.cn).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCST.2016.2518618
detailed introductions and corresponding limitations of these
approaches.
In recent years, Sun et al. [4] have developed a synchronous
formation control approach that enables mobile robots to
maintain the desired formation during the whole motion period
instead of accomplishing the formation at the final time only.
This approach has several advantages.
1) Compared with classical methods, this approach has
simple control structures and promising application
prospects due to the distributed framework and high
capability.
2) Based on the cross-coupling technology, each robot can
achieve accurate pose tracking while synchronizing its
motion with neighbors in the formation.
3) Since the disturbance in one robot will be responded
by all robots in a synchronous manner, this approach
has a stronger robustness and can achieve more accurate
formation performance [13].
Based on the synchronization concept [4], [14], a lot of
further studies have been conducted [15], such as finite-time
synchronous formation control of mobile robots [16], adaptive
learning control for spacecraft formation [13], and coordinated
motion control of transportation vehicles [17].
In real applications, in order to take advantages of
microelectronics, high-speed computers, and communication
networks, it is more preferable to use the digital controller
than the continuous-time controller [18]. At the same time,
in real applications, the resources of communication networks
(such as the available bandwidth and the total energy) are
limited [19]. Communicating using the sampled-data can
reduce the overall communication load of the whole system
and increase the efficiency. So in practice, in order to save
the communication resources, the information exchanged in
mobile robots is expected to be as little as possible, i.e.,
the sampling period is expected to be as long as possible.
However, increasing the sampling period may result in an
unstable control system and the failure of cooperative tasks
of mobile robots. So how to take the sampling period into
consideration theoretically in system design and estimate the
upper bound of the sampling period that guarantees mobile
robots to maintain desired formations is an important issue
in the formation control. In addition, due to the limited com-
munication resources, random disturbances, and/or multihop
communication requirements, the communication delays in
information exchange channels are inevitable. Without con-
sidering the communication delay in cooperative robot tasks
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