Distributed formation stabilization for mobile agents using
virtual tensegrity structures
YANG Qingkai
1,3
, CAO Ming
2
, FANG Hao
1,3
CHEN Jie
1,3
HUANG Jie
1,3
1. School of Automation, Beijing Institute of Technology, Beijing 100081, P. R. China
E-mail: fangh@bit.edu.cn
2. Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, Groningen 9747 AG, The Netherlands
3. Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing 100081, P. R. China
Abstract: This paper investigates the distributed formation control problem for a group of mobile Euler-Lagrange agents to
achieve global stabilization by using virtual tensegrity structures. Firstly, a systematic approach to design tensegrity frameworks
is elaborately explained to confine the interaction relationships between agents, which allows us to obtain globally rigid frame-
works. Then, based on virtual tensegrity frameworks, distributed control strategies are developed such that the mobile agents
converge to the desired formation globally. The theoretical analysis is further validated through simulations.
Key Words: Formation stabilization, Tensegrity structure, Global convergence, Euler-Lagrange dynamics
1 Introduction
In recent years, distributed control of multi-agent systems
has attracted a significant amount of research efforts due to
its broad applications, such as search and rescue, area cov-
erage and reconnaissance, and exploration in unknown en-
vironment [1–3]. Among various topics of coordinated con-
trol, one active research direction is the formation control
problem, where the mobile agents are guided to a prescribed
formation, likely then maneuvering as a cohesive whole.
Even though a wide range of issues have been studied,
and hence several theoretical frameworks have been estab-
lished to design control strategies, see, for example, [4]
[5] establishing estimation strategy for Euler-Lagrange sys-
tems with partial states available, [6][7] using matrix theory
and graph theory, [8] based on gradient-descent control ap-
proach, graph rigidity theory [9][10], networked small-gain
theory [11], sample-data for circle formation [12], to name
a few, it should be noted that the desired formation shape
can only be guaranteed to be locally stable in most of the re-
search. In particular, based on the graph rigidity approach, it
is challenging to coordinate a group of mobile robots glob-
ally converging to the prescribed formation [13].
Efforts have been made on the topic of global stability
of distributed formation control. For instance, the global
behavior of three agents maintaining triangular formations
is discussed in [14][15], where distance based gradient-like
control laws are proposed, respectively. To analyze global
stability for autonomous robots, a differential geometric ap-
proach is addressed and applied to the triangular formation
control [16]. The global asymptotic performance is achieved
by adding an adaptive perturbation to any agent’s movement
direction in [17]. It is worth mentioning that the control
strategies in these works are only valid in the case of three
agents forming triangular formations, which requires all-to-
all interactions. Besides, the position estimation based for-
mation control problem for single-integrators in the plane is
This work was supported by Foundation for Innovative Research
Groups of the National Natural Science Foundation of China (No.
61321002), Projects of Major International (Regional) Joint Research Pro-
gram NSFC (No. 61120106010), NSFC (No. 61175112), Fujian Institute
of Education Research Project (No. 2014ZD-06).
studied in [18]. It has been shown that the global conver-
gence can be realized if and only if the interaction graph has
a spanning tree.
In contrast to previous work, we focus on dealing with the
distributed formation stabilization problem for the configu-
rations in general position
1
in the Euclidean space of any di-
mension. Motivated by the deployable and stable properties
of tensegrity structure [20], we propose to use such a virtual
structure, a class of geometry structures from architectural
engineering, to analyze the characteristics of global stabil-
ity for a set of mobile agents modeled by Euler-Lagrange
equations. In this paper, we firstly design a novel algorithm
to compute the sparse stress matrix based on the given de-
sired configuration, whose elements determine the members
of the structure. Then, the virtual tensegrity structure will be
constructed through the mapping between the agents (resp.
edges) and the nodes (resp. inextendable cables and incom-
pressible struts). Finally, under the interaction constrains,
we propose distributed control strategies to steer the agents
to prescribed formation globally up to translation.
The applications of tensegrity structure in formation con-
trol have gradually draw the researchers’ attentions, see,
e.g.,[21–23]. However, most of the existing results are only
applicable to the one-dimensional (collinear shape) [21]or
planar formations [22][23]. In addition, even though in [23],
the construction of virtual tensegrity structure has been taken
into consideration, the proposed algorithm is highly likely to
result in complete underlying graph, which is not practical
in most of the applications.
The main contributions of this paper lie in a set of new
methodologies to achieve global stability in distributed for-
mation control using virtual tensegrity structures. More pre-
cisely, we propose a novel algorithm to assign the members
among all the agents, such that universally (thus globally)
rigid tensegrity structures can be obtained. The distinct point
here is that we can guarantee the global property without re-
quirement for complete graphs based on our algorithm. Fur-
ther, we effectively apply the virtual tensegrity structures in
1
A configuration is in general position if no k points lie in a (k − 1)
dimensional affine space for 1 ≤ k ≤ d [19].
Proceedings of the 34th Chinese Control Conference
Jul
28-30, 2015, Han
zhou, China
447