Obstacle Avoidance for Multi-Agent Systems Based on Stream Function
and Hierarchical Associations
XIAO Wenzhi
1,2
, FANG Hao
1,2
,
LI Jixiang
1,2
,
CUI Jing
1,2
1. School of Automation, Beijing Institute of Technology, Beijing 100081, China
E-mail: xwzded00@gmail.com
2. Key Laboratory of Complex System Intelligent Control and Decision Ministry of Education, Beijing 100081, China
Abstract: This paper deals with the problem of obstacle avoidance for multi-agent systems. A novel framework is presented
which combines the stream function with the artificial potential field. The introduction of stream function makes obstacle
avoidance smoother while interactive potential guarantees stability of the system. A dynamic structure with visibility constraint
and hierarchical associations is further explored to improve the performance. Finally, results of simulation as well as experiment
on Pioneer3 robots verify the validity of the proposed method.
Key Words: multi-agent, obstacle avoidance, stream function, hierarchical associations
1 Introduction
Recent years have witnessed a tremendous interest in the
control of multi-agent systems[1-5]. Multi-agent systems
consists of agents and their environment, and could achieve
global optimization in decentralized approach relying only
on interactions between robots. Advantages of these system
include robustness, fault tolerance, flexibility as well as
adaptability compared with systems constructed by
individual agent[1], or monolithic systems. Multi-agent
systems are potential in practical areas such as sensor
networks, unmanned aero vehicles, self-assembly of
connected mobile networks, automated parallel delivery of
paloads, among many others[2-4].
The swarm problem is a fundamental and classical issue
which has been investigated extensively in the field of
multi-agent systems[6]. For swarm problems, agents have to
reach and maintain a desired formation, avoiding collision
from obstacles and other agents, while moving towards a
certain direction, with only limited local informations.
Artificial potential field (APF) is a commonly used
method for control of swarm systems. By constructing
potential field, this method defines interaction forces
between neighboring agents and addresses desired spacing
of the group. In complex environments, obstacles are often
treated as special agents and potential field can be thus
applied[6, 7]. However, for APF method, there exists local
minima problem, and should be revised. By introducing the
concept in fluid mechanics, stream function method are used
in obstacle avoidance for mobile robots[8, 9] which has no
local minima and smoother trajectories.
The basic premises of stream function are introduced in
Section 2. Section 3 describes the control law combining
APF and stream function method, of which the stability is
analyzed. In Section 4, the control law is amended with
visibility constraint and hierarchical associations to generate
better performance. Section 5 and 6 presents the results of
simulation and experiments, and finally Section 7 provides
the conclusion.
*
This work is supported by Beijing bionic robot and system the key
laboratory and NSFC projects numbered 60925011, 61120106010, and
61175112.
2 Preliminaries
2.1 Stream Function
There are two kinds of fluid motions: rotational flow and
potential flow. The rotational flow has not only the forward
motion, but also the rotation around its instantaneous axis,
and is easy to generate vortices. While in potential flow
there exists only translational motion. In this paper we
discuss ideal potential flow, of which the flow is
irrotational[10, 11].
Potential flow and velocity potential: In fluid dynamics, a
potential flow is described by means of a velocity
potential
, which is a scalar function of space and time. The
flow velocity
f
u
is a vector field equal to the gradient of the
velocity potential
:
f
Ñ=
f
u
(1)
Where
ivuu
f
+=
, and
x
u
¶
¶
=
f
,
y
v
¶
¶
=
f
(2)
Since the curl of a gradient is equal to zero, it is obvious
that
0
φ
, and consequently, the curl of the velocity
field
f
u
, is zero:
0=´Ñ
f
u
(3)
Which implies that the potential flow is an irrotational
flow.
Stream function : In incompressible two-dimentional
flows, the velocity field satisfies the continuous condition,
that is,
0=
¶
¶
+
¶
¶
y
v
x
u
. And if we define a function,
),( yx
y
so that
y
u
¶
¶
=
y
,
x
v
¶
¶
-=
y
(4)
we have
udyvdxdy
y
dx
x
d +-=
¶
¶
+
¶
¶
=
yy
y
(5)