Download - Academy Publisher

5
In order to overcome the shortcomings of in literatures
[2] and [3], Xue and Zeng[4] proposed an isotropic
limited-range perceive swarming model that can in
harmony with real biological swarms well, and improve
the coordination motion behavior of multi-agent systems.
0
60
40
-5
5
20
5
0
0
g(y)
0
-5
-5
-20
Figure 2. The paths of the swarm members in Ref. [2]
Chen and Fang[3] proposed an isotropic local perceive
swarming model, the attraction-repulsion functions
considered in this study could avoid collisions, but the
model could not agree well with the nonlinear
characteristics.
-40
-60
-6 -4 -2 0 2 4 6
y
Figure 5. The attraction/repulsion function g(⋅ ) in Ref. [4]
8
6
100
4
80
2
60
0
40
-2
20
-4
0
100
-6
-8
-6 -4 -2 0 2 4 6
50
0
0
20
40
60
80
100
z
Figure 3. The attraction/repulsion function g(⋅ ) in Ref. [3]
100
80
60
40
20
Figure 6. The paths of the swarm members in Ref. [4]
Based on the inspiration from biology, referring to the
known results in literatures [4], we consider a swarm of
M individuals (members) in a n–dimensional Euclidean
space, assume synchronous motion and no time delays,
and model the individuals as points and ignore their
dimensions. The equation of collective motion of
individual i is given by as follows
M
i
i j
( x ) + g( x −x
),
i 1, L M
i
x& = −∇
=
x ∑
i σ , .(1)
j=
1, j≠i
0
100
50
y
0
0
Figure 4. The paths of the swarm members in Ref. [3]
20
40
x
60
80
100
i n
Where x ∈ R represents the position of individual
i ; - ∇ ( x
i )
x
iσ stands for the collective motion’s
direction resting with the different social
attractant/repellent potential fields environment profile
around individual i ; g ( ⋅)
represents the function of
attraction and repulsion between the individuals members.
g ⋅ functions are odd (and therefore
The above ( )
86