Direction switch behavior to enclose a target
Masao Kubo, Nhuhai Phung, Hiroshi Sato
Dep. of Computer Science, National Defense Academy of Japan, Hashirimizu 1-10-20
Yokosuka, Kanagawa 239-8686, Japan
E-mail: [email protected], [email protected], [email protected]
www.nda.ac.jp/cs/stuff/masaok.html
Abstract
This paper discusses a target enclosing behavior when a part of the orbit is blocked. Usually, a orbit to enclose a
target supposes to be clear. However this often takes place in realistic environment. For this issue we propose
microscopic methods to emerge macroscopic search capability to enclose a target. The group of robots change their
direction according to the blocked part.
Keywords: Self organized swarm system, target enclosing, swarm robotics, phase transition.
formation by trial and error. In general such a system
has to balance exploration and exploitation of collective
level adequately. The phase transition property of
boids[12] is adopted as this controller.
1. Introduction
Recently, self-organized swarm system[3] which has
more sophisticated and intelligent plasticity is required
for real world application because it is too complex and
dynamic. In this paper, target enclosing behavior of
robot collective is discussed from this point of view.
Fig. 2. Target enclosing under a difficult condition
This paper is composed as follows. Firstly, the proposed
scenario that macroscopic states of a collective can be
switched between exploration and exploitation is
explained. Next a method that the scenario is realized
for enclosing task for a robotic swarm. Here 2
microscopic rules, namely, an action selection scheme
based on majority decision and a self generating noise
rule are proposed. Finally a series of computer
simulation shows that the proposed robotic collective
Fig. 1. Target enclosing under an ideal condition
When a part of the orbit to be enclosed with a robot
collective is blocked there is no way of producing
alternative formations to enclose. For this issue we
proposes micro level modifications to emerge intelligent
macroscopic dynamics as they find a new better
© The 2017 International Conference on Artificial Life and Robotics (ICAROB 2017), Jan. 19-22, Seagaia Convention Center, Miyazaki, Japan
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Masao Kubo, Nhuhai Phung, Hiroshi Sato
can behave flexible under conditions which a simple
collective is suspended.
Fig. 7. Model of the enclosing a target algorithm: α, β.
2. The proposed scenario
macroscopic states
of
switch
of
Fig.1 shows a typical example of the problem of
enclosing a target that a target is surrounded by moving
robots. Target enclosing, target capturing and
circumnavigation discuss similar topics [13] [5] [4] [9]
[2] [11] [6] [7] [14]. This seems to be a fundamental
formation of a collective for disaster site because this
behavior builds up a dense but ordered robots around a
given spot.
Usually, research in these domain suppose that the orbit
is clear. However, this is not true in real environment.
For example, a cliff around a target in mountain range
makes this difficult because of space limitation. Also an
invisible unusual strong air current makes robots fly
difficult. We aim to build a self organized swarm system
to enclose targets which can perform more adaptable.
In this paper, one of the following 2 formations
according to their environment arises. The first
formation is the ideal one shown in Fig.1. The second
formation is shown in Fig.2. The group of the robots
stays the part of the orbit to find a path. Once the
blocked region is solved, the group can form the first
formation immediately.
In order to realize such various group behaviors, if a
problem occurs, it is necessary for the group to develop
itself that searches for a better formation. Also, if it
finds a good formation, the group also needs to
converge it that every agent seems to agree with. It is
necessary to balance both searching for formation at the
collective level and utilizing the search results.
For this issue the phase transition trait of boids based on
noise [12] is adopted. It is known that when the noise
applied to particles in a particle group simulating boids
exceeds a certain strength, the behavior of boids
changes from a consistent state to a disordered state.
Fig. 3. Phase transition of boids.
Fig. 4. Example of a synchronized formation.
Fig. 5. Example of a disordered formation.
Fig. 6. concept of proposed collective level adaptation by self generating
noise.
© The 2017 International Conference on Artificial Life and Robotics (ICAROB 2017), Jan. 19-22, Seagaia Convention Center, Miyazaki, Japan
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Direction switch behavior to
Fig.3 shows an example of the transition. This indicates
the degree of consistency of boid directions when noise
is applied to boids whose Separation, Cohesion, and
Alignment ratios are 1.3, 1.0, and 1.0 [10]. In the case
where a small amount of noise is added (Noise < 0.3),
since the deviation of the corresponding boids is
corrected by the remaining of the group, the overall
behavior does not change. The state of the group at this
time is shown in Fig.4. Almost all are moving in the
same direction. On the other hand, when the amount of
noise exceeds the threshold (Noise > 0.3), it varies
sharply. Fig.5 shows the state when Noise = 1. It turns
out that individuals are facing different directions.
Here, utilizing this dynamics, realization of collective
search activity to recover from a failure and switching
of modes of its use are realized. This conceptual
diagram is shown in Fig.6. When a group is in an
appropriate formation (A), it is assumed that some
trouble has occurred. An agent that detects this
malfunction selects an action which is different to others.
As a result, the whole swarm changes to the state of B.
If this detected defect is temporary, this noisy action is
corrected and returns to state A. On the other hand,
when many similar defects are detected, the macro state
shifts to the C state. In the C state, each agent randomly
changes their actions, so multiple formations will be
tested as future formation candidates. As the number of
agents supporting a good formation increases, the
swarm shifts to macro state D and eventually reaches A.
In the following, we show how to implement the target
enclosing problem as a method to embody the concept
of this collective search state and decision making
process.
We have already made a similar presentation[7].
However, the verification was not done with a general
simulator and there was no way to verify. Therefore, in
this paper we adopted a general agent model [10] that
the source code is published and a model at the time of
collision, and we verify this concept again.
3. Implementation to the target enclosing
algorithm
3.1. The proposed algorithm
The proposed algorithm is shown as follows[7]. This
uses only bearing information about target and its
neighbor[9][14]. Additionally this model can change
their direction to enclose a target.
Let n be the number of agents. The agents are
numbered as P1,…,Pn. Agent Pi determines its action
according to its nearest agent Pj and the nearest target t
as follows.
vi
i
f
(1)
i
dir(Pi )(
vi
r
k cos
(2)
i)
where dir(Pi ) {1, 1} represents its direction to enclose
the target.
dir(Pi )
1
direction(Pi ) CW
1 direction(Pi ) CCW
(3)
f, k are positive constants． direction(Pi ) {CW ,CCW }
means the direction of agent Pi. direction(Pi ) is
determined basically by majority decision as follows.
A i,t
{Pi | Pi
direction(Pi,t )
CW
(4)
P j | rcom }
1
| A i,t
1|
CCW
dir(P j )
P j A i,t
1
dir 0
(5)
otherwise
dir is a random number chosen with a uniform
probability from the interval [ A i,t , A i,t ] .
A i,t
dir
A i,t
(6)
where is a positive constant. As the number of agents
in the neighborhood increases, the noise applied
becomes stronger, and the agent randomly selects the
enclosing direction. Similarly, if there are many agents
in the vicinity that select its direction randomly, they
become disorderly locally and search for new collective
behavior is done. This state is performed until the high
density state is eliminated.
© The 2017 International Conference on Artificial Life and Robotics (ICAROB 2017), Jan. 19-22, Seagaia Convention Center, Miyazaki, Japan
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Masao Kubo, Nhuhai Phung, Hiroshi Sato
In this section, we show the performance of the proposed
model. The parameters are defined as follows: r 300 ,
n 20 , T 1 , rcom 100 ,
0.1 , f 1 , f 1 .
Fig.8 shows the result of enclosing the targets without
any blocked area. Each half of agents enclose the target
from different direction. The two sub groups collide and
consequently the direction of all agents becomes same
by the equation 8.
Fig.9(1) - (8) shows the result of the proposed algorithm
in case of orbit restricted. The line shown for crossing a
circle represents a wall that is difficult to pass. When
hitting this wall the robot bounces according to the rule
described in subsection 3.2. Here we explain a typical
transition. When the agent reaches the obstacle the
direction is reflexively changed. As a result, agents
gather near the wall as shown in Fig.9(4), (5). As a
result, trying to avoid defect by try and error by the
equation 6 near here. As the density gets higher, the
noise of the equation 5 becomes larger, and the number
of agents moving in a direction away from the wall
increases. As a result, as shown in Fig.9 (6), it escapes
from the vicinity of the obstacle. As they get out, the
density decreases, so the direction to enclose the target
of the agent is fixed.
From the above, it turns out that the proposed method
can generate group behavior suitable for the difference
in environment around the target.
Fig. 8. A snapshot of the formation of the proposed swarm under an ideal
condition.
Fig. 9. Snapshots of the formation of the proposed swarm under condition
which 2 parts of the orbit are blocked.
Fig. 10. Interval time span of switch of their direction at obstacles.
3.2. Collision to wall
Instead of the past work [7], in case of collision with the
wall, according to [10] we changed direction
reflectively and the speed was taken as the maximum
speed.
Fig. 11. Transition of the proportion of CW.
4.
Experiment
© The 2017 International Conference on Artificial Life and Robotics (ICAROB 2017), Jan. 19-22, Seagaia Convention Center, Miyazaki, Japan
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Direction switch behavior to
4.1. The trend of changes of their direction
Next, we investigated the relationship between the time
interval at which the enclosure direction changes and .
In the experiment in the previous subsection, we found
that the group moves between two obstacles. It is
thought that swarms can be reconstructed promptly if
the time required for conversion is short. The time
required T c sec is shown in Fig.10 using the cumulative
probability density distribution P T c t . Although it
was found that 60% could change direction quickly, it
turned out that it was difficult to change direction even
after 12,000 seconds had elapsed. Fig.11 shows the ratio
of CW in the direction of direction. 1 or 0 indicates that
all correspond to CW or CCW. However, it became 1 at
time = 200, and since it was 1 many times again before
reaching 0, it was confirmed that it took time for trial
and error. Improving the time required for this change is
a future task.
5.
3.
4.
5.
6.
7.
8.
Conclusion
In this paper, we investigated the case where the orbit to
enclose a target is physically restricted in the target
enclosing problem as a part of the basic technology
development for the self - organizing swarm system.
Here we proposed micro level algorithms, namely
behavior selection based on majority voting and
spontaneous noise generation function in order to
realize macroscopic state switching between
exploitation and exploration. This is based on the fact
that the phase transition phenomenon occurs due to the
magnitude of noise in the boids model. As a result of
verifying the proposed method by computer
experiments, it was found that formation can be
switched according to the environment if there is
sufficient time.
9.
10.
11.
12.
13.
14.
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