Direction switch behavior to enclose a target

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.


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.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 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.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 P -489 can behave flexible under conditions which a simple collective is suspended.

The proposed scenario of switch of macroscopic states
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] [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.

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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.

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.
where dir(P i ) {1, 1} represents its direction to enclose the target.
f, k are positive constants． direction(P i ) {CW ,CCW } means the direction of agent Pi. direction(P i ) is determined basically by majority decision as follows.
dir(P j ) dir is a random number chosen with a uniform probability from the interval [ A i,t , A i,t ] .
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.

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.

Experiment
In this section, we show the performance of the proposed model.The parameters are defined as follows: r 300 , n 20, T 1, r com 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.P -492

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.

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.

Fig. 8 .Fig. 9 .
Fig. 8.A snapshot of the formation of the proposed swarm under an ideal condition.

Fig. 10 .
Fig. 10.Interval time span of switch of their direction at obstacles.