99
A School of Robotic Fish for Pollution Detection in Port
x i P b where τ is the mean run length and τ 0 is the mean run length in the
absence of concentration gradients, α is a constant of the system based on
the chemotaxis sensitivity factor of the bacteria, and P b is the fraction of the
receptor bound at concentration C. In this work, C is taken as the present
reading taken by the robotic agent. k d is the dissociation constant of the bacterial chemoreceptor, and dP b dt is the rate of change of P b .
The following modified flocking controller is used to realize the flocking
control for agent x i .
x t
f
i ( ) = −K( dist(t) − d)( x i ( )
t − x j (t)) + B
(5.5)
where D( )
t = x t
i ( ) − x j ( )
t ; B = H( x t
i ( ) − x h ( )
t ) ; x h ( )
t i s the position of the
agent with the highest measurement in the neighborhood of x i . The neighborhood is determined by the communication radius of each robot agent.
K > 0 is the magnitude of the repulsion force between agent x i and agent
x j . Constant H is the attractant gain for the force between agent x i and the
agent x h with the highest environmental quantity measurement in the
neighborhood.
The two behaviors are then combined and the new position of the agent x i
calculated using x i :
x t
f
i ( + 1) = β(t) + ( Fx i ( t) + Bx
b
i ( t))
(5.6)
where both constants F = 0.01 and B = 0.94 are gains for the flocking and the
bacteria behavior, respectively.
Before combining the two behaviors together, the bacterial chemotaxis
controller was subjected to tests using two metrics of environmental exploration and source convergence. Fifty robots were used in our simulations
for each change in parameter value to gain an accurate view of the effects
of the parameter value change. Each parameter was increased from 2 to 30
in increments of two and results were recorded from each investigation.
Each robot moved independently without knowing about other robots in the
environment.
In addition, each simulation ran for a short time of 2.5 minutes because
given a long enough time, all robots would eventually find the source
and would not give an opportunity to investigate the effect of parameter
changes. The source was placed at coordinates of (x, y) = (400, 400) and the
agents were randomly placed at (x, y) = (250, 150) with a standard deviation of 5. In the bacteria chemotaxis experiments, the velocity was kept
constant.
As shown in Figure 5.11, the larger the standard run length is, the larger
the area covered by the robots is and the longer it takes to converge at the
source. The reason for this is that greater run length values tend to reduce
A School of Robotic Fish for Pollution Detection in Port
x i P b where τ is the mean run length and τ 0 is the mean run length in the
absence of concentration gradients, α is a constant of the system based on
the chemotaxis sensitivity factor of the bacteria, and P b is the fraction of the
receptor bound at concentration C. In this work, C is taken as the present
reading taken by the robotic agent. k d is the dissociation constant of the bacterial chemoreceptor, and dP b dt is the rate of change of P b .
The following modified flocking controller is used to realize the flocking
control for agent x i .
x t
f
i ( ) = −K( dist(t) − d)( x i ( )
t − x j (t)) + B
(5.5)
where D( )
t = x t
i ( ) − x j ( )
t ; B = H( x t
i ( ) − x h ( )
t ) ; x h ( )
t i s the position of the
agent with the highest measurement in the neighborhood of x i . The neighborhood is determined by the communication radius of each robot agent.
K > 0 is the magnitude of the repulsion force between agent x i and agent
x j . Constant H is the attractant gain for the force between agent x i and the
agent x h with the highest environmental quantity measurement in the
neighborhood.
The two behaviors are then combined and the new position of the agent x i
calculated using x i :
x t
f
i ( + 1) = β(t) + ( Fx i ( t) + Bx
b
i ( t))
(5.6)
where both constants F = 0.01 and B = 0.94 are gains for the flocking and the
bacteria behavior, respectively.
Before combining the two behaviors together, the bacterial chemotaxis
controller was subjected to tests using two metrics of environmental exploration and source convergence. Fifty robots were used in our simulations
for each change in parameter value to gain an accurate view of the effects
of the parameter value change. Each parameter was increased from 2 to 30
in increments of two and results were recorded from each investigation.
Each robot moved independently without knowing about other robots in the
environment.
In addition, each simulation ran for a short time of 2.5 minutes because
given a long enough time, all robots would eventually find the source
and would not give an opportunity to investigate the effect of parameter
changes. The source was placed at coordinates of (x, y) = (400, 400) and the
agents were randomly placed at (x, y) = (250, 150) with a standard deviation of 5. In the bacteria chemotaxis experiments, the velocity was kept
constant.
As shown in Figure 5.11, the larger the standard run length is, the larger
the area covered by the robots is and the longer it takes to converge at the
source. The reason for this is that greater run length values tend to reduce