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Proceedings ArticleDOI

A bio-inspired plume tracking algorithm for mobile sensing swarms in turbulent flow

06 May 2013-pp 921-926
TL;DR: A stochastic model for plume spikes based on the Poisson counting process, which captures the turbulent characteristic of plumes, is proposed and an approach to estimate the parameters of the spike model is proposed, which allows for path planning algorithms for mobile sensing agents in the smoother field instead of in the turbulent plume field.
Abstract: We develop a plume tracking algorithm for a swarm of mobile sensing agents in turbulent flow. Inspired by blue crabs, we propose a stochastic model for plume spikes based on the Poisson counting process, which captures the turbulent characteristic of plumes. We then propose an approach to estimate the parameters of the spike model, and transform the turbulent plume field detected by sensing agents into a smoother scalar field that shares the same source with the plume field. This transformation allows us to design path planning algorithms for mobile sensing agents in the smoother field instead of in the turbulent plume field. Inspired by the source seeking behaviors of fish schools, we design a velocity controller for each mobile agent by decomposing the velocities into two perpendicular parts: the forward velocity incorporates feedback from the estimated spike parameters, and the side velocity keeps the swarm together. The combined velocity is then used to plan the path for each agent in the swarm. Theoretical justifications are provided for convergence of the agent group to the plume source. The algorithms are also demonstrated through simulations.

Summary (2 min read)

Introduction

  • Localizing gas/odor sources are of great importance in various scenarios such as finding the leaks of poisonous chemicals, searching for survivors after a disaster, and detecting fire in its early stage.
  • Low values of Reynolds numbers indicate smooth variations in chemical concentration, which imply well-defined gradients of the chemical concentration.
  • The goal is to control a swarm of mobile sensing agents to detect and track a plume source from initial locations that are downstream to the source.
  • The authors investigate the mechanism of the turbulent flow field and propose a stochastic modeling method for plume spikes using Poisson processes that describes the characteristics of chemical plumes.
  • Section III discusses methods for estimating spike parameters.

II. PROBLEM FORMULATION

  • The authors assume a plume is generated from a single source releasing chemicals into a turbulent flow field.
  • A swarm of mobile sensors are deployed into the fluid.
  • This problem is challenging since the chemical concentration within a plume created by a turbulent flow has very high spatial and temporal variation (see Fig. 1), therefore existing gradient based methods for smooth fields do not apply.
  • The magnitude and duration of detected spikes may have been utilized by the crab to direct its motion towards the chemical source.
  • High rate of successful source seeking behaviors have been observed from the experiments.

III. MODELING AND DETECTING SPIKES

  • Based on the experimental data in [22], the authors learn that when a mobile sensor moves in a chemical plume at constant speed, the measurement of concentration along its trajectory will display spikes as shown in Fig.
  • Suppose a mobile sensor can detect spikes using the thresholding method, then the rates λ12 and λ21 can be inferred from the beginning and ending of consecutive spikes.
  • The authors will later design controllers based on the noisy estimates of the rates λ̂12(t) and λ̂21(t).
  • And suppose the chemical source is located at position r0.

IV. PLUME TRACKING CONTROL

  • The authors design control strategies for a swarm of mobile sensing agents to locate a plume source based on the estimated plume spike parameters.
  • The authors strategy is inspired by recent observations of fish behaviors that fish speeds up when the light intensity increases, and slows down when the light intensity decreases so that the fish school is able to converge to the darkest area in a light field [20].
  • Let ri represent the position of the i-th agent and rc represent the center of the group.

A. Determining Velocities of the Agents

  • The authors can prove that, under the formation control law (7), the relative distance between every two agents converges to a constant [21].
  • Given the above system, the authors introduce the following proposition stating that the agent group will move towards the plume source.

V. SIMULATION RESULTS

  • The simulation is setup by first generating a simulated two dimensional turbulent plume field that matches experimental data.
  • These parameters then determine the rates for spikes λ12 and λ21 used in their simulation.
  • During the waiting time, agents measure plume intensities and detect spikes as in Fig.
  • The figure suggests that smaller waiting time generates longer trajectories.

VI. CONCLUDING REMARKS

  • The authors plume sensing strategy is inspired by blue crabs.
  • The authors propose a stochastic method to model plume spikes detected by mobile sensing agents and estimate the rate parameters of the spikes.
  • Then, the authors are able to transform the measured spike fields into a smooth scalar field.
  • The authors control and path planning strategy is inspired by the source seeking behaviors of fish schools.
  • The authors prove the convergence of the moving direction of the agent group towards the plume source in the transformed field.

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A Bio-inspired Plume Tracking Algorithm for Mobile Sensing Swarms
in Turbulent Flow
Dongsik Chang, Wencen Wu, Donald R. Webster, Marc J. Weissburg, and Fumin Zhang
Abstract We develop a plume tracking algorithm for a
swarm of mobile sensing agents in turbulent flow. Inspired
by blue crabs, we propose a stochastic model for plume
spikes based on the Poisson counting process, which captures
the turbulent characteristic of plumes. We then propose an
approach to estimate the parameters of the spike model, and
transform the turbulent plume field detected by sensing agents
into a smoother scalar field that shares the same source with
the plume field. This transformation allows us to design path
planning algorithms for mobile sensing agents in the smoother
field instead of in the turbulent plume field. Inspired by the
source seeking behaviors of fish schools, we design a velocity
controller for each mobile agent by decomposing the velocities
into two perpendicular parts: the forward velocity incorporates
feedback from the estimated spike parameters, and the side
velocity keeps the swarm together. The combined velocity is then
used to plan the path for each agent in the swarm. Theoretical
justifications are provided for convergence of the agent group
to the plume source. The algorithms are also demonstrated
through simulations.
I. INTRODUCTION
Localizing gas/odor sources are of great importance in
various scenarios such as finding the leaks of poisonous
chemicals, searching for survivors after a disaster, and de-
tecting fire in its early stage. To detect and track chemical
sources in an unknown environment, mobile sensing agents
are deployed in the field, and various approaches have been
developed such as building a map of the flow field [1]–[4],
gradient-based [5]–[9] and gradient-free algorithms [10].
The fluid flow environment, in which a chemical source
is present, varies depending on different Reynolds numbers.
Low values of Reynolds numbers indicate smooth varia-
tions in chemical concentration, which imply well-defined
gradients of the chemical concentration. At medium to
high Reynolds values, chemical dispersion is dominated by
turbulent mixing, which produces poorly defined and time-
varying gradients [11]–[13]. The turbulent flow fluctuation
at large Reynolds number brings difficulties in designing
control strategies for mobile sensing agents because it is
The research work is supported by ONR grants N00014-09-1-1074, and
N00014-10-10712 (YIP), and NSF grants ECCS-0841195 (CAREER) and
CNS-0931576
Dongsik Chang, Wencen Wu, and Fumin Zhang are with the School
of Electrical and Computer Engineering, Georgia Institute of Tech-
nology, Atlanta, GA, 30332, USA {dsfrancis3, wwencen3,
fumin}@gatech.edu
Donald R. Webster is with the School of Civil and Environmental
Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
dwebster@ce.gatech.edu
Marc J. Weissburg is with the School of Biology,
Georgia Institute of Technology, Atlanta, GA, 30332, USA
marc.weissburg@biology.gatech.edu
impossible to use analytical methods or simple numerical
simulations to predict the characteristics of odorant plumes
[11]. To successfully navigate mobile sensing agents, various
algorithms have been developed inspired by biology such as
E. coli [6], [10], beetles [10], blue crab [14], [15], silkworm
moth [7], [16]–[18], and bees [19].
Inspired by behaviors of blue crabs, Webster et al. [15]
develop and implement a plume tracking algorithm in a
controlled turbulent flow environment. They develop a sig-
nal processing strategy that is able to replicate behavioral
responses of blue crabs tracking a chemical stimuli. To
answer the challenge that the characteristics of the turbulent
flow is difficult to measure, they install sensor arrays on
an experimental vehicle to detect plume spikes and estimate
frequencies of the detected plume spikes. The spike infor-
mation is then processed by the tracking system to guide the
upstream and cross-stream motions of the vehicle so that it
can move towards and declare the plume source.
Inspired by their results, we investigate the plume tracking
problem in turbulent fluid fields using mobile sensing agents.
The goal is to control a swarm of mobile sensing agents to
detect and track a plume source from initial locations that
are downstream to the source. We investigate the mechanism
of the turbulent flow field and propose a stochastic model-
ing method for plume spikes using Poisson processes that
describes the characteristics of chemical plumes. We define
Poisson counters to indicate the detection of a spike, the
duration of which is implied by the rates of the Poisson
counters.
For the plume tracking system, we design velocity controls
for an N-agent group to move towards a plume source. A
novel design of our strategy is that instead of letting the
agent group locate a plume source in a turbulent fluid field,
we transform the detected turbulent flow field into a smooth
scalar field, the gradient of which is well-defined, so that we
can design control laws for the agent group in the smooth
field. Inspired by recently observed fish behaviors [20] and
our previous work on non-gradient source-seeking algorithms
[21], we decompose the velocities of each agent into two
parts: One part maintains the constant distance among agents,
and the other part, which is proportional to the estimated
duration of spikes, controls the entire group to move towards
the plume source. We prove that, under the control laws, the
moving direction of the agent group converges to the gradient
direction of the smooth field. The computed velocities are
then used by each agent to plan its path forward, which leads
the group to the plume source in the turbulent flow.
The rest of the paper is organized as follows. Section

Fig. 1. Flow visualization of the chemical plume in a controlled
turbulent flow.The view is from above, with the flow moving from
left to right.
II introduces the modeling of chemical plume spikes us-
ing Poisson counters. Section III discusses methods for
estimating spike parameters. Section IV presents control
strategies for controlling two mobile robots to track a plume
and the corresponding path planning algorithm. Section V
demonstrates simulations results of the proposed algorithm.
Section VI presents concluding remarks.
II. PROBLEM FORMULATION
We assume a plume is generated from a single source
releasing chemicals into a turbulent flow field. A swarm of
mobile sensors are deployed into the fluid. Each platform
is able to measure the level of chemical concentration at its
current location and move freely in the fluid, overcoming the
flow. The research goal of this paper is to develop a source
seeking algorithm to enable the swarm to move to the source
from initial locations that are downstream to the source,
where plume can be measured. This problem is challenging
since the chemical concentration within a plume created by
a turbulent flow has very high spatial and temporal variation
(see Fig. 1), therefore existing gradient based methods for
smooth fields do not apply.
In [15], based on experimental data collected from plumes
in turbulent field, it is shown that sensors distributed across
the body of a crab are able to detect spikes in the chemical
concentration. The magnitude and duration of detected spikes
may have been utilized by the crab to direct its motion to-
wards the chemical source. An algorithm has been proposed
to control an experimental platform equipped with three
sensors to emulate this source seeking behavior of a crab.
High rate of successful source seeking behaviors have been
observed from the experiments. However, the mechanism
behind such success have not been revealed in [15], which
prevents its application to a swarm of mobile sensors.
III. MODELING AND DETECTING SPIKES
Based on the experimental data in [22], we learn that
when a mobile sensor moves in a chemical plume at constant
speed, the measurement of concentration along its trajectory
will display spikes as shown in Fig. 2. A spike can then
be detected by comparing the measurement with a given
threshold. The occurrences of spikes display a random na-
ture. Another important observation is that as the sensor gets
close to the plume source, the average frequency of spike
Time(s)
Beginning of Spikes
Ending of Spikes
Concentration (C)
Fig. 2. Concentration measured along the trajectory of a moving
sensor in a turbulent chemical plume.
arrival decreases in applying a constant threshold [22], and
intuitively the duration of each spike becomes longer.
We now introduce a stochastic model to describe the
random occurrences of spikes along the trajectory. First, we
define the spike indicator as s = {s
1
,s
2
}, where s
1
,s
2
Z.
When s = s
1
, there is no spike at the current position of
the mobile sensor, and s = s
2
indicates otherwise. The spike
indicator s satisfies a stochastic differential equation driven
by Poisson counters as below:
ds = (s
1
s)dN
12
+ (s
2
s)dN
21
, (1)
where dN
12
is the Poisson jump process that triggers the state
s to jump from s
1
to s
2
, and dN
21
is the Poisson jump process
that triggers the state s to jump from s
2
to s
1
. Along the
trajectory, a state jump from s
2
to s
1
indicates the beginning
of a spike and a jump from s
1
back to s
2
indicates the ending
of a spike. These transitions happen randomly as Poisson
processes. The rates of the jump process dN
12
is λ
12
and the
rates of dN
21
is λ
21
, these rates determine how frequently
state transitions happens. Therefore, λ
12
and λ
21
affect the
duration of a spike as well as the averaged frequency of the
occurrences of the random spikes.
Suppose a mobile sensor can detect spikes using the
thresholding method, then the rates λ
12
and λ
21
can be in-
ferred from the beginning and ending of consecutive spikes.
Consider the current time as t, and suppose j-th spikes have
been detected along the trajectory of the mobile sensor. Let
us denote by T
j
and T
0
j
the beginning and ending time of the
j-th spike, respectively. We will use the timings for spikes
j 1 and j to estimate the rate of state transition as
ˆ
λ
12
(t) =
1
T
j
T
0
j1
ˆ
λ
21
(t) =
1
T
0
j
T
j
.
(2)
Equations (1) and (2) models the timing of spikes. Next,
we consider the noises or imperfections in the sensor that
cause variations in the measurements of the concentration.
These variations will cause inaccuracy in determining the
timing of the state transitions. Therefore the
ˆ
λ
12
(t) and
ˆ
λ
21
(t)
in Eq. (2) are noisy estimates for the true values of the rates.

0 1 2 3 4 5 6 7
−2
−1.5
−1
−0.5
0
0.5
1
1.5
Time (s)
Jump state
Fig. 3. Simulated timing of spikes modeled by the stochastic
Poisson processes. s
1
= 1, s
2
= 1, and σ = 0.08. The dotted
blue line indicates the true value of the state s without noise. The
added Gaussian noise severely corrupted the state s, and will cause
significant uncertainties in the timing estimates.
To model the effect of sensor noises on the transition timing,
we assume s is also corrupted by zero mean, Gaussian noises
with variance σ . Fig. 3 illustrates a case when s
1
= 1,
s
2
= 1, and σ = 0.08.
We will later design controllers based on the noisy esti-
mates of the rates
ˆ
λ
12
(t) and
ˆ
λ
21
(t). However, to evaluate the
performance of our controller design, we provide a ground
truth for λ
12
and λ
21
that matches the results in [22]. Let
r R
3
be the current location of the sensor in the field. And
suppose the chemical source is located at position r
0
. Let the
distance between the sensor and the source be d
p
= kr
0
rk,
We assume that λ
12
is a monotonically increasing function
of the the distance d
p
, and λ
21
is inverse proportional to the
distance, e.g.,
λ
12
= k
λ
1
g(d
p
)
λ
21
= k
0
λ
g(d
p
),
(3)
in which k
λ
and k
0
λ
are constants chosen by design. A simple
choice of g(·) is to let g(d
p
) = d
p
.
Define a function
f (d
p
) =
λ
12
+ λ
21
λ
12
=
k
0
λ
k
λ
g(d
p
)
2
+ 1, (4)
which is a smooth function of distance d
p
. Since the source
is located at d
p
= 0, where the function f (d
p
) has a unique
minimum value 1, the problem of finding the plume source in
the turbulent field is now equivalent to finding the minimum
point in the smooth field f (d
p
). The only challenge here is
that the function f (d
p
) has to be estimated from the sensor
measurements. Using the estimates
ˆ
λ
12
(t) and
ˆ
λ
21
(t), the
mobile sensor can compute a noisy estimate of f (d
p
) as
ˆ
f (d
p
) =
ˆ
λ
12
+
ˆ
λ
21
ˆ
λ
12
. (5)
Therefore, through stochastic modeling, we have converted
a source seeking problem within a turbulent field into a
Fig. 4. Decomposition of the velocities of the agents in a N-agent group.
minimum seeking problem in a smooth field corrupted by
non-Gaussian noises.
IV. PLUME TRACKING CONTROL
In this section, we design control strategies for a swarm of
mobile sensing agents to locate a plume source based on the
estimated plume spike parameters. Our strategy is inspired
by recent observations of fish behaviors that fish speeds up
when the light intensity increases, and slows down when the
light intensity decreases so that the fish school is able to
converge to the darkest area in a light field [20].
Suppose N sensing agents are deployed in a plume. Let
r
i
represent the position of the i-th agent and r
c
represent
the center of the group. Then, we derive r
c
=
1
N
N
i=1
r
i
.
As introduced previously, for i = 1,2, ..., N, let d
p,i
be the
distance between the plume source and the i-th sensing agent.
Without loss of generality, let us assume the plume source
is located at position r
0
= (0, 0). Therefore, d
p,i
= kr
i
k.
A. Determining Velocities of the Agents
Define the inertial frame as X
I
and Y
I
. Arbitrarily select a
baseline q as an unit vector that forms an angle θ with the
inertial frame X
I
. Define q
to be the vector perpendicular to
q that forms a right handed frame with q. q and q
intersects
at r
c
. As illustrated in Fig. 4, for each agent, we decompose
its velocity into two parts [21]: v
i
, which is perpendicular to
q, and v
//
i
, which is aligned with q and maintains formation.
Then, v
i
= v
i
+ v
//
i
. For v
i
= v
i
sinθ
cosθ
, we design
v
i
, i = 1,2, as
v
i
= K
ˆ
f (d
p,i
) +C, (6)
where K and C are constants selected by design.
Along direction q, let r
//
i
be the projection of location r
i
onto vector q, as illustrated in Fig. 4. For agent i, we define
set N
i
to contain the closest agents to agent i to the right and
to the left along direction q. For example, as shown in Fig.
4, N
1
= {2}, N
i
= {i1,i +1},i 6= 1,N, and N
N
= {N 1}.
The goal is to design v
//
i
so that the relative distance from
r
//
i
to r
//
j
,i 6= j, converges to a constant a
0
i j
. Furthermore,
we require that v
//
c
=
1
N
N
i=1
v
//
i
= 0. Therefore, for v
//
i
=
v
//
i
cosθ
sinθ
, we design v
//
i
as
v
//
i
= k
p
jN
i
((r
j
r
i
) ·q a
0
j,i
), (7)

where a
0
i, j
= a
0
j,i
. We can prove that, under the formation
control law (7), the relative distance between every two
agents converges to a constant [21]. Given v
i
and v
//
i
, each
agent now has its velocity given by
v
i
= (K
ˆ
f (d
p,i
) +C)
sinθ
cosθ
+ k
p
jN
i
((r
j
r
i
) ·q a
0
j,i
)
cosθ
sinθ
, (8)
and v
//
c
=
1
N
N
i=1
v
//
i
= 0, we obtain the velocity of the
formation center as
v
c
= (
1
N
K
N
i=1
ˆ
f (d
p,i
) +C)
sinθ
cosθ
. (9)
If we arbitrarily choose the baseline q =
r
i
r
j
kr
i
r
j
k
, in which
i 6= j, then the angular velocity of the group can be calculated
as
˙
θ = ω =
v
i
v
j
k r
i
r
j
k
=
K
k r
i
r
j
k
(
ˆ
f (d
p,i
)
ˆ
f (d
p, j
)). (10)
Since the noise in the estimation of
ˆ
f (d
p,i
) is unstruc-
tured and complex, we use
ˆ
f (d
p,i
) = f (d
p,i
) to analyze the
convergence of the moving direction of the group to gradi-
ent directions. If we use Taylor expansion to approximate
f (d
p,i
), we have
f (d
p,i
) = f (d
p,c
) + f (d
p,c
) ·(r
i
r
c
) +H.O.T, (11)
where d
p,c
is the distance from the formation center to the
plume source, f (d
p,c
) is the gradient of f (d
p,c
) at d
p,c
,
and H.O.T represents higher order terms in the above Taylor
expansion. Denote the angle between the gradient direction
f (d
p,c
) and the inertial frame X
I
as α [π , π ]. Then, we
derive from Equation (10) that
˙
θ
=
K
k r
i
r
j
k
( f (d
p,c
) ·(r
i
r
j
)) = K( f (d
p,c
) ·q)
= K k f (d
p,c
) k (
f (d
p,c
)
k f (d
p,c
) k
· q)
= K k f (d
p,c
) k sin(θ α
π
2
). (12)
Choose the state to be θ α , then we obtain
˙
θ
˙
α = K k f (d
p,c
) k sin(θ α
π
2
)
˙
α. (13)
When k f (d
p,c
) k6= 0, the above system has a stable
equilibrium θ α =
π
2
and an unstable equilibrium θ α =
π
2
. Given the above system, we introduce the following
proposition stating that the agent group will move towards
the plume source.
Proposition 4.1: If the gradient direction α is constant,
that is,
˙
α = 0, then, as t , lim
t
θ (t) = α +
π
2
. If the
rate of change
˙
α 6= 0 is considered as an input to the system
(13), then θ α =
π
2
is an equilibrium of (13) that is input-
to-state stable (ISS).
Proof:
If
˙
α = 0, we choose a Lyapunov candidate function as
V = ln(cos(
θ α
π
2
2
)). (14)
We calculate
˙
V = tan(
θ α
π
2
2
)(
˙
θ
˙
α)
= 2K k f (d
p,c
) k sin
2
(
θ α
π
2
2
) tan(
θ α
π
2
2
)
˙
α
= 2K(1 ε) k f (d
p,c
) k sin
2
(
θ α
π
2
2
)
2Kε k f (d
p,c
) k sin
2
(
θ α
π
2
2
) tan(
θ α
π
2
2
)
˙
α
2K(1 ε) k f (d
p,c
) k sin
2
(
θ α
π
2
2
), (15)
when |
˙
α| Kε k f (d
p,c
) k | sin(θ α
π
2
)| and 0 < ε < 1.
Therefore, according to Theorem 4.19 in [23], if
˙
α is con-
sidered as the input, the system (13) is input-to-state stable
(ISS). If the input
˙
α = 0, θ converges to the equilibrium
point α +
π
2
. If the rate of change
˙
α is bounded, then at
the steady state, the deviation |(θ α
π
2
)| is also bounded.
Therefore, as t , lim
t
θ (t) = α +
π
2
, which indicates
that the agent group will move towards the minimum of field
f (d
p,c
).
B. Path Planning
Proposition 4.1 indicates that, if we use Eq. (8) as feedback
control for the velocities of the agents in continuous time,
the moving direction of the agent group will converge
to the gradient direction of field f (d
p
). However, in our
simulation, we do not control the velocities of the agents
in continuous time. We discretize the system and use the
designed velocities for the path planning of the agent group.
Denote r
i,k
as the position of the i-th sensing agent at time
instant t
k
. We propose the following path-planning algorithm.
Algorithm 1: Repeat the the following steps for i =
1,2,...,N. At location r
i,k
, the i-th sensing agent
1) takes measurements of the turbulent field values for a
finite time T , called the ”waiting time”.
2) estimates
ˆ
λ
12
and
ˆ
λ
21
based on the measurements,
estimates
ˆ
f (d
p
) based on Eq. (5), and using Eq. (8)
determines the velocity v
i,k
, which generates a planned
trajectory.
3) moves forward along the trajectory over a finite motion
horizon time τ so that r
i,k+1
= r
i,k
+ τv
i,k
.
Let k = k + 1 and repeat the above steps until the function
ˆ
f (d
p,i
) estimated by an agent is sufficiently close to 1,
indicating the vicinity of the source.
We will show in the simulation section that by using the
speed control of (6) and (7) and the path planning algorithm
1, a two-agent group is able to move towards the plume
source while maintaining a constant formation.

Distance from the source, [cm]
Frequency, [Hz]
Fig. 5. Frequency of concentration spikes [Hz] as a function of
distance from the source.
Fig. 6. An estimated field of f (d
p
) when the waiting time T =
{10,100} s. The plume source is located at (0,0). The rates λ s are
estimated using Eq. (2) for each time step, and then averaged over
the period of waiting time.
V. SIMULATION RESULTS
The simulation is setup by first generating a simulated two
dimensional turbulent plume field that matches experimental
data. The ground truth k
λ
and k
0
λ
parameters for the spikes
in such a field are selected from Fig. 5 from [22]. In the
figure, three spike samples are measured at each of five lo-
cations with different distances to the source. Since all three
measurements taken at distance 150 cm have the frequency
of 4 Hz, we choose the reference frequency f
r
= 4 Hz and
reference distance d
r
= 150 cm. Then, we let k
λ
= f
r
d
r
and
k
0
λ
=
f
r
d
r
. These parameters then determine the rates for spikes
λ
12
and λ
21
used in our simulation.
At each location in the plume field, we simulate a train
of spikes using the stochastic model in Eq. (1). We allow
a sensing agent at its current location to measure this train
for the waiting time T as described in Algorithm 1. Then,
a noisy estimate of the field f (d
p
) will be generated by the
agent. Fig. 6 plots this noisy estimate over the entire field
for T = {10, 100} s. When T = 100 s, we can see that the
field is close to a smooth field, but with smaller waiting time
T , we can observe that the field becomes more noisy.
We simulate two mobile sensing agents in the simulated
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8
−1
−0.5
0
0.5
1
Spike Measurement from Agent 1
Time (s)
Spike Indicator Estimate
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8
−1
−0.5
0
0.5
1
Spike Measurement from Agent 2
Time (s)
Spike Indicator Estimate
Fig. 7. Example of spikes estimated by mobile sensing agents from
plume measurements with s
1
= 1 and s
2
= 1.
0 50 100 150
−50
0
50
Agents’ Center Trajectory
x (Cm)
y (Cm)
Plume Source
Agent 1
Agent 2
Center Trajectory
Fig. 8. The trajectory of the center of two mobile sensing agents
in a plume tracking simulation. The plume source is located at
(0,0) and the agents are deployed at (150, 35) and (150,25).
The waiting time T = 100 s at each position and the agents move
forward for τ = 1 s after the velocities are determined.
turbulent fluid field. The simulated agents are initially de-
ployed at (150,35) and (150,25), and the two agents
will keep a distance |a
0
| = 10 cm. To enable the agents to
find the plume source in the field, Algorithm 1 is applied.
The agents will wait and estimate the averaged plume field
for the waiting time T , then make a move for τ = 1 s. Each
agent does not need the entire field information to navigate.
Instead, they require the spike parameters
ˆ
λ
12
,
ˆ
λ
21
only
at their current positions to compute
ˆ
f (d
p,i
) and v
i
in the
algorithm, which takes very small computational cost and
hence enables real-time implementation. For the controller
parameters in Eq. (8), we set K = 3, C = 3, and k
p
= 1.
Results of the algorithm 1 are illustrated by Figures 7 and
8. During the waiting time, agents measure plume intensities
and detect spikes as in Fig. 7. After estimating
ˆ
λ
12
and
ˆ
λ
21
using Eq. (2), the agents compute the velocities and
move forward for τ = 1 s. Fig. 8 shows the trajectory (the
green line) of the center of the two agents towards the
source. The ending positions of the two agents are marked

Citations
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References
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Journal ArticleDOI
01 Feb 2013-Science
TL;DR: It is revealed that this emergent problem solving is the predominant mechanism by which a mobile animal group responds to complex environmental gradients.
Abstract: The capacity for groups to exhibit collective intelligence is an often-cited advantage of group living. Previous studies have shown that social organisms frequently benefit from pooling imperfect individual estimates. However, in principle, collective intelligence may also emerge from interactions between individuals, rather than from the enhancement of personal estimates. Here, we reveal that this emergent problem solving is the predominant mechanism by which a mobile animal group responds to complex environmental gradients. Robust collective sensing arises at the group level from individuals modulating their speed in response to local, scalar, measurements of light and through social interaction with others. This distributed sensing requires only rudimentary cognition and thus could be widespread across biological taxa, in addition to being appropriate and cost-effective for robotic agents.

440 citations


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  • ...Our strategy is inspired by recent observations of fish behaviors that fish speeds up when the light intensity increases, and slows down when the light intensity decreases so that the fish school is able to converge to the darkest area in a light field [20]....

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  • ...Inspired by recently observed fish behaviors [20] and our previous work on non-gradient source-seeking algorithms [21], we decompose the velocities of each agent into two parts: One part maintains the constant distance among agents, and the other part, which is proportional to the estimated duration of spikes, controls the entire group to move towards the plume source....

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TL;DR: This article presents a survey of the existing methods of robotic odor localization, which have been organized into taxonomic classifications, and provides a framework in which to evaluate the methods, view how they relate to each other, and make qualitative comparisons.
Abstract: Robotic odor localization has become a prominent research area in recent years. It promises many valuable practical applications, and contributes to the knowledge of biological odor localization, which has in many cases been the source of inspiration. There have been a diversity of approaches, implemented in both simulated and practical experiments, with a wide variety of platforms, and in a number of environments. This article presents a survey of the existing methods, which have been organized into taxonomic classifications. This provides a framework in which to evaluate the methods, view how they relate to each other, and make qualitative comparisons. The methods are grouped at the highest level by environmental conditions, and then by the localization method which in most cases is closely associated with the type of sensors used.

292 citations


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  • ...At medium to high Reynolds values, chemical dispersion is dominated by turbulent mixing, which produces poorly defined and timevarying gradients [11]–[13]....

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TL;DR: This paper presents a behavior-based adaptive mission planner to trace a chemical plume to its source and reliably declare the source location and describes the methods and results from experiments conducted in November 2002, using a plume of Rhodamine dye developed in a turbulent fluid flow.
Abstract: This paper presents a behavior-based adaptive mission planner (AMP)to trace a chemical plume to its source and reliably declare the source location. The proposed AMP is implemented on a REMUS autonomous underwater vehicle (AUV)equipped with multiple types of sensors that measure chemical concentration,the flow velocity vector, and AUV position, depth, altitude, attitude, and speed. This paper describes the methods and results from experiments conducted in November 2002 on San Clemente Island, CA, using a plume of Rhodamine dye developed in a turbulent fluid flow (i.e., near-shore ocean conditions). These experiments demonstrated chemical plume tracing over 100 m and source declaration accuracy relative to the nominal source location on the order of tens of meters. The designed maneuvers are divided into four behavior types: finding a plume,tracing the plume, reacquiring the plume, and declaring the source location. The tracing and reacquiring behaviors are inspired by male moths flying up wind along a pheromone plume to locate a sexually receptive female. All behaviors are formulated by perception and action modules and translated into chemical plume-tracing algorithms suitable for implementation on a REMUS AUV. To coordinate the different behaviors, the subsumption architecture is adopted to define and arbitrate the behavior priorities. AUVs capable of such feats would have applicability in searching for environmentally interesting phenomena, unexploded ordnance, undersea wreckage, and sources of hazardous chemicals or pollutants.

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  • ...To detect and track chemical sources in an unknown environment, mobile sensing agents are deployed in the field, and various approaches have been developed such as building a map of the flow field [1]–[4], gradient-based [5]–[9] and gradient-free algorithms [10]....

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  • ...coli [6], [10], beetles [10], blue crab [14], [15], silkworm moth [7], [16]–[18], and bees [19]....

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TL;DR: In this paper, an approach and experimental results using a REMUS AUV to find a chemical plume, trace the plume to its source, and maneuver to reliably declare the source location are presented.
Abstract: Olfactory-based mechanisms have been hypothesized for biological behaviors including foraging, mate-seeking, homing, and host-seeking. Autonomous underwater vehicles (AUVs) capable of such chemical plume tracing feats would have applicability in searching for environmentally interesting phenomena, unexploded ordinance, undersea wreckage, and sources of hazardous chemicals or pollutants. This article presents an approach and experimental results using a REMUS AUV to find a chemical plume, trace the chemical plume to its source, and maneuver to reliably declare the source location. The experimental results are performed using a plume of Rhodamine dye developed in a turbulent, near-shore, oceanic fluid flow.

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"A bio-inspired plume tracking algor..." refers background in this paper

  • ...coli [6], [10], beetles [10], blue crab [14], [15], silkworm moth [7], [16]–[18], and bees [19]....

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Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "A bio-inspired plume tracking algorithm for mobile sensing swarms in turbulent flow" ?

Inspired by blue crabs, the authors propose a stochastic model for plume spikes based on the Poisson counting process, which captures the turbulent characteristic of plumes. The authors then propose an approach to estimate the parameters of the spike model, and transform the turbulent plume field detected by sensing agents into a smoother scalar field that shares the same source with the plume field.