comp int 10a particle swarm opt based robot for odor control

8/3/2019 Comp Int 10a Particle Swarm Opt Based Robot for Odor Control

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Wisnu Jatmiko, Kosuke Sekiyama,and Toshio FukudaNagoya University, JAPAN

Abstract: This paper provides a combination of chemo-taxic and anemotaxic modeling, known as Odor-GatedRheotaxis (OGR), to solve real-world odor source local-ization problems. Throughout the history of trying tomathematically localize an odor source, two common bio-metric approaches have been used. The first approach,chemotaxis, describes how particles flow according to localconcentration gradients within an odor plume. Chemo-taxis is the basis for many algorithms, such as ParticleSwarm Optimization (PSO). The second approach isanemotaxis, which measures the direction and velocity ofa fluid flow, thus navigating upstream within a plume tolocalize its source.

Although both chemotaxic and anemotaxic based algo-rithms are capable of solving overly-simplified odor local-ization problems, such as dynamic-bit-matching ormoving-parabola problems, neither method by itself is ade-quate to accurately address real life scenarios. In the realworld, odor distribution is multi-peaked due to obstacles inthe environment. However, by combining the twoapproaches within a modified PSO-based algorithm, odorswithin an obstacle-filled environment can be localized anddynamic Advection-Diffusion problems can be solved.Thus, robots containing this Modified Particle SwarmOptimization algorithm (MPSO) can accurately trace anodor to its source.

I. Introduction

Research for applications of robotic odor-sensing

technology has grown substantially. This work isbroadly categorized into the following two

groups: Artificial odor discrimination systems [1]

and odor source localization by autonomous mobile sensing

systems [2]. Artificial odor discrimination systems have been

developed for automated detection and classification of aro-

mas, vapors, and gases. Meanwhile, robotics applications for

odor localization have mainly been focused in detecting the

sources of toxic gas leaks and origins of small-scale fires.

This paper seeks to address odor source localization and

particularly investigates the application of tracing a fire to its

origin within a plume of smoke.

Many issues have hindered odor source localization in thepast. One of the common issues has been that most detection

of chemicals with mobile robots has been based on experimen-

tal setups where the distance between the source and the sen-

sor following an odor trail has been minimized to limit the

influence of turbulent transport [3][5]. Another issue has been

that of basing systems on the assumption of a strong, unidirec-

tional air stream in the environment [6], [7]. However, thus far

not much attention has been paid to the issue of odor localiza-

tion within a natural environment.

PHOTOSPIN&KPTPOWERPHOTOS

1556-603X/07/$25.002007IEEE MAY 2007 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 37


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38 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2007

The natural environment presents two major problems that

are addressed in this paper. The first problem is that in natural

environments the distribution of odor molecules is usually

dominated by turbulence, rather than diffusion. The other

problem is the influence of the wind, which is unstable in both

force and direction. Thus, when odor distribution is very com-

plex due to turbulent flow and wind instability, current mobile

robotic odor detection systems perform poorly. [2], [8][10].

To combat these natural environment issues, a new

approach exploiting Particle Swarm Optimization (PSO) is

presented in this paper. The PSO algorithm here is modified

to include chemotaxic and anemotaxic theory along with the

development of an Advection-Diffusion odor model for

obstacle-filled environments. This Modified Particle Swarm

Optimization (MPSO) is applied by multiple mobile robots

which localize an odor source by exploring an obstacle-filled,

natural environment where the odor distribution changes over

time [8][10].

II. Motivation

Particle Swarm Optimization (PSO) simulates behaviors of

bird flocking. Suppose the following scenario: a group of birds

is randomly searching for food in an area. There is only one

piece of food in the area being searched. Not all of the birds

know where the food is. So what is the best strategy to find

the food? The most effective approach is to follow the bird

nearest to the food. This scenarios was the inspiration for PSO,

which has then applied to optimization problems [11], [12].

When a standard PSO is used, it gives an answer that even-

tually converges to a single optimum. By converging to a sin-

gle answer, it looses the diversity necessary for efficiently

operating in a dynamic environment. When exploring a search

space, the standard PSO intrinsically limits the ability to adaptto changes in the environment. However, since PSO is used to

solve dynamic problems for other applications such as reinitial-

izing particle positions [13], [14], charged swarms [15][17],

limit memory [18], local search [19], split adaptive PSO [20],

fine-grained PSO [21], and hierarchical particle [22], it showed

promise as a feasible starting point for odor source localization.

A key to its successful implementation was to match it with

the correct hardware platform. Considering this, we chose two

simple mechanisms to develop a new algorithm for controlling

autonomous vehicles and ensured the mobile robot hardware

included multiple sensory capabilities (e.g., odometry,

anemometry, and olfaction) [23][25].

We improved the standard PSO in two ways. The first

modification was to make the standard PSO capable of detect-

ing a change in the environment; and, consequently, take

explicit actions to increase diversity and facilitate a shift to the

new optimum. Thus, the PSO now accounted for dynamic

problems. Secondly, multiple populations were used to search

for new optima or to track an already-known local optima.

This modified PSO algorithm, with detection of environmen-

tal changes, along with responding mechanism, was imple-

mented into the hardware.

Another implementation to the PSO algorithm was based

on electrical charge theory, which uses two types of robots

neutraland charged robots. The potential field method is widely

used in path-planning of autonomous mobile robots due to its

elegant mathematical analysis and simplicity. The goal of this

model is to have a number of sub-populations explore the all

the optima in order to find the best local optimum. To explore

the local optima, part of the population splits off each time anoptimum is discovered and remains neutral while investigat-

ing that optima. Meanwhile, the remainder of the population,

the charged robots, continues to search for new local optima.

The process is repeated until better solutions are found. In

essence, while the neutral swarm particles optimize, the sur-

rounding charged swarm particles maintain diversity to cope

with dynamic changes in the locations of covered peaks. We

applied electric field potential theory to the PSO algorithm by

using multiple populations in our tests; and thus kept a balance

of diversity and convergence of optima.

Solving odor source localization problems in dynamic envi-

ronments requires hardware and software platforms [23][25].

During the initial design stages, software evaluation is preferredbecause it allows easy comparison of different localization strate-

gies for various environmental scenarios. This paper presents a

two-dimensional (2-D) simulation implementation that address-

es tradeoffs between computational efficiency and inclusion of

realistic hardware parameters. The 2-D simulation assumes that

the plume tracing occurs at a near-constant altitude that is only a

few meters above the ocean floor or ground level. The 2-D

algorithms presented can be extended directly to three-dimen-

sional (3-D) problems, but implementation for three dimensions

requires a significant increasing in computation capacity.

FIGURE 1 Demonstration of the inability of standard PSO to follow dynamic changes in the environment.

C(x,y)=

OdorDistribution

I. Environment III. Robot Re-Adaptation

Trap in Local Maximum

(x, y) Position of Robots

II. Environment Changed IV. Trap in Local Maximum


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MAY 2007 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 39

III. Particle Swarm Optimization Framework

Many complex real-word optimization problems are dynamic,

and change stochastically over time. These problems require

measurements that account for the uncertainty present in the

real world. Evolutionary algorithms (EAs), especially Particle

Swarm Optimization (PSO), have proven successful in a num-

ber of static applications as well as dynamic and stochastic opti-

mization problems. They are particularly successful because

they draw their inspiration from the principles of natural evo-

lution, which is a stochastic and dynamic process [26], [27].

The interaction of the robot with the PSO algorithm is

described as follows: Suppose that a population of robots is

initialized with certain positions and

velocit ies; let xi( t) and Vi( t)

denote the position and the velocity

vector of the i-th robot at the itera-

tion time t( t= 1, 2 . . . ). In addi-

tion, let p i and pg be defined as the

best local and the best global posi-

tion found in plume distributionthat is under evaluation by the

robot at position xi( t). The posi-

tion and the velocity are updated to

improve the fitness function at each

time step. When a robot discovers a

pattern that is better than any previ-

ously found, the positional coordi-

nates are stored in the vectorp i, the

best position found by robot i so

far. The difference between p i and

the current position xi( t) is stochas-

t ical ly appended to the current

velocity V i( t). This causes a changeto the trajectory the robot would

take at that position. The stochasti-

cally weighted difference between

the populations best position pgand the individuals current position

xi is also added to the velocity, in

order to adjust for the next time

step. These adjustments to the robot

behavior direct the search around

two best positions.

The value ofpg (the best global position for concentration of

the gas) is determined by comparing the best performances of all

the members of the population. The performances are defined

by indices from each population member; and the best per-

formers index is assigned as the variable g. Thus, pg represents

the best position found by all members of the population.

Each robot is equipped with an ad-hoc wireless network

and global positioning system (GPS). Through the ad-hoc net-

work, each robot transmits and collects the information about

the gas concentration, while the position of the robot is deter-

mined by the GPS.

FIGURE 2 Logic Diagram of Detection and Response of a PSO to dynamic changes in the environment.

If pg-old=pg-new

Detect Environment(pg Every t Iterations)

Standard PSO

Respond(Spread Randomly at t steps)

Start

Stop

Yes

No

Success Find the Sourcepg= Convergence Criteria

orUn-Success Find the Source

t= Max Step

Yes

No

FIGURE 3 Demonstration of Detection and Response of the MPSO to dynamic changes of the environment.

C(x,y)=

OdorDistribution

I. Environment III. Robot Re-AdaptationII. Environment Changed IV. Detection and Response



Detection and ResponseProbabilistic RobotsCan Recover fromTrap in LocalMaximum


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A. Standard Particle Swarm Optimization

The concept of standard PSO is described in eq. (1) and (2).

Vi( t) = (Vi( t 1) + c1 rand()(p i( t 1) x i( t 1))

+ c2 rand()(pg( t 1) x i( t 1))) (1)

x i( t) =x i( t 1) +Vi( t) (2)

After finding the two best values, the particle velocity and

position is updated with eq.(1) and (2). The functions Rand()

and rand() are random functions returning a value between

(0,1). Coefficient is constriction factor, which is less than 1.

The coefficient c1 and c2 are learning parameters, where

c1 = c2 = 2.

The main problem with standard PSO applications in

dynamic optimization problems is that the PSO will eventually

converge to an optimum; it thereby looses the diversity neces-

sary for efficient exploration of the search space. Consequently,

the ability to adapt to a change in the environment is weak-

ened as shown in Figure 1.

B. Detection and

Responding PSO (DR PSO)

To deal with a dynamic problem, PSO should be improved

by incorporating the change detection and its responding

mechanisms. The change detection function is applied for

monitoring the global best information pg. If pg has not

been changed for a certain number of iterations, it implies

that another optimum solution might exist. After the detec-

tion of environmental changes, there must be a strategy for

effectively responding to a wide variety of changes. Howev-

er, if the whole population of robot has already converged

to a small area, it might be difficult to cope with the

extreme change. Therefore, a diversity extension mechanism

of the positional distribution is investigated when a change is

detected. For simplicity, all robots are assumed to spread at a

certain step to cope with the changes. (Figure 2 shows the

logic diagram of Detection and Responding PSO (DR

PSO); the conceptual demonstration of DR PSO is shown

in Figure 3.)

C. Charged PSO

Applying Coulombs law, a charged

swarm robot is introduced in order to

maintain diversity of the positional distri-

bution of the robots and to prevent

them from being trapped in a local max-

imum. This enhances adaptability to the

changes of the environment. Figure 4

shows the repulsion function for charged

swarm robots. Suppose that robot i can

observe the present position of the other

robots (xp = x i) and has a constant

charge Qi in order to keep a mutual dis-tance away and maintain positional

diversity. Two types of swarm robots are

defined: neutraland chargedrobots. For all

neutral robots Qi= 0; hence, no repul-

sive force is applied to the neutral robots.

Forcharged robots, the mutual repulsive

force between robots i and p is defined

according to the relative distance,

|x i xp| as follows;FIGURE 4 Interaction of the charged swarm robots.

Q1

Q2

Q3

Q4

Q0Q0

(x1x3)3x1x3

Q1Q3a1,3 =

2x1x2

Q1Q2 (x1x2)a1,2 =

rcore

rperc

a1,4= 0

rcore

Neutral Swarm

Charged Swarm

FIGURE 5 Demonstration of Charged PSO following dynamic changes in the environment.

C(x,y)=

OdorDistribution

I. Environment III. Robot Re-AdaptationII. Environment Changed IV. Charged PSO

Never Trap in

Local Maximum



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aip =

QiQp(x ixp)

r2c ore|x ixp||xi xp| < rc o re

QiQp

|xixp|3 (xi xp) rc o re < |xi xp| < rpe rc

0 rpe rc < |xi xp|

(3)

where, (i= p), rc o re denotes the diameter inside which a con-

stant, strong repulsion force is applied and rpe rc denotes the

recognition range of robot. Hence, if the mutual distance is

beyond rpe rc , there exists no repulsion force between the

robots. In the case of rc o re r rpe rc, the repulsion force is

dependent on the mutual distance. Then, taking the summa-

tion of the mutual repulsion force, robot i defines collective

repulsion force by:

ai( t) =

Np = i

aip (4)

where N is the number of the robots. The charged swarm

robot is described in equations (5) and (6)

FIGURE 6 Visualization of obstacle-filled environments used forexperiments.

Obstacles

(c) (d)

(a) (b)

FIGURE 7 Odor Source Localization in the Advection-Diffusion Odor Model with a Small Meander Feature.

(a)

(b)

(c)

Source Declaration

Can Recover fromTrap in Local Maximum

n = 0 n = 100

Finding the Plume Tracing the Plume Tracing the Plume


n = 200 n = 499

Finding the Plume Tracing the Plume Tracing the Plume

n = 200 n = 445n = 0 n = 100

Source Declaration

Finding the Plume Tracing the Plume Tracing the Plume Tracing the Plume


n = 0 n = 100 n = 200 n = 1,000



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Vi( t) = (Vi( t 1)+ c1 rand()(p i( t 1) x i( t 1))

+ c2Rand()(pg( t 1) x i( t 1)))+ ai( t) (5)

x i( t) = x i( t 1)+Vi( t) (6)

where, the first part of eq. (5) is responsible for finding and

convergence to the optimal solution, while the second part

maintains diversity of the swarm distribution and prevents

robots from being trapped in a local maximum. Also, if all

robots are set to the neutral, Charged PSO (CPSO) is reduced

to the standard PSO, as described in eq. (1) and (2). The con-

ceptual idea of Charged PSO is shown in Figure 5.

IV. Implementation Framework

The odor source localization problem in dynamic environ-

ments is related to several issues from biology, physical chem-

istry, engineering and robotics. This paper proposes a

comprehensive approach to offer a sound technical basis for

odor source localization in a dynamic environment.

A. Environment

As an odor source distribution model, the Odor Gaussian

Distribution model has been adopted for previous work

[8], [9], [28], [29]. In this paper, we adopted an extended

Advection-Diffusion odor model by Farrell et al. [30]

because of its efficiency. It represents time-averaged results

for measurement of the actual plume, including chemical

diffusion and advective transportation. In addition, the

Advection-Diffusion odor model has a key factor to

approximate the meandering nature of the plume, in

that the model is sinuous.

The Advection-Diffusion model is composed of a large

number of advected and dispersed filaments. Given a large

number of filaments, the overall instantaneous concentration

at xo = (x, y) is the sum of the concentrations at that loca-

tion contributed by each filament:

C(xo, to) =

M

t=1

Ci(xo, to) (7)

FIGURE 8 Odor Source Localization in the Advection-Diffusion Odor Model with a Small Meander Function.

(a)

(b)

(c)

Finding the Plume Tracing the Plume

Trap in Local Maximum Trap in Local Maximum

t = 0 t = 100 t = 200 t = 1,000


Tracing the Plume Tracing the Plume

t = 0

Tracing the Plume Tracing the PlumeFinding the Plume Source Declaration

t = 200 t = 485t = 100

S

Can Recover fromTrap in Local Maximum

Source DeclarationTracing the Plume Tracing the PlumeFinding the Plume


t = 200 t = 564t = 100t = 0


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where C is the concentration of the plume (molecules/cm3), tois the number of iterations, and M is the number of filaments

currently being simulated.

The Advection-Diffusion gas concentration at the location

xo due to the i-th filaments is expressed by:

Ci(xo, to) = q83

exp r2i( to)R2i( to)

(8)

ri( to) = |xo p i( to)| (9)

where q is the amount of odor released, Ri is the parameter

controlling the size of the i-th filament; and Pi is changing

positions of the i-th filament. (For further explanation on this

model, see [30], section two and three.)

This model generates plumes that meander; in addition, the

meander is coherent with the flow fields in the sense that

downwind odor distribution from the source is the result of

advection by the flow. Therefore, we extend the original

equations from [30] to incorporate the obstacles in the envi-ronment. As a result, the environment becomes more realistic

and complicated as shown in Figure 6.

B. Robot Behavior

The gas source localization algorithm used in this work can be

divided into three subtasks: plume finding, plume traversal and

source declaration. Random search is employed until one robot

encounters the plume. After finding the plume, the second task

of the plume traversal proceeds. Particle Swarm concept will be

applied to following the cues determined from the sensed gas

distribution toward the source. The last task is the source decla-

ration based on the certainty that the gas source has been found.

If a robot senses the gas density that is beyond a certain thresholdvalue, it means that the gas source location is specified; and

hence, the searching behavior is termi-

nated. Moreover, the search is terminat-

ed if the swarm robots fail to localize the

odor source by the maximum iteration

time step.

To ensure that the performance of

proposed strategies is applicable to the

hardware experiments, the simulation

must contain the key features of the

hardware setup. Firstly, the robot has

a maximum velocity at which it can

move. Hence, the value of velocityvector can be restricted to the range

[Vmax,Vmax]. In this simulation,the maximum velocity is set to 0.05

(m/s), by following definition:

Vi( t) = min(Vi( t),Vmax) (10)

Secondly, in order to incorporate a

collision avoidance mechanism,

which is not considered in the standard PSO algorithm, we

assume that infrared sensors are equipped on each robot.

Then the parameters of sensor noise and threshold value are

added to model sensor responses. Assume that iteration time

tof the robot in eq. (1) to (6) and iteration time to in eq. (7)

to (9) is different time step resolution. Time correlation

between time step t and time step to is explained as follow:

The time scale of t has higher resolution than that of time

step to and count up is represented as:

to + 1 = to + t (11)

t is the interval time step to in terms of time step t. Hence;

to is represented with tby:

to = t

t

(12)

where [X] is the Gausss symbol. The sensor response is

defined by:

S( t) =C

t

t

+ e( t) IfC > 0 Otherwise

(13)

where S is the sensors response, C is the gas concentration, e

is the random sensor noise with e C, and is sensorsthreshold.

Finally, the basic concept of PSO algorithm uses a

common assumption, that all robots have accurate GPS

that give the robot its global location and no error

model is used for the position. These errors should be

modeled as well to provide a more realistic situation.For this reason, a random position error sensor was

FIGURE 9 Average convergence time of CPSO and DR PSO, given a dynamic small meander feature.

Comparison Between Charged and DR PSO to Find the Odor Source

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Charged PSO

109

8

7

6 610

1418

22Area[M

M]

Numbero

fRobots

[N]

NumberofIterations(t)

DR PSO


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added, as defined by:

xi( t) = (xi( t 1)+Vi( t))+De rror (14)

De rror =

xe rror ye rror

(15)

xe rror = rand()

RAN D MAX 100RE (16)

ye rror =

rand()

RAN D MAX

100

RE (17)

where RE is the range of error, and xe rror = ye rror is an error

position.

C. Experimental Results from a Dynamic, Obstacle-Free

Environment

The Advection-Diffusion model has a meander feature

that is generated out of small meander and large meander

(extreme changing). Figure 7 shows the visualization for

odor source localization in an Advection-Diffusion odor

model with small meander, while Figure 8 shows the case

with a large meander. A standard PSO cannot solve the

problem in dynamic environment as shown in Figure 7(a)

and in Figure 8(a). The robots were trapped in the local

maximum area due to the loss of diversity of the spatial dis-

tribution function.

Experimental results of DR PSO are shown in Figures

7(b) and 8(b). The change

detection function is used for

monitoring the global best

information pg. Ifpg is not

changed for 20 iterations,

there is a possible optimum

change and the value ofglobal best will be reinitial-

ized to zero (global best =

0). Therefore, the random

spread mechanism of posi-

tional distribution is applied

when a change occurs. All

robots spread for 10 steps to

cope with the changes, and

then robots recover from the

local maximum.

The effect of re-initializa-

tion of the global best and

spreading implies loss of infor-mation gathered during the

search thus far. As an alterna-

tive adaptation, the CPSO

approach is introduced. Exper-

imental results of the CPSO

are shown in Figures 7(c) and

8(c). Because they maintain

diversity of positional distribu-

tion, the robots escape from

being trapped in local maxi-

mum, even in large meander

simulations.

For more detailed analysis,the matrix performance

index, which represents

important parameters for

analysis is plotted. From previ-

ous results [8][10], the num-

ber of robots and the width of

the area with respect to the

iteration step to find the odor

source localization is important.FIGURE 10 Comparison of performance according to the number of robots, across 25 runs. Error barsindicate standard deviation and lower values indicate better performance.

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Interval-Confide

nce(t)

6 7 8 9 10

Area (MM)

Charged PSODR PSO

6 Robots

(a)

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Interval-Confide

nce(t)

6 7 8 9 10

Area (MM)

10 Robots

(b)

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Interval-Confidence(t)

6 7 8 9 10

Area (MM)

14 Robots

(c)

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Interval-Confid

ence(t)

6 7 8 9 10

Area (MM)

18 Robots

(d)

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Interval-Confid

ence(t)

6 7 8 9 10Area (MM)

22 Robots

(e)

Charged PSODR PSO

Charged PSODR PSO

Charged PSODR PSO

Charged PSODR PSO


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The results of the PSO and the change in the plume

are defined in the parameters values shown in Table 1

[30]. Figure 9 shows results from the matrix performance

index within the small meander environments. Figure 9 also

concludes that CPSO is more has a better convergence time

for finding an odor source location that the DR PSO. The

standard deviation and confidence limits

of the results from the CPSO and DR

PSO analyses were compared and are

demonstrated in Figure 10.

From the comparison between the

CPSO and DR PSO methods given a

dynamic small meander feature in Fig-ure 1, increasing the number of robots

not only increases the performance of

both CPSO and DR PSO results, but it

also increases the stability (decreases the

standard deviation) of the results, espe-

cially for the CPSO. The figure demon-

strates the scalability of the algorithm with respect to the

problem domains. The performance of both algorithms

(shown in Figures 9 and 10) are not satisfactory when a

using small number of robots. These results suggest that at

least 10 or more robots should be employed in order to

obtain satisfactory results.

The matrix performance index for the large meander envi-ronment is shown in Figure 11. Given a large meander feature

(see Figure 11), the results were similar

to those of a small meander feature

(Figure 9). However, the performance

is worse compared to those of small

meander environment. On the other

hand, the results from both the small

and large meander environments show

that the CPSO produced better results

than DR PSO.

D. Experimental Results

for a Dynamic,Obstacle-Filled Environment

The discussion above was concentrated

on odor source localization in an obsta-

cle-free environment. However, a more

realistic problem setting requires the

presence of obstacles that affect the dif-

fusion of odor distribution and robot

behaviors during exploration. In the real

world, the odor distribution changes

over time and has multiple peaks, especially in obstacle-filled

environments. For this reason, we extended the original equa-

tions from Farrell et al [30] to incorporate influences due to

obstacles.

In order to analyze the performance of our comprehensive

algorithm within an obstacle-filled environment, we conduct-

ed simulations under various scenarios. Three scenario envi-

ronments were tested: 1) A scenario with no obstacles, 2) A

scenario containing two obstacles, and 3) a scenario containing

five obstacles. (See Figure 6Note that we did not use the

environment containing 10 obstacles shown in this figure.)

A collision avoidance function was introduced to control

the velocity of the robots in an obstacle-filled environment.Again, DR PSO and CPSO algorithms results were calculat-

FIGURE 11 Average convergence time of CPSO and DR PSO, given a dynamic large meander feature.

Comparison Between Charged and DR PSO to Find the Odor Source

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Charged PSO

109

8

76 6

1014

1822

Area[MM]

Numbero

fRobots

[N]

Number

ofIterations(t)

DR PSO

DETECT RESPOND TIME-SET CONVERGENCE MAX.

c1, c2 FUNCTION FUNCTION ROBOTS r core rlimit Q p(t) VALUE ITERATIONS

2 0.5 20 ITERATIONS 10 STEPS 6,10,14,18,22 0.5 M 1 M 1 COULOMB 10 STEPS 200 PPM 3600 STEPS

TABLE 1 MPSO parameters uses for all experiments.

Nevertheless the main problem with standard PSO

employed in dynamic optimization problems is that PSO

will eventually converge to an optimum; and looses the

diversity necessary for efficient exploration of the searchspace, and then consequently weaken the adaptability to

a change in the environment when such a change occurs

as shown in Figure 1.


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ed, as shown in Figure 13. In addition, the average conver-

gence time for a dynamic change of the environment is plot-

ted, as shown in Figure 14. Figure 14 demonstrated that the

CPSO results are superior to DR PSO, especially when the

number of the robots is greater than 10. This result is similar

to the comparison of CPSO and DR PSO given previously,

leading to the conclusion that CPSO is more powerful com-

pared to DR PSO.

For further analysis of the CPSO algorithm, the effects

of robot positioning and odor sensing error were investi-

gated. Table 2 shows the average convergence time in the

case of a dynamic change of the environment. Fourteen

robots were employed in an environment containing two

obstacles environment. From Table 2, the influence of

position and odor sensing error causes only a slight decline

of the performance. The positioning error of 50 (cm) is a

realistic assumption when considering the dimension of the

robot as 10 [cm].

V. Extension with Wind Utilization

In this section, the integrat ion of chemotaxis and

anemotaxis properties to the PSO is introduced. Again,

chemotaxis causes the Modified PSO robots to follow a

local gradient of the chemical concentration, while an

anemotaxis-driven PSO measures the direction of the

fluids velocity and navigates upstream in the plume to

find the odor source. This methodology is well known

as odor-gated rheotaxis (OGR) since it is employed by

animals to find food.

The logic of OGR is

clear. If an agent senses a

plume, the mean flow of

that plume must be bearing

chemicals from the source ofthe plume toward the agent;

and, therefore, a movement

against the mean flow will

reduce the agents distance

from the source. If the agent

looses contact with a previ-

ously detected plume during

its navigation upstream, the

agent may overshoot the

source. If he has lost contact

with the plume, the agent

moves back and forth across

the path on which he knewthe flow was located to re-

contact the plume. This

back and forth movement is

termed casting and is a typi-

cal behavior of individualis-

t ic animal s such as the

American Lobster. In Parti-

cle Swarm Optimization,

the algorithm not only

shares individualistic infor-

mation but also shares social

information. This following

section details the adaptationand implementat ion of

OGR into the MPSO.

A. Conceptual Idea

As explained in Eq. (1) and

(2) earlier, unless the posi-

tion and velocity are updat-

ed in the PSO algorithm,

there is no guarantee theFIGURE 12 Comparison of performance according to the number of robots, across 25 runs. Error barsindicate standard deviation and lower values indicate better performance.

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

06 7 8 9 10

Area (MM)

(a)

6 Robots

Interval-Confidenc

e(t)

6 7 8 9 10Area (MM)

(c)

14 Robots

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

06 7 8 9 10

Area (MM)

(b)

10 Robots

Interval-Confidenc

e(t)

4,000

3,500

3,000

2,5002,000

1,500

1,000

500

0

Interval-Confide

nce(t)

4,000

3,500

3,000

2,5002,000

1,500

1,000

500

06 7 8 9 10

Area (MM)

(d)

18 Robots

Interval-Confide

nce(t)

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

06 7 8 9 10

Area (MM)

(e)

22 Robots


Charged PSODR PSO

Charged PSODR PSO

Charged PSODR PSO

Charged PSODR PSO

Charged PSODR PSO


11/15

robot direction will follow the

plume upstream to the source. To

combat this issue we utilized wind

information.

Assume the velocity from the

basic PSO becomes an intermediate

velocity (Vi( t)) from which the

robots can know the direction of

the wind (W( t)) at every step in

time. Gas is emitted from the

source of a coordinate system (x, y)

as in Figure 15, where the x-axis is

taken as the downwind direction.

The movement of the robot can be

controlled by analyzing the angle

( ) between the intermediate

velocity vector of the robot and

the wind direction vector. Note

that the angle is a relative direc-

tion, it s mean depends on thedirection of the wind at this time

step. (In Figure 15, the angle

between x-axis and wind direction

is zero). With this concept, the

robot movement not only will follow

the gradient of the chemical concentra-

tion but also will follow the direction

upstream of the wind. As a more

detailed explanation, let us reformulate

Vi( t) and W( t) as vectors defined as

follows:

V

i( t) = vxex + vy

ey (18)

W( t) = wxex + wyey (19)

The angle of the two vectors Vi( t) and

W( t) in two-dimensional space becomes

an inner product and is defined as:

= cos1

Vi( t) W( t)

Vi ( t)W( t)

(20)

From Figure 15 and Eq. 1820, we

have many variables to control the veloci-

ty Vi( t) of the robot. We will explain

two implementations of using the winddirection in the MPSO.

B. Implementation I:

Used Forbidden Area

In wind utilization implementation I, we let the angle in Eq.

20 describe a forbidden area. The forbidden area represents an

area where the robots have high likelihood of going the wrong

direction (i.e. the robot direction will not follow the upstream

to the source within this area). If the angle ( ) is inside the for-

FIGURE 14 Average convergence time in an obstacle-filled environment.

Comparison Between Charged and DR PSO in Obstacle Environment

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Charged PSO

10

2

0 610

1418

22NumberofObstacles Numbero

fRobots

[N]


DR PSO

FIGURE 13 Proposed approaches for odor source localization in an Advection-Diffusion odormodel with two obstacles.

(a)

(b)

Finding the Plume Tracing the Plume Source Declaration

Finding the Plume Tracing the Plume Source Declaration

ODOR SENSOR ERROR (ppm)POSITION ERROR (cm) 0 0.2 1

0 344 104 380 160 392 13650 544 143 574 151 625 331100 825 221 890 101 1025 2331

TABLE 2 Time development of success rate in obstacleenvironment used CPSO with employed uncertain sensorparameters. (Repeated 25 times)



12/15


bidden area, there must be some action

taken to avoid this area. In this simulation,

for simplicity reasons, the action taken is to

terminate the robot (i.e. let V i( t) = 0).

Otherwise, the intermediate velocity of

robot (Vi( t)) will become the velocity of

the robots (Vi( t)). The conceptual idea of

this implementation, with a different for-

bidden area is shown in Figure 16.

The modified PSO with Wind Uti-

lization I (WUI) concept is described

from Eq. 2123. (Other parameters still

follow the basic PSO concept parameters.)

Vi( t) = (Vi( t 1) + c1 rand()(p i( t 1) x i( t 1))

+ c2 rand()(pg( t 1) x i( t 1))) (21)

V i( t) =

0 if < |forbidden|Vi( t) Otherwise

(22)

x i( t) = x i( t 1) +V i( t) (23)

In Figure 16, the angle between the x-axis and the down-

wind direction is zero. If there is any angle between the x-axis

and the downwind direction, the algorithm adapts automati-

cally by comparing the relative angle between vectors Vi( t)

andW( t).

C. Implementation II: Using the () Parameter

The weakness of implementation of Wind Utilization I is

that it needs tuning of the forbidden area parameter. Forimplementation, we use the control-

ling parameter to decide the

velocity of the robot. After getting

the intermediate velocity of the

robot, Vi( t), the Wind Utilization

II (WUII) algorithm will calculate

the angle ( ) as mentioned in Eq. 20.

Then the controlling parameter, ,

is calculated. The continuation func-

tion for the controlling parameteris described as follows:

(W( t),Vi( t))=

1

2(1(W( t),Vi( t))) (24)

where the relation of the angle and

the controlling parameter are

shown in Figure 17.

The modified PSO with Wind

Utilization II (WUII) concept is

FIGURE 15 Modified particle swarm optimization with wind utiliza-

tion concept.

(0,0) x

y

W(t)

V*i(t)

xi(t)

Odor Source

FIGURE 16 Utilization of the wind for a forbidden area (note x-axis is taken as the downwinddirection).

Forbidden Areafor Observe Robot

(0,0) x

W(t)

V*i(t)

y

(a)

(0,0) x

W(t)

y

V*i(t)

(b)

Forbidden

Forbidden

Forbidden

Forbidden

Forbidden Areafor Observe Robot

However, if the whole population of robot has already

converged to a small area, it might be difficult to cope

with the extreme change. Therefore, a diversity extension

mechanism of the positional distribution is investigated

when a change is detected. For simplicity, all robotsare assumed to spread at a certain step to cope

with the changes.


13/15


described from eq. (25) to eq. (27):

Vi( t) = (V i( t 1) + c1 rand()(p i( t 1) x i( t 1))

+ c2Rand()(pg( t 1) xi( t 1))) (25)

Vi( t) = Vi( t) (26)

The result the of the algorithm using the forbidden area func-

tion |forbidden | 45 compared to the results of using CPSO

are shown in Figure 19. In Figure 19, the results intersect. This is

partly due to a difference the gap space between obstacles, whichdepends on the number of obstacles in the environment. For an

environment with only two obstacles, the results for the CPSO

and WUI algorithms were very similar. However, for and envi-

ronment with five to ten obstacles (a complex environment), the

WUI-45 is obviously superior compared to the CPSO algorithm.

The weakness of implementing Wind Utilization I, is the

need for tuning the forbidden area parameter (i.e., tuning

from |forbidden | 30, |forbidden | 45

, |forbidden| 60 ). If

the robot stays in the area |forbidden| 45 the results are

promising. For implementation, we use the controlling

parameter to decide the velocity of the robot. Then we

compared the results with the CPSO algorithm, as shown inFigure 20. In Figure 20, the results again intersect. For an

environment with only two obstacles, the

results for the CPSO and WUI algorithms

were very similar. However, for and envi-

ronment with five to ten obstacles (a com-

plex environment), the WUII is superior

compared to the CPSO.

The results for WUI-45 and WUII

were similar. For more detailed analysis, we

compared the two analyses as shown in

Figures. 21 and 22. (Figure 21 is for a five-

obstacle environment and Figure 22 is for a

ten-obstacle environment.)Finally, the effect on positioning and

odor sensing error for the robots was inves-

tigated. Table 3 shows the average conver-

gence time in the case of a dynamic change

of the environment for the WUII algo-

rithm. Fourteen robots were employed

with two obstacles in the environment.

The WUII results in Table 3 were similar

to those of the CPSO given in Table 2,

FIGURE 17 Continues the function for controlling the velocity of the

robots.

1

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

10 /2 3/2 2

Plot of Controlling Parameter Compare with Angle

2

Controlling

Parameter

Angle

FIGURE 18 Conceptual idea wind utilization with () parameter.

(0,0) x

y

= 90

W(t)

Vi*(t)

= 90

(0,0) x

y

W(t)

Vi(t) = 0.5Vi*(t)

Vi(t) = 0.707Vi*(t)

(0,0) x

y

W(t)

Vi*(t)

= 135

(0,0) x

y

W(t)

= 135

(a)

(b)

FIGURE 19 Average convergence time in an obstacle environment, given the algorithmWind Utilization I.

Comparison Between Charged PSO and Wind Utilization I (Angle = 45)

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Charged PSO

10

5

20 6

10

1418

22NumberofObstacles Numbero

fRobots

[N]


WUI-45


14/15


showing that the influence of position

and odor sensing error cause only a slight

decline in the performance.

VI. Conclusions

The PSO was implemented for control-

ling autonomous robots to search for an

odor source in dynamic, obstacle-filled

environments. When comparing CPSO

and DR PSO results, the CPSO gave

better results for the convergence time to

find an odor source location. A wind-uti-

lization function for OGR was also

implanted with the CPSO algorithm and

compared in the WUI-45 and WU-II

analyses. Both these analyses WUI-45 and

WUII showed promising results. Further-

more, the WUII algorithm, which uses

the parameter for controlling the

velocity of the robot, had success evenwithout a tuning parameter for noise and

variable sensor parameters.

Acknowledgement

The authors are grateful to Prof. J. A. Farrell

from the University of California, Riverside,

U.S.A., for his support in advanced turbulent-

environment source-code.

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Another popular biomimetic approach is anemotaxis-

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ODOR SENSOR ERROR (ppm)

POSITION ERROR (cm) 0 0.2 1

0 644 179 794 297 894 199

50 984 511 1071 814 1100 714

100 1150 514 1210 712 1325 613

TABLE 3 Time development of success rate in obstacleenvironment used WUII with employed uncertain sensorparameters. (Repeated 25 times)

comp int 10a particle swarm opt based robot for odor control

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