A New Model for Solving the Simultaneous Object Collecting and

Shepherding Problem in Flocking Robots

Ellips Masehian and Mitra Royan

Industrial Engineering Department, Tarbiat Modares University, Tehran, Iran

Keywords: Robot Flocking Systems, Shepherding, Object Collecting, Fuzzy Expert System, Obstacle Avoidance.

Abstract: Shepherding behavior is a class of collective behaviors in flocking systems which requires that a swarm of

mobile robots enter an area populated with known or unknown obstacles, collect a flock of static or dynamic

particles (objects), and guide them safely to a predefined goal position. Applications of this behavior are in

sheep or duck shepherding and fishing. In this paper, a new algorithmic model is developed for online for-

mation control, decision making, behavior selection, and motion planning of a team of homogeneous and

anonymous (no leader and follower) flocking robots which simultaneously perform object collecting and

shepherding tasks. The model’s architecture is enriched with various complex flocking actions such as flock

deformation, flock split and merge, flock expansion, and flock obstacle avoidance. Contributions of this pa-

per include (i) defining a new class of problems for flocking robots called Simultaneous Object Collecting

and Shepherding (SOCS) problem, (ii) incorporating online obstacle sensing and avoidance methods in the

flocking behavior, and (iii) developing a fuzzy expert system for determining the strategy of environment

exploration. The fuzzy inference engine provides an effective way to minimize the time spent on collecting

objects while maximizing the gain obtained by object collection, in a way that the flock’s formation and in-

tegrity is maintained. The proposed model was implemented on a number of simulations and produced ra-

tional and satisfactory results.

1 INTRODUCTION

Swarm robotics is an interesting branch of artificial

intelligence, which is inspired from natural behav-

iors of bees, ants, fish, birds, etc. Flocking, as a

basic collective behavior in swarm robotic systems,

has being studied for a decade. In general, flocking

is a natural phenomenon where a group of animals

move together as a single entity. The motion of

flocking robots is a result of integrated actions of all

members in the group, such that each member acts

based on a local perception of its surrounding.

Reynolds (1987) proposed the following three

fundamental rules for simulating flocking and herd-

ing behaviors:

Separation: when flock members get very close to

each other (closer than a ‘repulsion range’), they

must move away each other via a repulsive force. As

a result, sufficient free space around each member is

guaranteed.

Alignment: each member should be moving along

the general direction of its neighboring members.

Cohesion: members should move toward the center

of its local neighbors. As a result, they stay close to

the group, until they sense repulsive forces.

The logic behind these rules is that while each indi-

vidual follows relative simple rules, when taken as a

whole, they move as an organized group. Brett

(2009) presented many applications for flocking

behaviors, like mobile sensor network, surveillance,

control and covering problems, or transporting large

objects. The whole group tries to adjust its velocity

and align with other agents in the flock, while main-

taining the predetermined pattern and avoiding ob-

stacle collisions, and move toward the goal while

trying to minimize collisions between the members

of the flock.

There are varieties of problems in the literature

that require and utilize flocking as a behavior of

swarm robots. Many problems are demonstrated in

different environments which may be totally un-

known or partially known to the group. Some of

them consider leader–follower models, where the

flock leader’s velocity may or may not change dur-

ing the task. The way the robots communicate with

each other is important for the flock’s successful

Masehian E. and Royan M..

A New Model for Solving the Simultaneous Object Collecting and Shepherding Problem in Flocking Robots.

DOI: 10.5220/0004161600960105

In Proceedings of the 4th International Joint Conference on Computational Intelligence (ECTA-2012), pages 96-105

ISBN: 978-989-8565-33-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

task execution. Generally, they have a local commu-

nication and should enter the environment, obtain

information about the surrounding, and update and

share their acquired information.

In the following we categorize the main ap-

proaches of solving flocking problems in free space

or in presence of multiple obstacles:

Leader–follower Methods: In Leader-Follower

approaches, one robot assumes the leader role and

the rest of the flock follows it. The leaders use a

tracking strategy to lead the flock toward the desti-

nation. In general, one agent acts as a group leader

and the others just follow the separation, alignment,

and cohesion rules, resulting in leader following

(e.g., Xiong et al. (2008)).

Roadmap–based Methods: Searching and moving

toward the goal in this type of flocking problems is

accomplished based on the global information and the

roadmap of the environment imposed on the system.

Bayazit et al. (2002) proposed three distinct group

behaviors: homing, exploring and shepherding, that

exploit global knowledge of the environment with the

use of medial axis probabilistic roadmap.

Control Theory–based Methods: In this approach,

each robot has to follow a certain control theory law

to converge to a stable state. These control laws can

be used to coordinate the motion of each flock

member that is capable of local sensing and commu-

nication, and can be related to both kinematics and

dynamics of robots (e.g., Sharma et al. (2009) and

Navarro et al. (2008)).

Fault Tolerant Methods: These types of methods

assume that the flock there is a possibility of a faulty

robot to fail during a task execution such that the

crash can be either permanent, or temporary and

recoverable in future. Also, there is a model in lead-

er-follower flocks when the leader crashes and the

group choose another leader to guide the flock.

1.1 Shepherding

Shepherding is an interesting flocking behavior: it is

a cooperative task of controlling a group of agents

by one or more groups of agents via employing

repulsive forces. In the literature there are single and

multiple shepherd variations for the shepherding

behavior, of which the multi robot type can be

viewed as a kind of task manipulation that has appli-

cations more than just herding a group of animals.

Brett (2009) proposed different cooperative ap-

plications for shepherding behaviors like collecting

oil spilt from oil tankers, keeping animals off of

airport runways, and keeping people from dangerous

areas such as unsafe waters, construction zones or

other restricted areas. In spite of this, shepherding

has received little attention up to now, and there are

many open problems to be worked in future.

In the literature, shepherding has been used

merely for controlling and directing a number of

known objects toward a goal, sometimes in presence

of obstacles. By considering the influence of the

shepherd’s (robots) motion on the flock (objects),

the flock can be prevented from scattering and can

be controlled easier. Christopher et al. (2010)

showed in the robot sheepdog project how a robotic

system that gathers a flock of ducks in a circular

arena based on the potential field algorithm is used

to generate movements for each duck and maneuver

them safely to a predetermined goal position. Garrell

et al. (2009) proposed a new approach for guiding

people in open areas of urban settings by using mul-

tiple robots acting in a cooperative way.

2 THE SOCS PROBLEM

In all of the shepherding-related researches it is

assumed that the collectible objects (particles), as

well as workspace obstacles, are fully known. How-

ever, in some real-world applications like fishing

there is no information about the number and distri-

bution of collectible objects (e.g. fish). Information

about obstacles is also missing when operating in

unknown environments. Therefore, the flock must

identify and collect objects, while simultaneously

shepherding them toward a goal region.

In this paper we propose a new class of problems

called “Simultaneous Object Collecting and Shep-

herding (SOCS)” for flocking robots. The SOCS

problem has some real-world applications, such as

collecting distributed mines in an unsafe area, col-

lecting oil spills or trashes off the sea, casting a fish

net and directing the hunted fish toward the ship (an

instance of 3D space problem).

In offline mode, when there exists a full

knowledge about the workspace (including objects

and obstacles) before the robots start their task exe-

cution, the SOCS problem is analogous to the Trav-

eling Salesman Problem (TSP), in which a salesman

starts his trip from a city, visits each and every city

he plans to visit only once, and return to his starting

city. Mathematically, the TSP is about finding a

Hamiltonian tour on a given graph, which is an NP-

hard problem, meaning that the time to optimally

solve the problem grows exponentially as the num-

ber of cities increases. In fact, we can draw parallels

between cities in the TSP and objects (or clusters of

ANewModelforSolvingtheSimultaneousObjectCollectingandShepherdingProbleminFlockingRobots



objects) in the SOCS, and between the salesman in

the TSP and the flock in the SOCS. The only differ-

ence is that the flock should not necessarily return to

its starting position, and that the flock is not limited

to visit a certain location only once (this relaxation

still does not reduce the NP-hardness of the prob-

lem).

In online mode, however, the robots must ac-

quire environmental knowledge through their sen-

sors, both about collectible objects and obstacles,

and so the SOCS problem interweaves the shepherd-

ing task with sensor-based motion planning and

obstacle avoidance. In the SOCS problem we as-

sume that collecting each object by the flock has a

gain or reward, and the flock has a limited time to

execute its task. The ideal situation would be to

collect all objects and direct them to the goal point

in minimum time. Put differently:

The SOCS problem is to maximize the gain of

collecting objects by a flock while minimizing the

total time.

This problem, however, is NP-hard in both offline

and online modes, and so finding the optimal solu-

tion is not practical for large number of objects.

Instead, we have proposed a heuristic method to

overcome the complexity and produce a collective

behavior for gathering scattered objects and shep-

herding them toward the goal region in online mode.

The main contributions of this paper include:

(i) Defining a new class of problems for flocking

robots called the Simultaneous Object Collecting

and Shepherding (SOCS) problem,

(ii) Incorporating online obstacle sensing and avoid-

ance methods in the flocking behavior, and

(iii) Developing a fuzzy expert system for determin-

ing the strategy of environment exploration. The

fuzzy inference engine provides an effective way to

minimize the time spent on collecting objects while

maximizing the gain obtained by object collection,

in a way that the flock’s formation and integrity is

maintained.

The proposed model was implemented in a number

of simulations and produced rational and satisfactory

results.

3 OUTLINE OF THE PROPOSED

MODEL

Our proposed model for solving the online SOCS

problem is composed of two main ‘Exploration’ and

‘Exploitation’ behaviors, and two auxiliary ‘Fuzzy

Expert System’ and ‘Motion Planning’ modules.

The Exploration behavior is adopted when the

flock intends to explore the environment for collect-

ing objects. Here the main emphasis is on covering

the environment as much as possible and moving

toward regions with dense population of objects, as

temporary goals. On the other hand, the Exploitation

behavior is triggered when the flock has collected

sufficient number of objects, or the available time is

nearly over. In this case, the flock heads toward the

final goal and collects all objects on its way.

The Fuzzy Expert System Module is utilized for

deciding about where the flock should move to col-

lect more objects (hence more gain), and when to

stop collecting and move toward the final goal, such

that the task is finished within a time limit.

The Motion Planning Module implements the

Potential Fields method for helping the flock to

avoid obstacles locally, and move toward either the

final goal region or a temporary goal near a cluster

of collectible objects. The module also decides about

executing some complex actions like stretching,

shrinking, splitting and merging. In this way, the

flock becomes a deformable and coherent group,

which during its navigation in the environment, can

shrink or elongate to pass through narrow passages,

or split and merge when encountered with obstacles

or corridors (while retaining its connectivity and not

losing any collected object), and shepherd the ob-

jects toward the goal region.

The model’s assumptions are as follows:

1. The workspace is planar, bordered, and initially

unknown to the robots. It contains static polygonal

obstacles which should be avoided.

2. The robots are homogeneous, circular, and can

move in the workspace without kinodynamic con-

straints. They are equipped with range sensors for

identifying both obstacles within the range R

obs

(Figure 1) and particles within the range R

part

< R

obs

We also assume that there are no localization and

sensing errors.

3. The robots form a flock by taking on the shape of

a circular arc, with its open segment facing forward.

The flock’s integrity is maintained by regulating and

equalizing the robots’ velocities with each other. The

flock must finish its task within a time limit T

max

and

collect at least Q

min

particles.

4. The particles are small circular objects scattered

over the workspace, which may be fixed or moving.

Collecting a particle has a gain for the flock.

5. The goal region is known to the robots and once

the flock’s center lies inside that region the search is

terminated.

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Table 1 introduces some of the more important

variables and parameters of the model.

Figure 1: Identifying the surrounding obstacles through

range-finder sensors.

Table 1: Variables and parameters of the model.

Symbol Description

(t) Position vector of robots at time t

(t) Position vector of particles at time t

(t) Velocity vector of robots at time t

(t) Vector of particles velocities at time t

Q(t) Number of collected particles inside the flock at

time t

D(t) Distance between the flock’s center and the final

goal at time t

C(n) Capacity of the flock with n robots; n = 1, …, N

obs

Robots’ sensing range for detecting obstacles

part

Robots’ sensing range for detecting particles

Rmax

Maximum distance between two neighboring robots

for maintaining connectivity

Rmin

Minimum distance between two neighboring robots

for avoiding collision

Radius of the flock’s circular shape

Safety radius for particle p

Gain of collecting particle p

max

Upper bound of the allowable time interval

min

Lower bound of the allowable time interval

min

Minimum required number of collected particles

In the beginning, N robots reside in a Depot, and

an initial number of them (calculated based on the

parameters D

Rmax

and D

Rmin

) are selected to form the

flock by adjusting their positions on the circumfer-

ence of a circular arc with radius R

(Figure 2). The

arc’s angular span is between 180 and 270 degrees,

with its open segment facing toward the moving di-

rection. When the flock collects as much particles as

it can accommodate (i.e., C(n)), it checks the possibil-

ity (regarding time and cost) of an expansion by in-

corporating one or two robots settled in the depot. The

flock explores the workspace by being attracted to

areas with higher number of objects until either there

is no object left, or the available time is over. The

overall architecture of the model is shown in Figure 3.



Figure 2: Simultaneous object collecting and Shepherding:

The robots collect objects by trapping them inside their

arc-shaped flock and direct them toward the goal.

4 FLOCKING BEHAVIORS AND

ACTIONS

Our proposed flocking system has two basic behav-

iors: Exploration (covering the environment to find

as much particles as possible) and Exploitation

(moving toward the final goal). These techniques are

applied to the entire flock as an integrated shape.

Besides, other actions like traversing through narrow

passages, splitting, merging and deformation can

occur during the Exploration and Exploitation.

4.1 Exploration Behavior

In the Exploration behavior, each robot senses its

surrounding within the range R

part

and finds a num-

ber of particles around it. Then, all robots communi-

cate their obtained knowledge of environment, and

by integrating the whole knowledge, create a map of

the distribution of nearby particles. The sensed ob-

jects are then clustered into a few groups, and the

group with the most particles (and hence, the highest

gain) is marked for exploration. The center of this

cluster is fixed as a temporary goal and the flock

starts moving towards it. The flock’s motion is guid-

ed and obstacles are avoided using the Potential

Fields method (discussed in section 4.3). An area is

considered explored when the flock passes over it.

This collaborative effort of exploring the envi-

ronment is repeated from a temporary goal to anoth-

er until either there are no sensed but uncollected

particles left, or the flock cannot accommodate more

objects due to fullness of its capacity. The capacity

C(n) of a flock with n robots is determined based on

the safety radius of particles (S

), and the maximum

Flock

Particles

Goal

Depot



Obs

ANewModelforSolvingtheSimultaneousObjectCollectingandShepherdingProbleminFlockingRobots



Figure 3: The proposed architecture for solving the SOCS problem.

Motion Planning Module

Exploration Behavior

Exploitation Behavior

Set a temporary goal in

the nearest dense area

Is there an area

densely populated

with particles?

Calculate the nearest

obstacle

Yes

Fuzzy Expert System Module

Sensing the environment

and identifying obstacles

and particles

Robots move to a start

point and form a

circular flock

Does the flock face

a narrow passage?

Estimating the time to reach

the temporary goal

Estimating the current

distance to the final goal

Are there any

unused robots

in the depot?

Is there sufficient

space inside the

flock to collect

articles?

Executing the motion

planning module

Hunting particles in

the flock’s way

Moving toward the

final goal

Is the

temporary

oal

Calculate effective

potential forces

Make a move according to

the Potential felids

Start

Fuzzy inference engine

Set a temporary goal in

a random area

Moving toward the

temporary goal

Executing the motion

planning module

Hunting particles in

the flock’s way

Is the final

goal reached?

Stop

Calculating the number of

collected particles

Yes

Deformation

action

Expansion

action

Split/Merge

action

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and minimum allowable distance between the robots

Rmax

and D

Rmin

, respectively). If no objects are

marked for collection, a temporary goal is randomly

set in an unexplored area and the flock moves there,

while caging and shepherding all collected particles.

In case that the flock is too full to hunt another

particle, it invokes the Expansion action.

4.1.1 Expansion Action

As the flock gets larger, for preserving its connectiv-

ity and preventing the inner particles from escaping

from it, the robots should remain in a proper dis-

tance from their neighbors. If this is not possible due

to the outward pressure exerted by the inside parti-

cles, the flock needs to call for extra robots to join

the flock. Adding a robot to the flock, however,

takes time and cost which should be compared and

balanced with the gain which will possibly be ob-

tained by hunting more particles. Figure 4 shows a

schematic view of how new robots are joining the

flock after the flock’s robots move outwards and

form an expanded flock along a larger arc, making

room for the newcomers.

Figure 4: Expansion of the flock makes room for adding

more robots, and hence accommodating more particles.

4.2 Exploitation Behavior

Unlike the Exploration mode in which the flock does

not have any final destination and navigates through

the workspace to collect more and more objects, in

the Exploitation behavior the flock is attracted to-

ward the one and only final goal, which might be a

cage for ducks or a pier in fishing. Exploitation can

be viewed from two perspectives: (1) moving

straight to the goal after collecting a sufficient num-

ber of objects and approaching the time limit, and

(2) intensifying the search around ‘good’ areas, that

is, those with higher probability of having dense

particles. In such a case, the flock selects the closest

dense area and sets it as a temporary goal.

As it will be explained in section 5, the Fuzzy

Expert System module decides the proper time for

switching from the Exploration mode to the Exploi-

tation mode based on elapsed and available times

and the flock’s current distance to final goal region.

When the flock is in the Exploration mode but has

no space for hunting more particles (and there are no

robots left in the Depot for the Expansion action),

then Exploitation mode must start.

For both the Exploration and Exploitation behav-

iors of flock is guided toward its temporary or final

goal using the famous Potential Field method (Khat-

ib, 1986), as described below.

4.3 Motion Planning Module

The Motion Planning module is responsible for

guiding the flock from a point toward another point

such that no collision is occurred between any robot

and obstacle, and the traversed path is short, smooth,

and safe. This module is activated in both Explora-

tion and Exploitation behaviors, and is based on the

well-known Artificial Potential Fields method, pro-

posed by Khatib (1986). In this method, the robot is

directed toward the goal as if it is a particle moving

in a gradient vector field. Gradients can be intuitive-

ly viewed as forces acting on a positively charged

point-robot which is attracted to the negatively

charged goal. Obstacles also have a positive charge,

which forms repulsive forces to repel the robot away

from them.

Specifically, in our model, the sum of the follow-

ing three forces draws a robot in the flock toward the

goal while keeping it off from obstacles:

− Repulsions from the other robots,

− Repulsion from the closest detected obstacle,

− Repulsion from the particles inside the flock,

− Attraction toward the temporary or final goal.

The combination of repulsive and attractive forces

will hopefully direct the robot from the start location

to the goal location while avoiding obstacles. Vari-

ous applications of the Potential Fields approach in

coordinating a multi robot system are present in the

literature for many different tasks. For example, in

the collision avoidance problem, the group cohesion

property can be maintained using an artificial poten-

tial field that is dependent entirely on the relative

distances between the agents (Tanner et al., 2003).

As mentioned earlier, a circular arc pattern is ap-

Initial flock

Extended

flock

Two new robots are added

ANewModelforSolvingtheSimultaneousObjectCollectingandShepherdingProbleminFlockingRobots

101



plied for shepherding the collected particles: this

works well in workspaces with relatively large free

spaces. However, in cluttered environments with

narrow or maze-like passages, the flock might not

navigate easily, while keeping its full round shape.

As a matter of fact, a number of challenges have

been identified by researchers in recent works on

pattern formation: Varghese and McKee (2010)

showed that transformation of patterns is necessary

when a robotic swarm needs to react to obstacles in

the way of its motion, and presented a mathematical

model for swarm pattern formation based on the

foundations of the Complex Plane.

In order to properly react against the encountered

obstacles and passageways, the flock can launch two

effective actions: Deformation, and Split and Merge.

4.3.1 Deformation Action

Encountering narrow passages is a big challenge for

flocks. Although different group formations may be

used in relatively open areas, there are few shapes

suitable for passing through narrow regions, which

are generally shrunk along one axis and elongated

along the other axis (Figure 5). Also, in during Ex-

pansion action, the flock may encounter obstacles as

it expands, and so it has to deform. A reconfigura-

tion can be achieved by repositioning all or a few

agents in the pattern, which can lead to the defor-

mation of the pattern.

Care should be taken to maintain the maximum

and minimum distances between any two neighbor-

ing robots so that the flock is not disintegrated.



Figure 5: An example of a narrow passage: The flock’s

diameter is larger than the width of the passage and so

cannot enter it without deformation.

4.3.2 Split and Merge Action

According to the workspace and obstacles condi-

tions near and on the way of the flock, it may prefer

to split into two or more smaller flocks to be able to

detour an obstacles or pass through a narrow pas-

sage, and merge together afterwards, while trying

not to lose any collected particle (Figure 6).



(a) (b)



Figure 6: The flock faces two separate groups of dense

particles and decides to split: (a) The flock is splitting, (b)

the flock moves toward the particles in two small flocks,

5 FUZZY EXPERT SYSTEM

The overall objective of the proposed model is to

solve the SOCS problem in the online mode: that is,

maximizing the total gain (i.e., covering the whole

unknown workspace) while minimizing the total

completion time.

In order to successfully solve this problem, the

model must be able to make right decisions at the

global search level, that is, when to explore, and

when to exploit. This is done by implementing a

Fuzzy Expert System module. On the other hand,

local strategies are planned by the Motion Planning

module, by deciding how to avoid an obstacle and

when to undergo a deformation or a split and merge.

As it is obvious from the definition of the SOCS

problem, it has two independent conflicting objec-

tives: minimizing execution time and maximizing

object collecting gain (as shown in (1)), in which T

is the time of finishing the whole task and G

is the

gain of the particle p:



min max















(1)

In our proposed method, we assume a time interval

min

, T

max

] during which the flock is allowed to

execute and accomplish the collecting and shepherd-

Width of the

narrow passage

Average velocity

of the flock

Diameter

of the

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102

ing tasks, and also a required minimum number of

particles Q

min

to be collected by the flock. As a re-

sult, the flock must do its best to collect as much

particle as possible and reach the goal region before

spending a time more than the defined upper limit.

Naturally, the flock should choose areas with highest

number of objects (i.e. densest area).

For deciding when to abandon the Exploration

behavior the flock needs to estimate the time to

reach the goal region from its current position,

which can be done by calculating the distance D(t)

between the flock’s current average position

()tX

and the goal position X

Goal

via a simple straight line

heuristic, as in (2):

Goal R

() ()

ttXX

(2)

Given the velocity of the flock V

(t) and the remain-

ing time (T

max

– t), the flock can find out if it has

enough time to further explore the workspace by

visiting another temporary goal or it is time to move

directly toward the final goal. Actually, the critical

distance D

(t) is a distance that the robot can trav-

erse within the remaining time:





Rmax

() ()

ttTtV

(3)

Similarly, the flock must terminate the Exploration

behavior whenever it cannot collect more objects,

even after utilizing all its N robots in the Depot. That

is, when (3) holds, in which C(N) is maximum pos-

sible capacity.

Q(t) ≥ C(N), (4)

Since a robot in a formation must handle additional

problems such as avoiding collision with other

members of the flock and relying on usually-

incomplete sensory data to detect the obstacles’

locations, time and distance calculations in (2) and

(3) are not always exact and real. On the other hand,

a flock formation should be able to successfully

operate in a real-time world with lots of noisy data

and must deal with the uncertainties found in such

an environment. Consequently, in order to cope with

these problems and possible localization and sensing

errors, a fuzzy-based approach is adopted to make

decisions about the flock’s next behavior. This will

make the model more robust and responsive toward

unexpected variations in sensing or motion.

We define fuzzy membership functions for three

variables: (1) time, t; (2) number of collected objects

at time t, Q(t); (3) direct distance to the final goal,

D(t); respectively as μ

, μ

, and μ

, illustrated in

Figure 7. As can be seen, right parts of all these

functions tend to zero; this means that for example

when the time exceeds its upper limit, it is high time

to exploit the search toward the goal region, or when

the number of collected objects exceeds the maxi-

mum possible capacity, Exploration must end.

Figure 7: (a) Fuzzy membership functions for (a) Elapsed

time, (b) Flock’s distance to goal, (c) Quantity of particles.

Introducing fuzziness in decision making reduces

the risk of making wrong decisions in the presence

of incomplete perception or improperly-set parame-

ters and thresholds. A number of fuzzy rules can be

defined for integrating the above membership func-

tions and decision variables. A typical fuzzy rule

contains commonly used linguistic modifiers (like

low, medium, high) and has the following structure:

RULE R

IF Elapsed time is Low, AND

Collected quantity is Low, AND

Distance to the final goal is Large, AND

Distance to the nearest temporary goal is Low

THEN Behavior = Exploration

We can also blend the above fuzzy membership

functions into a single Fuzzy Decision criterion:









    



= min , ,

ti D i Q i

FD t D Q

tDQ

 

 

(5)

after which the behavior is determined by comparing

(

)

(

)

min

max

1−

0−

min

C(N)

1−

0−

0.7D

0.9D

1−

0−

0.5−

(

)

ANewModelforSolvingtheSimultaneousObjectCollectingandShepherdingProbleminFlockingRobots

103



the criterion’s value with a threshold α, as:



Exploitation if <

()=

Exploration if

Behavior t





(6)

6 SIMULATION

In order to assess the efficiency of the proposed

model in simultaneously collecting and shepherding

workspace objects we programmed it in Matlab

and

implemented on a number of simulations. The per-

formance measures were time, number of collected

particles, and the total gain of particles.

Figure 8 shows a typical input to the SOCS prob-

lem. There is a Depot with 11 robots at the lower

right corner, three polygonal obstacles and 64 parti-

cles scattered over the workspace. The obstacles and

particles are unknown to the robots, and the final

goal is located at the top center. Collecting a particle

has a gain of 3 points, and each second of runtime

exceeding the upper time limit has a 0.5 point penal-

ty. The T

max

was set to 400 seconds.

We used the PSO algorithm for simulating and

coordinating the movements of particles inside the

flock. The particles are dynamic and change their

position and speed over time. As the robots move,

they push the particles forward while preventing

them from leaving the flock. At each iteration the

particles try to adjust their velocities with the ‘best’

velocity among themselves so far, with movements

and positions of their neighbors, and with the aver-

age velocity of robots (Kennedy and Eberhart,

1995). The best direction is the one that has the

lowest deviation between the flock’s average direc-

tion of and direction of each particle.

Figure 9 shows the experimental result: the flock

moved from the Depot with 6 robots, sensed the

obstacles and detected and collected 37 particles,

with a gain of 111 points. The figure also reveals

that the flock selected 5 temporary goals before

exploiting toward the final goal region, and did not

use additional robots available in the Depot. The

total runtime was 412 seconds, about 3% longer than

the upper time limit, and for the same reason the

flock lost (412−400) × 0.5 = 6 points, making the

total gain equal to 111 − 6 = 105 points.

We could not find any model in the literature to

compare with our proposed model in online mode.

So we considered the TSP problem as a benchmark

to compare with our model in offline mode, i.e.,

assuming that the flock has complete information

about the obstacles and objects. On the other hand,

for the TSP formulation, the particles were clustered

into different groups and the center of mass of each

group was taken as a city (site). Also, in order to

implicitly consider the presence of obstacles, dis-

tances between cities were calculated based on their

geodesic distance, and the start and goal points were

added to the set of cities.



Figure 8: A sample workspace used for testing the model.



Figure 9: The traversed path and collected objects. Note

the partial perception of the obstacles through range-finder

sensors.

We solved a number of problems with different

workspaces and various numbers of clusters by both

the TSP and our model. As the results show in Table

2, the proposed model performs quite comparable to

the optimal solutions obtained by solving the mTSP

models.

Depot

goal

Start

IJCCI2012-InternationalJointConferenceonComputationalIntelligence

104

Table 2: Comparison of the TSP and proposed models.

Model

No. of

sites

Criteria

Path length

No. of collected

particles

No. of visited

sites

Proposed

11 30.69 28 out of 63 5

10 31.89 31 out of 60 7

7 21.54 26 out of 61 6

TSP

11 35.37 36 out of 63 7

10 28.32 20 out of 60 5

7 40.13 61 out of 61 7

7 CONCLUSIONS

In this paper, we have proposed a new class of prob-

lems called Simultaneous Object Collection and

Shepherding (SOCS), in which a flock of robots

must collect some objects and guide them to a goal

region. The problem is analogous to the Traveling

Salesman Problem which is NP-hard. We also in-

corporated online obstacle sensing and avoidance

methods in the flocking behavior, and proposed a

fuzzy expert system for determining the strategy of

environment exploration. The model is enriched

with a number of complex group actions like defor-

mation, expansion, split and merge. A potential

advantage of the proposed model is its ability in

adapting its behavior to a previously-unknown envi-

ronment and simultaneously performing collecting

and shepherding tasks.

Future works will focus on extension of the

model to dynamic environments where the obstacles

or even the goal are not static and their movements

are unpredictable over the time. Also we can consid-

er the situation in which the flock has the opportuni-

ty for discharging its contents in a depot and contin-

ue collecting more objects. Also, adding the physical

properties of the environment like steepness, rough-

ness, etc. which can affect the robots’ paths and

velocity adjustments can be interesting.

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ANewModelforSolvingtheSimultaneousObjectCollectingandShepherdingProbleminFlockingRobots

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