A Global Integrated Artificial Potential Field/Virtual Obstacles Path Planning Algorithm for Multi-Robot System Applications

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1163
A Global Integrated Artificial Potential Field/Virtual Obstacles Path
Planning Algorithm for Multi-Robot System Applications
Abdelrahman M. Hassan1, Catherine M. Elias1, Omar M. Shehata1 and Elsayed I. Morgan1
1 Multi-Robot Systems (MRS) Research Group, German University in Cairo, 5th Settlement New Cairo, 11432,
Cairo, Egypt
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - In this paper, a global off-line path planning
approach is implemented using an energy-based approach
Artificial Potential Field (APF) for Multi-Robot Systems
(MRSs). A 3-D potential map is created by using simplified
potential functions. Both attraction forces between therobots
and the goal, and repulsion forces to repel the robots from the
obstacles and each other, are calculated to generate the 3-D
map. The local minima problem is handled in this paper using
the Virtual Obstacles (VOs) approach. The robot path is
generated starting from the robot initial position to the goal
based on the generated 3D potential map tobefollowed by the
mobile robots. All simulations are done using MATLab and
Virtual Robot Experimental Platform(V-REP). OntheMATLab
side, the APF controller is implemented to build the map and
generate robots paths. The robots are controlled to track the
paths and visualized in the V-REP environment.
Key Words: Multi-Robot Systems, Path Planning,
Artificial Potential Field, V-REP, Local Minima, Virtual
Obstacles
1. INTRODUCTION
Nowadays, Multi-Robot Systems (MRSs) are one of the most
growing areas in Robotics. As result of the technology in our
life and the demand on robots in many tasks and
applications, the challenges of MRS are increasing in a rapid
way every day. Single-Robot Systems (SRSs) tasks are being
more complex and expensive by time that is why MRSs are a
necessity. MRSs added more applications and challenges to
the Robotics field such as pollution monitoring, surveillance
of buildings [1], warehouse management, forest fire
detection and more applications. They evenreplacedSRSsin
many applications as the robustness and reliability can be
increased with more thanonesingle robot[2].Area coverage
and exploration [3] is one of the main applications in
robotics field in general. It was first developed with SRSs.
Simultaneous Localization and Mapping (SLAM) is an
application for robots that they generate a map for the
surrounding environment by locating the obstacles and
represent them in a way that allow the robots to navigate
any uncovered areas [4]. There is advantage in Multi-Robot
team that will improve the positioning accuracy, as every
robot will be scanning or mapping specific area. By
integrating all the maps, there will be a main map for the
whole place [5]. Search and Rescue is another challenge of
MRSs. First, the robot search for an object with specific
characteristics. Then when any robot finds this object, it
sends signals for all other robots.All robotsstandaround the
object and they carry it to a specific goal. This can only be
done through a team of robots, since one robot cannot
handle the object if it is big and heavy [6]. Task Allocation
application is used commonly in robots rescue missions,
where the group of robots has a set of tasks or goals that
must be done. Some tasks need more than one robot and
some tasks can be handled by only one. In order to organize
these tasks for the robots team, the Task allocation problem
is handled [7], [8].
2. PATH PLANNING
Path Planning is the controller of the robot motion,soitisthe
most essential part of the robot program. It is the
determination of a free path starting from the robot position
to the targeted goal. The robot environment consists of three
modules, the robot itself, the goal and the obstacles in
between. Path Planning can be divided in two main
categories, global path planning and local path planning. In
global path planning, the environment of the robot is already
known with all obstacles and their locations. The terrain is
static that is why a map can be generated with the path for
the robot. On the other hand, in local path planning, the
environment is unknown for the robot and can be dynamic.
In that case, the robot must gather information about the
environment in real time, and then update its control laws to
achieve its goal [9].
Artificial Potential Field (APF) is one of the classical
approaches that are used to implement the path-planning
controller. In 1986, Khatib [21] introduced the first APF
approach for real-time obstacle avoidance problem for
manipulators and multi-robot systems. Rimon and
Koditschek adopted in 1992 [10] the APF in as an approach
forexact robot motion planning and control usingnavigation
functions instead of the potential functions to solve the local
minima problem. Then in 2000,GeandCui[11]describedthe
problem of non-reachable goals with obstacle nearby when
using APF using a new repulsive function to solve it. As an
extension for their work, the potential field approach was
proposed as obstacle avoidance methods for robots in
dynamic environments in [12] in 2002. In addition, in 2005,
the authors used queues and formation vertices, besides the

APF for controlling the formation of group of robots to
improve the flexibility of therobot formationandinthesame
time, the group can avoid the obstacles [13]. Another paper
conducted by Hsieh, Kumar and Chaimowicz in 2008
proposed a decentralized controller for shape generation
with swarm of mobile robots [14]. A paper conducted by
Nagy in 2009 to implement a controller for multi-agent
system using Genetic Algorithm (GA)tobuildapotentialfield
for unknown environments [15]. Saez-Pons, Alboul et. al. in
2010 [16] used the APF forcontrollingthegroupformationof
multi-robot system called (GUARDIANS). Then in 2012 [17],
Valbuena and Tanner suggested new control for differential
mobile robot navigation using APF based on navigation
functions, then a transformationforthemathematicalresults
was introduced to obtain real-time velocities to be tested on
real robot. Also, Hsieh, Kumar and Chaimowicz in 2008 [18]
proposed an APF algorithm for mobile manipulator control
using simplified potential functions. In [19] Rajvanshi,
Islamused et. al. used the APF for controllingmobilerobotsin
both staticanddynamicenvironmentsin2015usingArtificial
Goals approach to solve the local minima problem.Andinthe
same year, Ahmed, Abdalla and Abed [20] proposed Particle
Swarm Optimization (PSO) method to modify the potential
field method used, in order to solve the problem of local
minima and optimize the path resulted by it.
In this Paper, an offline (global) path-planning algorithm
based on a modifiedAPFapproachisproposedforthecontrol
of multi robot system in any cluttered static environment.
The local minima problem is handled using the virtual
obstacle approach. The modification of the APF is for
generating the shortest path for the robots. Simulations are
used to verify the proposed approach using MATLab and V-
REP simulators.
The rest of the paper is organized as follows: Section 3
introduces the APF graphically, mathematically, and
introduces the local minima problem. Section 4 has the
mathematical modeland introduces the V-REPenvironment.
Section 5 has the simulations results. Section 6 is the
conclusion, and finally, Section 7 suggests future
recommendations for further researches.
3. ARTIFITIAL POTENTIAL FIELD
The Artificial PotentialField (APF) is one of the classicalpath
planning approaches that is used in robotics. Itcanbeusedin
global and local path planning. It can be also used in dynamic
or static environments. The concept about APF is to find a
mathematical function to represent the energy of the system
based on the idea of physical rules in potential fields.
Potential functions assume the existence of repulsive and
attractive forces acting on the robot in its world. Using both
repulsive and attractive forces, a path for the robot can be
created to its destination. The attractive force is generated
between the robot andthegoal.Itisresponsibleforattracting
the robot to the goal. The repulsiveforceisbetweentherobot
and the obstacles. Its main functionisforavoidingthem.Both
forces are generated by mathematical functions that are
represented graphically by high and low areas in the robot
space.
The general APF equation as [11], [15], [19] and [21]
introduced is as follows
)()()( qUqUqU repatt  (1)
where )(qUatt is the attractive isfunction,and )(qUrep isthe
repulsion function. By summing both functionstogether,the
total potential function is generated to be used inthecontrol
of the robots.
Fig -1: Total Potential Function
3.1 Attraction Potential Function
The Attractive Potential Function is divided in two terms,
conical potential and Quadratic potential. The conical
potential is used when the robot is far away from the goal.
On the other hand, the quadratic potential is used when the
robot is near the goal. The reference thatwill define whether
the robot is far or near is the term
*
goald .
*
*
2**
2
),(
),(
)(
2
1
),(
),(
2
1
)(
goalgoal
goalgoal
goalgoalgoal
goal
att
dqqdif
dqqdif
dqqdd
qqd
qU











(2)
where q is the position variable, ),( goalqqd is the distance
function, and  is the scaling factor.
This function is representing the potential that affect the
robot while the force that will drive the robot to reach the
goal will be generated from the negative gradient of this
function.
)()( qUqF attatt  (3)
As
*
*
*
),(
),(
)(
)(
)(
)(
goalgoal
goalgoal
goal
goalgoal
goal
att
dqqdif
dqqdif
qqd
qqd
qq
qU










 

(4)
Moreover, in other works, Hargas et. al. [18] used another
simplified version of the potential function. This equation

has the position of the robot and the goal; X and
Y coordinates, as the equation parameters.
])()[(
2
1
),( 22
FinFinaatt yyxxKyxU  (5)
where x and y are the coordinatesofthecurrentposition
of the robot, Finx and Finy are the goal coordinates, and aK
is the scaling factor.
And the attractive force will be defined as

















)(),(
)(),(
),(
),(
Fina
att
ya
Fina
att
xa
att
yyK
y
U
yxf
xxK
x
U
yxf
yx
yxU
(6)
where ),( yxfxa , ),( yxfya are the attractiveforcesinthex
and y directions respectively.
3.2 Repulsive Potential Function
There is always one goal at a time for the robot but the
obstacles are more than one. That is why the repulsive
potential function consists of all the repulsive fields of every
obstacle exists in the environment. Every obstacle has a
specific limited region that hasa repulsivefield,sothatwhen
the robot comes in that region, it will be repelled from that
obstacle. The term that would define the region for every
obstacle is *
Q . And the repulsive field for only one obstacle
is
*
*2
*
)(
)(
0
)
1
)(
1
(
2
1
)(
QqDif
QqDif
QqDqU
i
i
irepi










(7)
where )(qD is the distance to the obstacle,  is thescaling
factor, and i represent the order number of the current
obstacle.
The repulsive force would be represented as
)()( qUqF ii reprep  (8)
And
*
*
2*
)(
)(
0
)(
)(
1
)
)(
11
(
QqDif
QqDifqD
qDqDQU
i
i
iirepi










(9)
The total repulsive function for n number of obstacles is


n
i
reprep qUqU i
1
)()( (10)
While the simplified function as [18] introduced in their
works is
22
)()(2
1
),(
obiobi
o
rep
yyxx
K
yxU i

 (11)
where x and y are the coordinates of the current
position of the robot, obix and obiy are thi theorderobstacle
coordinates, and oK is the scaling factor.
And the repulsive force is















y
U
yxf
x
U
yxf
yx
yxU
rep
ya
rep
xo
rep
),(
),(
),(
),(
(12)
3.3 Local Minima Problem
As most of the previous works like [10-13], [17] and [19,
20] mentioned, local minima problem is a serious problem
that faces the traditional APF that is implemented by
Equation 2 and 7. This problem is caused when there is a
cavity in the obstacle or when the goal, the robot and the
obstacle are in the same line. This will cause the robot to be
trapped in a local minimum point in the potential field.
Virtual Obstacle technique will be used when the robot is
trapped in the obstacle cavities. The cavities would be filled
with virtual obstacle that would repel the robot out of it.
Virtual obstacles can be used also to solve the local minima
problem in this way as [19] proposed.
4. MODELING
In this model, the APF controller is applied on a multi-robot
system with full considerationoftherobotskinematics.Local
minima problem is handled by Virtual obstacles. The
Simulation is done using V-Rep Simulator and controlled by
MATLab. The robots usedare KheperaIII DifferentialRobots.
The potential function used here are a more simplified
version of Equation 5 and 11.Theapproachisoffline,sothere
is no need forreal-timecalculations,andtheequationscanbe
simplified. The attractive potential function used is:
22
)()( goalgoalaatt XIYJKU  (13)
where aK is the scaling factor, goalX and goalY are the
coordinates of the goal point, I and J are the coordinates of
the current Pixel of the map.
And the repulsive potential function used is:
22
)()( XIYJ
K
U o
repi

 (14)
where oK is the scaling factor, X and Y are the coordinates
of every point that represent an obstacle.
The aim of these two equations is to build a new map but this
map will have the potential form where every pixel of the
map will have specific weight representing the potential of
this pixel as in Figure 2.

Fig -2: The 3D Potential Map
4.1 Differential Drive Kinematics
The KheperaIII robot is a differential mobile robot. The
differential robot is the robot that depends on only two
wheels to move. Both wheels are mounted on the same axis
but are driven by differentactuators.Byvaryingthespeedsof
the two motors, the robot can perform different types of
motion.
The general requirements for any mobile robot to move
are the linear and the angular velocities. However, the
differential robots have only inputs for the velocity for each
wheel in rpm. So, a controller function is used to change the
required linear and angular velocities into the velocities of
the left and right wheels.
Fig -3: Differential Robot Diagram
Dudek and Jenkin [22] introduced in their book the
kinematics of the differential drive. The angular velocity of
the robot at any instant is rotating around an Instantaneous
Center of Curvature ICC. The radius of curvature R and the
angular velocity of the robot  can be expressed by
)(
)(
2
1
lr
lr
VV
VV
R


 and
l
VV lr )( 
 (15)
where rV and lV are the left and right velocities, l is the
distance between the two wheels and R isthedistancefrom
the ICC to the midpoint of l .
The kinematics model of the differential drive can be
represented as
lr
l
r
r
r
l
r
r
r
y
x






















































)sin(
2
)cos(
2
)sin(
2
)cos(
2



(16)
Where T
yx ][  is the position vector of the mobile
robot, r is the wheel radiusand T
lr ][  istherightandleft
wheels angular velocities.
4.2 V-REP
Virtual Robot Experimentation Platform (V-REP) is a
robotic simulator that is used for the experimentationin this
work. It is an open source software and ithasdirectlink with
MATLab. Its script can be written as MATLab script.Itcanbe
linked to MATLab as a remote API.
The environment used in the simulations consists of
KheperaIII mobile robots, Vertical Vision Sensor, Obstacles,
5mx5m Floor, and the goal will be marked in red point as in
Figure 4.
Fig -4: The V-REP Environment used in the Simulations
5. RESULTS
This model has two sides; MATLab and V-REP. The MATLab
side will generate a 2D and 3D potential map for the
environment while the V-REPwill showreal-timesimulation
for the trajectory tracking of the robots. In the camera
screen, the goal is represented as an orange area, The floor
size is 5m×5m, and the (0,0) is at the left and the (5,5) point
is at the right. In the vision sensor screen, the robot is
represented by a small red circle, the obstacles are gray

rectangles, the point (0,0) is at the top leftandthepoint(5,5)
is at the bottom right of the vision sensor screen. The first
experiment as in Fig. 5 has only one robot with two
obstacles, to make initial test for the whole simulation. The
robot is positioned at point (2.5,0.5), and the goal is at
(1.5,4). The experiment takes 12 seconds calculating
potentials time, 37 seconds total simulation time and 28
seconds real time (recorded video). The path length is 70
unit length and can be approximated to 4.22 meters. The
samples are taken every 10 seconds as in Figure 5c, 5d, 5e
and 5f. The last experiment as in Figure 6 has three robots
with an obstacle. This obstacle has geometrytocreatea local
minima point. The aim if this experiment is to test the multi-
robot system with solving the local minima problem. The
robots are positioned at points (1.5,0.5), (2.5,0.5) and
(3.5,0.5), and the goal is at (2.5,4.5). The experiment takes
113 seconds calculating potentials time, 158 seconds total
simulation time and 36 seconds real time (recorded video).
The paths lengths are 86, 92 and 93 unit length and can be
approximated to 5.19, 5.55 and 5.61 meters respectively.
The samples are taken every 12 seconds as in Figure 6c, 6d,
6e and 6f.
( c )
( d )
( e )
( f )
Fig -5: First Experiment Results
( a )
( b )

( a )
( b )
( c )
( d )
( e )
( f )
Fig -6: Second Experiment Results
6. CONCLUSION
Choosing specific path planning approach is a serious
problem in any robotic application. Some applications need
the path planning to be fast without focusing on how
accurate it is. Other applications need the path is to be very
accurate. APF is one of the classic approaches of the path
planning, and it has more than one way to be implemented.
APF concept is built on representing the robot environment
with potential field, where the obstacles have high potential
and the goal has low potential. This causes the robot to be
attracted to the goal and in the same time repelled from the
obstacles. In case of multi-robot system, every robot is an
obstacle for the other robots, so the robots cannot collide
with each other. The proposed approach combinesbothAPF
and Virtual Obstacles approaches. The validity of the
proposed approach is tested and simulated using MATLab
and V-REP as a real-time simulator. The experimentsresults
show the effectiveness of this paper approach.
7. FUTURE WORK
There are many ways to enhance the results of the
simulations and to make it more practical to use in real life.
First, to make the result more practical, the potential field
should be used as on-line path planning approach to make
real-time closed-loop controller for each robot. Second, to
enhance the result of the path generated, an optimization
technique should be used like Genetic Algorithm GA or
Particle Swarm Optimization PSO, that will give optimized
control parameters andgeneratetheshortestpath.Third, for

using this approach on hardware, KheperaIII or similar
mobile robots are the recommended robots to be used.
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