Optimized Robot Path Planning Using Parallel Genetic Algorithm Based on Visible Midpoint

Motahar Reza. et al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 7, ( Part -2) July 2016, pp.01-06
www.ijera.com 1|P a g e
Optimized Robot Path Planning Using Parallel Genetic Algorithm
Based on Visible Midpoint
Motahar Reza, Saroj K.Satapathy, SubhashreePattnaik, Deepak Pandaand Prince Raj
High Performance Computing Lab, School of Computer Science and Engineering, National Institute of Science
and Technology, Berhampur,-761008, India
ABSTRACT
An analysis is made for optimized path planning for mobile robot by using parallel genetic algorithm. The
parallel genetic algorithm (PGA) is applied on the visible midpoint approach to find shortest path for mobile
robot. The hybrid ofthese two algorithms provides a better optimized solution for smooth and shortest path for
mobile robot. In this problem, the visible midpoint approach is used to make the effectiveness for avoiding
local minima. It gives the optimum paths which are always consisting on free trajectories. But the
proposedhybrid parallel genetic algorithm converges very fast to obtain the shortest route from source to
destination due to the sharing of population. The total population is partitioned into a number subgroups to
perform the parallel GA. The master thread is the center of information exchange and making selection with
fitness evaluation.The cell to cell crossover makes the algorithm significantly good. The problem converges
quickly with in a less number of iteration.
Keywords:GA,PGA,Robot pathplanning,cluttered environment
I. INTRODUCTION
Path planning is a crucial problem in
mobile robotics. A mobile robot must be able to
searchcollision free paths to navigate from a start
position to a goalposition in an environment with
barriers.What path generated by robot, must be
optimized under some certain criteria that is most
important to the robot. The criteria may be shortest
path, smoothest path or safest path.From the mid
80s, different predictable methods have been
developed to solve the robotnavigation problem
[1], such as global C-space methods [2], potential
field methods [1], and neural networks approaches
[3].Path planning problem can be solved by
different conservative algorithms, such asthe
potential field, Road Map cell decomposition
[1].All most all approacheswere based on the
concept ofconfiguration space. These approaches
show lack of adaptation and a non
robustactivities. Soeach method has its own
strength over others in certain aspects, but also has
some drawbacks. To get rid from the limitation of
these procedures, researchers explored variety of
solutions. In [4] ,Fuzzy Logic and Neural
Network approach is implemented to handle the
path planning problem. Genetic Algorithm (GA) is
proposed in 1975 [5], andcan be employed to
control a robot moving in a configuration space
which has static obstacles and/or dynamic obstacle
[6, 7].
GA has a greater impact on this field. The
basic feature which makes GA’s attractive in
solving such types of problem, is that they are
inherently parallel search techniques and can
search for optimal in dynamic environments [7,
8] . GA can be used to optimize the path of a
mobile robot moving in an environment which
has number of static barriers. Some of the
proposed methodologies in [9] suffer from different
type of problems. They include (1) requires large
memory spaces when dealing with dynamic
andlarge sized environments (2) time
consuming(3) computationally expensive . In the
last decade, genetic algorithms have been
widely used to generate the optimum path by
intriguing the advantage of its strong
optimization capability. This work is aggravated
by our earlier work presented in [10].The parallel
genetic Algorithm (PGA) gives good result and
quickly converges to get the optimum result. There
is number of processes available to implement
PGA based on their information exchange [11]. A
pseudo parallel GA can be used to find shortest
path in a configuration space. The concept can be
implemented by the number of chromosomes vary
on the number of evolution [12]. In this study, we
provide an initial idea based parallel genetic
algorithm along with midpoint algorithm to select
the shortest path in cluttered environment which
will be able to handle static obstacles.
As per above discussion, in this paper, we
propose a procedure to find an optimized path for
robot in a cluttered environment by using PGA.
This paper is organized as follows. Section 2
introduces problem statement for robot path
planning (RPP). Section 3 discusses the proposed
methodology for RPP. Section 4 presents the
RESEARCH ARTICLE OPEN ACCESS

simulation results and demonstrates the solution for
RPP. Finally, section 5 discusses some conclusions
and considers possible future work.
II. PROBLEM DESCRIPTION
The robot navigation planning problem
is usually formulated as follows: a mobile robot
is takenas a point robot and a complete
description of configuration space which is 2-
dimensional by nature. We must have to plan a
obstacle free path between two specified
locations, a source and a destination. The path
should be a collision free and satisfies certain
optimization criteria (i.e., shortest path).
According to the above discussion, path planning
problem is categorized as an optimization problem.
Researchers uses various methods to solve the
path planning problem as per the two common
factors, the environment type (i.e., static or
dynamic) and Path planning algorithms (i.e., global
or local) . The Work spaceused for the problem is a
static environment. The static environment is
defined as the environment which doesn’t
contain any moving objects other than a
navigating robot.Acomplete awareness about the
search space and that all terrains of the space
should be static, is required for implementing
global path planning algorithms. Local path
planning suggests that path planning is being
implemented while the robot starts it’s navigation;
in other words, these algorithms provide the
collision free movement in local region of
robot.Fig.1 defines a model in which the black
color objects are the obstacles in a 2-dimensional
area with a start and goal point. The robot must
move from start point to goal point without
collision.
Figure 1:A Model for Robot path planning
III. PROPOSED METHODOLOGY
In our proposed methodology, we have
followed two steps to provide an optimized result.
(1) Implement visible midpoint approach and (2)
implement parallel genetic algorithm to optimize
the path. The necessity of first step is to generate a
graph where all paths available in configuration
space lies on free trajectories available in
configuration space. And in second step, the
optimized path will be generating by the use of
genetic algorithm.
A. Visible midpoint approach
Visible midpoint approach is a type of
classical path planning which provides a graph
consists of all collision free paths in the
configuration space. This approach provides two
important activities:
1. This approach avoids the local minima in the
configuration space.The Local minima is such
a case where no results can be found in the
configuration space.
2. The paths generated in the configuration space
are the safest path because it doesn’t touch the
obstacle lines.
The cluttered terrains are the main reasons
to put the robot in local minima situation. Local
minima can be easily avoided by using visible
midpoint algorithm because in each cluttered
environment,there must be some paths which can
helps robot to overcome the cluttered environment.
Main focus of this algorithm is the generation of
mid points in free trajectories. The mid points are
generated according to the obstacles present in the
environment. The paths are generated by
connecting all the visible mid points available in
configuration space and should not touch any
obstacles present in the environment.Fig.2
represents the graph for line obstacle by using said
algorithm and Fig.3 represents the graph for square
type obstacles by the help of visible midpoint
algorithm.
Figure 2:Visible midpoint output of Line Obstacle
Figure 3:Visible midpoint output of square
obstacle

B. Optimized path by Parallel Genetic
algorithm
This step gives the optimum result for
path planning. There are many parallelization-
based methods for increasing the genetic algorithm
execution speed. We have implemented master
slave parallelism with genetic algorithm. The
methodology takes theprimary population from the
result provided by midpoint algorithm. The
population contains number of individuals (i.e.,
chromosomes). Each candidate from the population
represents a solution for the given problem under
study. In our case, each solution is in fact a path
from source to destination in the search space. The
entire graph is decomposed into group of cells..
Each cells consists of a number of nodes and the
information related to each cell is stored in a two
dimensional matrix. The data for a single cell
consists of the number of nodes is having along
with the neighbor cells. Then the minimum edge
connecting one cell to all other cells is stored in
another adjacent matrix. Then the cell where the
source and destination node is present is
determined by traversing through the entire cell
matrix. Then starting from the source node another
node is determined by taking the minimum of all
the nodes connected to it. When a node is selected
for the path its duplicity is also checked with
previously determined paths. If the node finds
duplicity the node is discarded and other
neighboring nodes are checked. Once the condition
is satisfied the nodes is included in the path. The
path is determined by connecting nodes to nodes
and repeating the above procedure till the
destination node is found. The entire process is
repeated a number of times to get a desired number
of paths.( 10 to 20 path) as initial population. Each
path now represents a chromosome which is further
optimized with the application of parallelgenetic
algorithm.We have done the thread level
parallelism to implement parallel GA. The master
thread hold the responsibility of selection and
fitness evaluation where as slaves are responsible
for making crossover and mutation of genetic
algorithm. In our proposed methodology, we have
divided all the population into sub populations.
Each sub population is assigned to each thread.
After making crossover and mutation, the new
population is submitted to master thread.
1. Initialization
The size of initial population is n and can
be taken for the implementation purpose. Therefore
the chromosomes are represented as {C-
1,C2…..Cn}.Each chromosome has its own fitness
value and the fitness value is calculated as the sum
of paths from start to goal. This means a path is the
collection of paths from start to goal and can be
represented as:
P= 𝑝𝑖𝑛
𝑖=1
……………………..(1)pi=
𝑥𝑖+1 − 𝑥𝑖
2 − 𝑦𝑖+1 − 𝑦𝑖
2……(2)
The eq.(1) represents the total length of
path from a start point to goal point. Because a
complete path is the summation of paths in the
same trajectory from start point to goal point.Eq.(2)
represents the length of a path segment from one
point (Xi+1, Yi+1) to another point (Xi, Yi).
2. Fitness function
Fitness function performs a vital role in
any evolutionary process using GA. Master Thread
is having the responsibility to evaluate the fitness
of each chromosome. Thequick search towards the
optimal solution can be established by the
appropriate selection of objective function. The
optimal path is the shortest path fromsource to
destination in our problem statement. Thus, the
fitness function is having the responsibilityto locate
the optimal path. The total number of intermediate
path is may be the shortest path, which therobot
needs to take to reach the destination. Therefore the
cost of a path is the fitness function for our
problem.Eq.(1) along with Eq.(2) can be used as
the fitness function.
3. Population Partition and Selection
Whole population is equally divided into
subpopulation (see Fig 4).Each set in the
population is then submitted to an unique thread for
further calculation. The subpopulation contains the
chromosome pairs as per the selection made by the
algorithm. Selection process is made according to
the common points available in chromosome. If N
is the total chromosome then
N= 𝑁𝑖𝑛
𝑖=1 ................…………………… (3)
Where Ni is the chromosome size. Each group
contains even number of chromosomes.

Figure 4: Create sub populations
4. Crossover
Then the crossover algorithm is applied to
pair of chromosomes. The crossover is done by
determining the crossover points for each pair. The
crossover points are calculated by taking the cell
common to both the chromosomes. The entire cell
matrix is again traversed to find the cell common to
both the chromosomes excluding the source cell
and destination cell.
After determining the crossover point four
nodes are determined as s1, d1, s2, d2 where s1 and
d1 are the successor nodes and predecessor node
respectively connected to the common cell’s node
of first chromosome and s2 and d2 are the
successor nodes and predecessor node respectively
connected to the common cell’s node of second
chromosome of a pair. The crossover node is
determined to carry out the crossover procedure.
The crossover node of the first child chromosome
is determined by checking the existence of path
from s1 as well as from d2 to the nodes of the
common cell of second chromosome. If the cross
over node is found then the first crossover path is
calculated .The first crossover path is calculated by
taking the source node till the successor node of
first chromosome (s1) then crossover node and
finally the predecessor node till the destination
node of second chromosome (d2).
The crossover node of the second child
chromosome is determined by checking the
existence of path from s2 as well as from d2 to the
node of the common cell of first chromosome. If
the cross over node is found then the second
crossover path is calculated .Then the second
crossover is done by taking the source node till the
successor node of second chromosome (s2) then
crossover cell node and finally the predecessor
node till the destination node of first chromosome
(d1). Fig.5 represents the chromosome selected for
crossover.Fig.6 represents the new chromosomes
generated throw the help of crossover step.
Figure 5:Crossover Step1 Output
Figure 6:Crossover Step2 Output
5. Mutation
After getting the child chromosome pair
the mutation operator is applied on the
chromosomes. The nodes are interchanged in
between the chromosomes to determine the new
child chromosomes after mutation. Before the
nodes are interchanged the existence of path for the
new node is also checked.
Both the crossover and mutation method is
applied to rest other pairs of chromosomes. After
crossover of the entire parent set, all the
chromosomes including the parent chromosomes
and the new child set of chromosomes are again
sorted according to the fitness function in
ascending order. The new selected n-chromosomes
are again submitted to master thread for further
iteration.
IV. ALGORITHM STEPS
M <-Cell Matrix (M1*M2)
N<-No. of chromosomes
Pc<-Crossover Probability
Pm<-Mutation Probability
ALGORITHM (M, N, Pc, Pm)
1. Start with population of n paths generated by
Visible midpoint approach
2. Calculate the path distance from source to
destination using eq.1 and eq.2 of each
chromosome Ni in the population.
3. Divide the population into subpopulation with
equal size of chromosome. The subpopulations
are submitted to sub threads for further
evaluation.
4. Repeat the following steps until N offspring
have been created in sub threads:
a. Select a pair of parent chromosomes from the
current population.

b. With probability Pc crossover the pair at a
randomly chosen point. If no crossover takes
place, form two offspring that are exact copies
of their respective parents. Crossover is done
by cell wise manner. The crossover point is
determined according to the common cell in
cell matrix for both the chromosomes.
c. Mutate the two offspring at each locus with
probability Pm and place the resulting
chromosomes in the new population.
If N is odd, one new population member
can be discarded at random.
5. Return the current population to Master thread.
6. If the solution is close to the optimum after
several iteration, thengo to next step.
7. Else Go to Step-2.
8. End
V. EXPERIMENTAL RESULT
We have implemented both the approach
in a high performance computing Server with a
Dell Power Edge R610Rack Server with Dual Intel
XeonQuadcoreE5620 @2.93 GHz processors with
a total 4 servers (64 Processors) 12GB RAM /
3x300 GB SAS HDD/ RAID – 5/RPS/ Dual
NIC.TheMovementspace for robot is taken as
700*500 pixels. For our experiment, the graph is
divided into group of 25 cells (5 * 5).Fig.7
represents the first step of proposed algorithm. In
this experiment we have taken the obstacles as
Square type.Fig.8 represents the second step that is
optimized path from start point to goal point by
using PGA. Fig.9 represents midpoint based
visibility graph. In this experiment we have taken
the obstacles as Line and which generates the Local
Minima.Fig.10 represents the parallel genetic
algorithm path from start point to goal point. In our
experiment we have taken only 200 chromosomes
which are then decomposed into 10 groups for 50th
iterationswhere the chromosomes belong to
different regions.Fig.11 shows the optimized value
which is the distance from start to goal with respect
to the number of iteration.GA provides the final
result after 17th
iteration whereas PGA gives
optimum result around 10th
iteration. The value is
notgoing to change further.
Figure 7: Visible midpoint output for Squared
Obstacles
Figure 8: Optimized path By PGA for Squared
Obstacles
Figure 9:Visible midpoint output for Line
Obstacles
Figure 10:Optimized path By PGA for Line
Obstacles

Figure 11:Fitness value vs Iteration
VI. CONCLUSION
Parallel Genetic Algorithm is easy to
apply on path planning problem because the path
planning problem is a quite related to travelling
Sales problem. The result, what we get from this
implementation is effective as compared to
classical path planning problem because the time
complexity of classical path planning problem with
Simple GA is high as compared to PGA. The
problem converges quickly with in a less number
of iteration. But we have seen that the mutation
doesn’t put any drastic changes on the result. The
cell to cell Crossover makes the algorithm
significantly good. The ultimate objective of
developing a fully independent robot is beyond the
scope of the research carried out for this
dissertation. This paper necessarily focuses on a
more specific component of an independent robot.
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