Abstract- Robot path-planning is known to be NP-hard

Abstract- This paper proposed another robot navigation algorithm in light of
gene expression programming, and introduced another idea named
“parallel-chromosome” to mitigate the downside that the robot can’t
move back when meeting obstacles and proposed an extraordinary encoding
technique to lessen the space cost. A “fitness function penalty” was
advanced to choose the fitness values. Trials demonstrate that BPGEP beats
conventional GA-based algorithms by altogether enhancing the success rate of
finding an optimal path.


Keywords- Gene Expression Programming, Path Planning,
Parallel-Chromosome, Fitness Function Penalty, Mutation

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I.   Introduction

has turned into an amazingly quickly developing marvel affecting all features
of regular day to day existence. Along these lines, autonomously navigating
robots has moved toward becoming progressively imperative. Motion planning is
one of the imperative assignments in intelligent control of a self-ruling versatile
robot which led to building an autonomous path planning robot. This paper
displays the research and simulations investigations of another quality gene
expression programming (GEP) based path-planning model which has been connected
in the real time environment. Robot path-planning is known to be NP-hard and
many other methods like genetic algorithms, simulated annealing and A* methods
have been used to solve this problem among which genetic algorithms proved
effective optimal technique. GEP consolidates the advantage of both Genetic
Algorithm (GA) and Genetic Programming (GP), while beating some of their
individual constraints. It is a decent answer for complex issues, for example,
NP problems, and combinatorial optimization problems. In this study the contributions
made were proposing a new concept named parallel-chromosome where a GEP
chromosome is separated into two parts: Function set and Terminal set and each
set would form a chromosome respectively. They named the new GEP algorithm as
BPGEP which would find the shortest path and give optimal solution i.e.
improving robot’s moving flexibility by increasing the search space. Also a new
population encoding method was developed to reduce the storage space. This
paper displays the research and simulations investigations of another quality
gene expression programming (GEP) based path-planning model which has been
connected in the real time environment.


A.    Importance and Significance of
the Topic

path-planning is a piece of an expansive class of issues relating to scheduling
and routing. Few techniques have been connected to the robot navigation
problem. The previous techniques used showed that when a robot meets an
obstacle, it was not able to avoid it and would follow the straight path as it
could only move vertical and horizontal directions. With further progress in
algorithms, the robot could in diagonal direction along with it horizontal and
vertical movement property but there remained one major drawback. The robot did
not have the capability to backtrack and avoid obstacles. An algorithm which
would help the robot move back and avoid obstacles was needed. This paper used
a phenomenon name “Parallel-Chromosome” which helped to improve the efficiency
of finding an optimal path and it improved the search space and the robot’s
moving flexibility.


II. GEP-based Robot Path Planning Algorithm  


2D path planner is used for the path planning and it determines the length and
width of the search space. The path planner also shows the location of the known
obstacles with some marking. Start and end point are also known and the robot
can move on all the free cells. Figure 1 describes the path planning example
with some obstacles and it has also shown two paths with different routes to

Fig.1. Path planning example with two
different cases.


Parallel Chromosome

Here Pc is denoted for two
chromosomes and is written as Pc= where F is one chromosome
containing the functions and T is another chromosome containing the terminals.
For this problem F chromosome contains the directions for which robot will move
i.e. F= {?, ?, ?, ?, ?, ?, ?, ?} and T chromosome = {1, 2, 3… n}
represents the number of steps the robot has passed. The interaction between
both the chromosomes is bijective and each position in F corresponds to same
position in T. As F chromosome contains all the directions it increases the
search space 1.


Initial Population

An initial population is generated
with random set of individuals and is denoted by B = {bi} and the storage space
for the population is given by p*(1+(n-1)(4+?log(n)?))
= O(pn(log(n)) bits, where p is population 1.


Fitness Function

The evaluation of the population
paths generated each time is based on the fitness of the path and fitness is
based on how suitable the path is. Path length, number of turns and number of
steps taken were the factors from which the fitness function  was generated 1.  


Operating a Selector

Roulette-wheel sampling is used to
select the individuals according to their fitness.



One-point recombination and two-point
recombination is used here because in all the recombination, two chromosomes
are chosen and paired for some exchange of material in between them hence
forming two more chromosomes.



The mutation operator is used to
check mutation probability for per single gene and decides whether to be
mutated or not. If it is to be mutated then a random number in T-chromosome is
assigned to a terminal and a random direction in F-chromosome is assigned to a
function accordingly.


III. Conclusion  

GEP-based algorithm yields the better execution on the search space
contrasted and different GA-based algorithms in robot path-planning. Change to
the conventional genotype structure of gene expression programming permits more
alternatives in robot path planning, subsequently it enhances the
accomplishment of robot route. While the achievement rate is high, there are
still trials where the new GEP neglects to locate a possible way. The
parallel-chromosome enhances the adaptability of route and tries to discover a
legitimate way as well as an ideal one.