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Map Generation and Path Planning for Autonomous
Mobile Robot in Static Environments Using GA
Karthikeyan U. Gunasekaran, Evan Krell, Alaa Sheta, Scott A. King
Department of Computing Sciences
Texas A&M University-Corpus Christi
Corpus Christi, TX 78412, USA
Abstract—In this paper, we present our initial idea of developing
an integrated an autonomous mobile robot system that can
explore an unknown environment. The proposed system consists
of three components 1) a map generation 2) path planning and
3) path tracking. The proposed approach allows a mobile robot
to navigate the unknown environment, avoiding obstacles and
following a defined path to reach the target position without
collision. Ultrasonic sensor data was collected via moving the
robot along the perimeter of the environment while incrementally
updating the occupancy grid using ultrasonic/laser sensor to
measure the distance between the obstacles and the edge of the
environment. This dataset will be converted to a map that is
used by Genetic Algorithms (GAs) to create an optimal route
from a pre-defined start and target points. The autonomous robot
system will travel between these points by following a trajectory
defined by waypoints estimated using GAs. The pure pursuit
(PP) algorithm is used for trajectory following. The proposed
system was tested in a real environment using LEGO robot
and in simulation using GAZEBO software. The results indicate
that the proposed integrated autonomous mobile robot system is
promising
Index Terms—Robot navigation system, Genetic Algorithm, Path
Planning, Metaheuristic Search Algorithms, Map Generation
I. INTRODUCTION
An autonomous robot is a physical agent that independently
interacts with its environment to perform tasks [6]. Intelligence
is desirable for a robot in order to make decisions that
increase mission success. Mobile robots are able to move
in an environment using wheels, legs, etc. For autonomous
operation, mobile robots should have a representation of their
environment, a mechanism for selecting targets, and a method
for efficiently navigating to a target. Combined with sufficient
localization capability, a detailed world representation allows a
robot to navigate effectively in a given environment. A ground
robot working on a factory floor could have a 2D grid where
each cell is either occupied or not. These are called "occupancy
grids" and enable path planning and navigation with a low
memory footprint [10]. Autonomously generating a map for
an unknown area remains a challenge, especially for complex
environments.
Many solutions have been implemented based on simultaneous
localization and mapping (SLAM); a mobile robot is placed
at an arbitrary, unknown location and incrementally builds a
map while determining its position relative to this map [6].
SLAM techniques are computationally intensive and require
much exploration [9]. This paper proposes a less intense
mapping technique that is very simple to implement and can
either wholly or partially map specific environments. Even a
partially-completed map can be a starting point to direct a
more complicated technique toward specific unknown areas
rather than exhaustive exploration. Once the map is available,
planning a collision-free path with minimal costs such as time,
energy, and distance is possible for robot navigation.
The path planning problem for autonomous robot system
remains a challenge because of the high computational effort
required; the problem is NP-hard [9]. The computational effort
of traditional shortest-distance algorithms such as Breadth-
first search, Dijkstra, and Bellman-Ford led to the develop-
ment of heuristic approaches that reduce the search space.
Metaheuristic algorithms and soft computing techniques have
been explored for path planning [15], [17] such as Genetic
Algorithms [18]–[20], Neural Networks [7], and Fuzzy Logic
[12]. The advent of metaheuristic search algorithms such as
GA, Particle Swarm Optimization (PSO) and Ant Colony
Optimization (ACO) approaches can be used to substantially
reduce computation [11], [17].
This paper is organized as follows. In Section II, we provide a
general overview of GAs. The adopted hardware and software
components are presented in Sectionhardware. The proposed
autonomous mobile robot system architecture is presented in
Section IV. The experimental results are given in Section V.
Finally, we provide a conclusion.
II. GE NE TI C ALGORITHM
GA is a bio-inspired search algorithm that applies Darwin’s
principles of natural selection to computational problems.
Survival of the fittest is used to gradually direct a random
set of solutions toward optimal ones. An individual’s fitness
improves as that individual moves in the direction of an
optimal solution. A single individual is represented as a
chromosome, which is a set of genes. Each gene corresponds
to a dimension of the problem. A fitness function scores the
individual based on the chromosome. Improvement occurs by
applying the genetic operations, crossover and mutation, to
chromosomes in the current population such that they repro-
duce and generate the next population. More fit chromosomes
are allowed to reproduce at a higher rate than weaker ones,
such that successive generations are more influenced by fitter
genes. The expectation is that components of feasible solutions
can be combined to yield a fitter solution.
GA is well-established in robotics. It has been used to tune the
parameters for path planning of a mobile robot, demonstrating
real-time performance in a dynamic, complex environment
[13]. GA was used within a multi-robot team playing soccer
[5]. GA was applied to the difficult task of controlling a hexa-
pod robot. The robot learned to walk by using the feedback
of walking trials as input to the evolution [14].
There has been much research in applying GA and similar
metaheuristic techniques to mobile robot path planning. The
majority of work in this area only evaluates the results as paths
generated in a 2D environment. Little work deals with creating
the map that will be used for path planning or demonstrating
the robot can adequately follow the path. Our work’s proposed
mapping scheme will allow the robot to generate a map
for path planning. Also, the Gazebo simulator is used to
show the paths are feasible for a robot in a 3D world with
realistic physics. Two recent (2017) studies demonstrate that
GA produces smooth, near-optimal paths [18], [19]. However,
in both cases, the map is known a priori, and no actual path
following is shown. There are a few cases that use real robots,
such as a 2010 study that included experiments where a robot
with range-finding sonars was able to navigate using the GA-
generated paths [20]. The map of the real environment was
known a priori.
III. HAR DWARE AND SO FT WARE
A. LEGO robot
The LEGO Mindstorm EV3 [4] is a popular robotics kit. The
EV3 brick is a programmable microcomputer, running Linux,
that controls the motors and sensors and provides Wi-Fi and
Bluetooth [16]. The digital EV3 ultrasonic sensor [1] generates
sound waves and reads their echoes to detect and measure
the distance between objects. This sensor measures distances
between 1 and 250 ±1cm.
B. Software Tools: Gazebo and MATLAB
Gazebo [2] is a robotics simulator suited to experiments in
algorithms, robot design, regression testing, and training of
machine learning systems. The gazebo is famous because of
its plethora of existing robots and environmental components
with realistic physics support and high-quality 3D graphics.
MATLAB [3] connects to Gazebo through the Robotic Oper-
ating System (ROS) interface. ROS abstracts communication
among robots and control software such that the MATLAB
code written for Gazebo should easily port to actual robots.
IV. PROPOSED AUTONOMOUS ROBOT SYSTEM
This paper proposes an integrated system with 2D map gen-
eration and trajectory following for an unknown environment.
Instead of exploring the interior of the space using expensive
SLAM techniques, the robot moves along the perimeter of
the environment and generates an occupancy grid. The robot’s
laser sensor is used to collect ranges and calculate the distance
to objects in the space. These distances are continually updated
in an initially empty grid. That grid is used to generate paths
to an arbitrary target location in the area. Optimal paths
are computed using GA. Trajectory following is performed
using pure pursuit [8]. A complete framework is demonstrated
where a robot can autonomously move to target locations in
an unknown environment. The proposed system hierarchy is
provided in Figure 1.
Map
Generation
Path Planning
(GA)
Trajectory
Following
(Pure Pursuit)
Fig. 1: Proposed Autonomous Mobile Robot System
A. Map Generation
To generate the map, the robot moves along the perimeter of
the environment while incrementally updating the occupancy
grid using laser scan sensor. Cell value of 1 indicates occupied
and 0 indicates free. This research assumes that the environ-
ment is static, the cells are independent of each other, and the
area of a cell is either completely free or occupied with an
obstacle.
To avoid collisions, if any part of the cell intersects an obstacle,
the entire cell should be considered as an obstacle. Increasing
the grid resolution decreases the free area that is viewed as an
obstacle. The resolution should be adjusted based on the needs
of the actual workspace the robot will be operated in. There
is a trade-off between map accuracy and path planning time
since the higher the number of cells the longer the search will
take. The mapping methodology is explained in Algorithm 1
with an example of a 4×4grid which spans 100cm ×100cm.
The area of each cell is 25cm2.
Figure 2 shows the sample environment where cells filled in
blue indicate obstacles. The robot starts at the point Aand
moves towards position B. It then turns left towards point C.
From C, it moves toward Dand finally reaches the starting
point A. The laser sensor measures the horizontal distance.
The point xis the position of the robot and yis either the
entire distance from location Ato D(100 cm or until the start
point of an obstacle). For example, if an obstacle is placed at
the fourth cell in the second row from the left top corner,
then ywould be set at the 75cm from the starting point x.
This process is repeated iteratively to measure the horizontal
Fig. 2: Sample environment with obstacles.
Algorithm 1: Basic steps of Mapping Algorithm
Input: Lidar Sensor Values (L), Row Length (RL), Cell
Length (CL), Total Distance (T D).
Output: Resultant Matrix, M
1begin Mapping
2Input Lis subdivided into four lists L1,L2,L3,L4.
3L3,L4are reversed and stored as L3r,L4r
4For i=1to2(L2c, L3rc)
5For i= 1 to row length RL
6Add cell length CL to each list values L2c, L3rc
7If L2c, L3rc greater than total distance T D
8Swap values with twice total distance
9Next for
10 For i= 1 to row length RL
11 Subtract T D from L2c, L3rc
12 Next for
13 Next for
14 For i= 1 to row length RL
15 For i= 1 to row length RL
16 Divide CL with each L1, L2c, L3rc , L4r
17 Update zero matrix with L1f, L2f, L3f, L4f
18 Next for
19 Next for
20 end Mapping
distance and vertical distance of the environment with respect
to the robot.
The sensor data is processed and a list is created from these
values as input for the proposed mapping algorithm. The
created list is named L, which is then sub-divided into four
lists. L1encompasses values from point A to B. L2stores
values from point B to C and similarly L3and L4store values
from point C to point D and from point D to point A. L3r
and L4rare reversed. In this example,
•Lfull = [25, 25, 50, 0, 0, 50, 25, 50,
75, 25, 0, 50, 25, 50, 0, 75]
•L1= [25, 25, 50, 0] •L2= [0, 50, 25, 50]
•L3r= [50, 0, 25, 75] •L4r= [75, 0, 50, 25]
From L2and L3the total distance, 100, is subtracted from
each element of the list after adding its cell length. In this
example at B1 instances, to 00 the cell length 25 is added
and then the total length 100 is subtracted which gives 75.
The corrected values of L2and L3are called L2cand L3c,
respectively.
•L1= [25, 25, 50, 0] •L2c= [75, 25, 50, 25]
•L3rc = [25, 75, 50, 0] •L4r= [75, 0, 50, 25]
The final lists are generated by dividing each element with the
cell length. The final list values are used as the plug-in value
which creates the matrix. For example, L1at A1 instance,
the value 25 is divided by the cell length (25) which gives a
resultant value of 1. The finalized list is called L1f. A zero
matrix is created. The number of rows and columns for the
matrix are equal to the resultant value arrived on the dividing
the number of elements present in Lby four. Here, the L
0100
0100
0010
1000
Update Zero Matrix by L1f
0100
0101
0010
1000
Update Zero Matrix by L2f
0100
0101
0010
1000
Update Zero Matrix by L3f
0100
0101
0010
1000
Update Zero Matrix by L4f
The final map
Fig. 3: Map generation update.
TABLE I: GA Representation of path: Sequence of waypoints.
x1y1x2y2... xnyn
count is 16, which when divided by 4 gives 4 which is called
n. Thus, a 4×4 zero matrix is generated.
•L1f= [1, 1, 2, 0] •L2f= [3, 1, 2, 1]
•L3f= [1, 3, 2, 0] •L4f= [3, 0, 2, 1]
The zero matrix is iteratively updated using each final list. The
indices for the obstacle is created using the final list. L1fand
L3fvalues are plugged in as column values and corresponding
row value are incremental values inserted, from zero to n−1.
Similarly, the L2fand L3fvalues are plugged in as row values
and corresponding column values are incremental values,
inserted from zero to n−1. These indices are assigned one.
The updated zero matrix is shown in Figure 3. The zero matrix
is incrementally updated with each new index created from the
final list values. The resultant zero matrix has one at different
indices which indicates the presence of obstacles.
B. Path Planning using GAs
Path planning is the process of generating a possible sequence
of intermediate waypoints between a start and goal. A possible
path takes the robot to the target position without colliding
with obstacles. The goal is to find a way that minimizes the
distance of the path while remaining collision-free. GA is
used to find solution paths Waypoints are coordinate values
in the robot’s environment, which is the GA search space.
The solution is stored in an array of size 2 times the number
of waypoints since each (even, odd)-pair of array values is a
waypoint. This representation is shown in Table I.
C. Fitness Function
The GA fitness function is used to evaluate the quality of an
individual’s chromosome. Distance minimization is computed
using the Euclidean distance (See Equation 1) between each
pair of waypoints to measure the path’s length. (Equation 2) is
the summation of each subpath between adjacent waypoints,
P athD.
DI ST (xi, yi, xj, yj) = q(xi−xj)2+ (yi−yj)2(1)
P athD=
n−1
X
i=1
DI ST (< xi, yi>, < xi+1, yi+1 >)(2)
D. Obstacle Avoidance
Collision avoidance is implemented by penalizing obstacle
presence along with a path. The Penalty (P) is set to an
arbitrarily high value to make paths containing collisions have
poor fitness. We have set the penalty to 10000. The SIN F is
defined as the infeasible portion of the map. This is shown in
Equation 3.
P athO=SIN F ∗P(3)
The full fitness function is comprised of the distance minimiza-
tion and obstacle avoidance functions. The complete fitness
function used in GA is shown in Equation 4.
F itnesspath =P athD+P athO(4)
V. EX PE RI ME NT S AN D RES ULTS
A set of simulation and real-world experiments with different
environmental setups were performed to verify the effective-
ness of the proposed algorithm. Simulation experiments were
implemented using Gazebo simulator and a MATLAB control
program. Real-world experiments are implemented using the
LEGO EV3 robot equipped with a single ultrasonic sensor.
A. Map generation in simulation
For simulation experiments, the full system of map generation,
path planning, and trajectory following was done in three
environments. Each environment was created by specifying
size and randomly generating obstacles in that space. The
three environments are: small-size room (Figure 4a), medium-
size room (Figure 4b), and large-size room (Figure 4c). The
small size room measures 5×5 meters and has 5 obstacles.
The medium-size room measures 10×10 meters and has 8
obstacles. The large-size room measures 20×20 meters with
35 obstacles. The environment layout in the simulation is
provided in Figure 4 (a), (b) and (c). The 2D occupancy
grids generated for all three environments based on real-time
simulation is shown in Figures 5 (a), (b) and (c).
B. Map generation in real-time
Experiments were implemented using the LEGO EV3 in a
laboratory setting. An environment was created by drawing
grid lines and a perimeter track onto a 100×100 cm section
of the floor. This environment is called Lab Environment.
Space was divided into a 5×5 grid where each cell is 20
cm2. This environment is shown in Figure 6. Boxes were
placed on certain grid cells to act as obstacles. The LEGO EV3
robot used a downward-facing light sensor to follow the red
track. A PID controller is used to follow this line. The robot
followed the track and used the ultrasonic sensor to generate an
occupancy grid using the proposed mapping algorithm. Map
generation produced the occupancy grid shown in Figure 7.
C. Path Planning Results
To generate the mobile robot path via the map created in
the previous stage, we run GAs for ten experiments with
various population sizes (i.e., 20, 35, 50, and 100) as shown
in Figure 8. In this case, the 2D-workspace has 10×10 grids;
the start point is at (1,1) and target at (10,10). The best GAs
convergence results were found with a population size of 100.
The fitness value represents the combined path distance and
obstacle penalty, so GA minimizes this value. The 0-point
of the y-axis is the lowest obtained fitness value. Due to
nondeterminism of GA, repeated trials are needed to confirm
that a near-optimal path can reliably be obtained.
The results of 10 trials using a population size of 100 are
shown in Figure 9. Figure 10 shows the best and worst
experiments as well as a curve generated by averaging points
of all experiments. This is intended to clearly illustrate the
bounds of the fitness and that the average achieves a relatively
smooth curve toward convergence. Figure 11 shows the actual
waypoints generated as points (blue "x"’s) in Gazebo. The
cones are the start and goal locations. The robot is seen moving
between waypoints.
The convergence graph using different population size is
shown in figure 8. We experimented with varying population
size namely, 10, 25, 50, 75, 100, 125. It is evident from the
convergence graph that the population size with 100 individ-
uals provides an optimal path, in our case, is the near-optimal
path between the starting and target point when compared with
another population size. Convergence of GA using the same
population size of 100 for 10 runs is shown in the Figure 9.
The graph for the mean, worst and best convergence using
same population size is shown in the Figure 10.
D. Trajectory Following using Pure pursuit
The trajectory following stage inputs the collision-free path
which has been generated by the path planning module. The
robot starts from the start point and reach the target point
by reaching each waypoint in sequence. Using pure pursuit
algorithm, the controller was initialized. The desired linear
velocity was 0.3 and look ahead distance was set to 0.5. The
Turtlebot following the waypoint in sequence on the medium-
size room environment in Gazebo is shown in the Figure 11.
VI. CONCLUSIONS AND FUTURE WORK
We present our idea of building an autonomous robot system
that can search an unknown environment of various sizes. On
doing that, we developed a 2D grid map for the unknown
environment. The generated map has the advantage over other
map generation in the literature that it can be produced with
less time compared to random environment exploration. For
the path planning, GA was able to develop an optimal set of
waypoints for the robot to follow from a designated start and
end-points.
(a) Small room (b) Medium room (c) Large room
Fig. 4: Three different environments used in the experiment.
Binary Occupancy Grid
0 20 40 60 80 100
X [meters]
0
20
10
60
80
100
Y [meters]
(a) Occupancy grid for small room
Binary Occupancy Grid
0 20 40 60 80 100 120 140 160 180 200
X [meters]
0
20
40
60
80
100
120
140
160
180
200
Y [meters]
(b) Occupancy grid for medium room
Binary Occupancy Grid
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
X [meters]
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Y [meters]
(c) Occupancy grid for large room
Fig. 5: 2D occupancy grid maps created by the system for the different environments.
Fig. 6: Lab environment with obstacles.
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0 20 40 60 80 100
0
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1
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