Mobile robot path planning with modified ant colony optimisation

Abstract

Automated navigation is a pivotal task of robotics research and the key challenge lies in robot motion on unknown dynamic terrain. The large number of solutions to robotic path planning, especially in unknown and dynamic environments, mainly rely on the heuristic methods. The most important factor for this choice is the fast convergence towards solution without supervision. In the proposed scheme we have used a modified version of ant colony optimisation. We incorporated the directional movement history of robot on a grid into a vector as a probability multiplication factor which helps to achieve a faster convergence and avoid unnecessary movements, e.g., looping. In this work we have devised a novel pheromone updation scheme. Along with this we have applied path smoothing to lessen the number of turns on the candidate optimal path. Effectiveness is shown through several extensive experiments and results clearly indicate the aptness of the proposed scheme.

Full text

106 Int. J. Bio-Inspired Computation, Vol. 9, No. 2, 2017
Copyright © 2017 Inderscience Enterprises Ltd.
Mobile robot path planning with modified ant
colony optimisation
Utkarsh Rajput* and Madhu Kumari
Computer Science and Engineering Department,
National Institute of Technology,
Hamirpur-177005, Himachal Pradesh, India
Email: utkarshrjpt@gmail.com
Email: madhu.jaglan@gmail.com
Email: madhu@nith.ac.in
*Corresponding author
Abstract: Automated navigation is a pivotal task of robotics research and the key challenge lies
in robot motion on unknown dynamic terrain. The large number of solutions to robotic path
planning, especially in unknown and dynamic environments, mainly rely on the heuristic
methods. The most important factor for this choice is the fast convergence towards solution
without supervision. In the proposed scheme we have used a modified version of ant colony
optimisation. We incorporated the directional movement history of robot on a grid into a vector
as a probability multiplication factor which helps to achieve a faster convergence and avoid
unnecessary movements, e.g., looping. In this work we have devised a novel pheromone updation
scheme. Along with this we have applied path smoothing to lessen the number of turns on the
candidate optimal path. Effectiveness is shown through several extensive experiments and results
clearly indicate the aptness of the proposed scheme.
Keywords: mobile robot; ant colony optimisation; ACO; path planning; path smoothing.
Reference to this paper should be made as follows: Rajput, U. and Kumari, M. (2017) ‘Mobile
robot path planning with modified ant colony optimisation’, Int. J. Bio-Inspired Computation,
Vol. 9, No. 2, pp.106–113.
Biographical notes: Utkarsh Rajput received his Bachelor of Technology in 2012 from Gautam
Buddh Technical University, Lucknow, Uttar Pradesh, India. He received his Master’s from
National Institute of Technology, Hamirpur, Himachal Pradesh, India. Machine learning and
robotics are his major interest areas.
Madhu Kumari is currently working as an Assistant Professor in the Department of Computer
Science and Engineering at National Institute of Technology, Hamirpur, Himachal Pradesh,
India. She received her Master’s and doctoral degrees from Jawaharlal Nehru University, New
Delhi. Her previous work mostly focused on exploration of different variants of reinforcement
learning in simulated Robocop soccer domain. She has worked on different aspects of
computational advertising based on sponsored search auctions. Her current research is more
aligned towards the deployment of machine learning techniques on application milieu like web,
text and social analytics.
1 Introduction
Mobile robots have their applications in diverse fields
ranging from dangerous environments, like mining and
nuclear industry to daily life applications, e.g., autopilot
robots for cars and household work. These robots can be
successfully used in hazardous environments where human
life can be endangered. For the development of mobile
robots, effective and efficient path planning methods are
necessary for the locomotion. Robot path planning is a
pivotal research problem and researchers are continuously
trying to develop methods that can be used an integrable
solution for this problem in a manner that can find the
optimal path in real time with least number of constraints.
But there has been less success achieved in this area.
Initially the main focus was on the path planning in static
environments where the obstacles are static and robot is the
only mobile entity. Major techniques which have been
extensively used in static environments based path planning
includes cell decomposition method (Choset, 2007),
visibility graph method (Mitchell, 1986), Voronoi diagrams
(Kalra et al., 2009), etc. In cell decomposition method
(Choset, 2007) environment map is decomposed into
different sized cells labelled as obstacle and free cell. A
possible navigation route for robot is through connected free
cells only. The incremental algorithm in Kalra et al. (2009)
uses techniques for constructing and updating generalised
Voronoi diagrams and thus finding the route through
unknown static environment. Genetic algorithm with

Mobile robot path planning with modified ant colony optimisation 107
B-Spline curve in Ju and Cheng (2011) has been used to
generate smooth paths in static environments for car like
vehicles. The research in this area of static environment
path planning is now almost saturated (Choset and Pignon,
1997; Simon, 1993) and there are very few possibilities of
further improvement.
The problem of path planning in dynamic terrains,
where the obstacles can also be mobile, that represents the
real world scenario, is still a major challenge of this
research purview. There are great possibilities of
improvement in this particular area, especially to exploit
local information to achieve globally optimally solution.
Various methods have been proposed so far the robot
movement planning in dynamic and unknown environments
with optimal cost. Potential field theory (Ge and Cui, 2000),
genetic algorithm (Tu and Yang, 2003; Hu and Yang,
2004), simulated annealing (Miao and Tian, 2013), neural
network (Simon, 1993), fuzzy logic (Reignier, 1994), etc.,
are most widely used methods for dynamic path planning.
Tuncer and Yildirim (2012) applies genetic algorithm with a
modified mutation operator to plan the path in dynamic
environment. A hierarchical fuzzy control system is
presented in Rulong et al. (2011) for multi-robot path
planning in which the robots are connected through a
network. Apart from these techniques, various heuristic
techniques for path planning have been proposed. An ant
colony optimisation (ACO) technique in Garcia et al. (2009)
makes use fuzzy evaluation function for selecting an
optimal path in the simple dynamic navigation terrain.
Zhangqi et al. (2011) presents an improvement of basic ant
colony algorithm that uses genetic algorithm to optimise the
parameters of ant colony algorithm. These heuristic
techniques have been proven to be a good improvement
over the classical approaches.
2 Modified ACO algorithm
ACO is a meta-heuristic that can be applied very effectively
to plan the path for mobile robot in dynamic terrains with
the help of very basic local information, even in unknown
environments. The basic ACO algorithm has been used
previously by Garcia et al. (2009) and Zhangqi et al. (2011),
but there is lot of scopes to improve the time consuming
probabilistic selection formula and pheromone updation
scheme. ACO algorithm is a swarm intelligence technique
(Duan and Luo, 2015; Wang et al., 2015) that simulates the
behavioural working of real ants. The ants use pheromones
to find their path from source to destination (Dorigo and
Stützle, 2004).
Simple ACO algorithm works moderately well in
terms of finding feasible path in dynamic environments
(Garcia et al., 2009). The time taken by the algorithm is
high and thus needs two main parts of the algorithm,
probabilistic formula and the pheromone updation scheme,
to be modified that can speed up the process to find a
solution in real time. Moreover, selection of one of the
many available feasible paths of same length based on
simple ACO approach may slow the process a little bit
because of varying nature of number of turns on the path.
To further improve the efficiency of the process on this
account and to get a smoother path, it can be extended to
include a path smoothing method that can reduce the efforts
of robot significantly without compromising the on the time
compared to the time elapsed in finding the path. The
complete approach can be explained in the three sections as
follows.
Figure 1 Sample 8 × 8 grid
2.1 Environment modelling
The robot navigation environment is modelled in the form
of a 2D square grid structure. The robot is considered to be
as a point robot. The grid is represented by Euclidean plane
on XY coordinate system towards the positive x and y-axes
having N grid cells numbered from 0 to N – 1. The cell
number can be calculated by the following equation (1),
provided the coordinates x and y on X-axes and Y-axes
respectively
n
Gyxn=+∗ (1)
where n is the number of grid cells in one dimension, that is,
the grid is of size n × n. Figure 1 shows a grid of size 8 × 8.
Top left corner is the origin on Euclidean plane, positive X
direction is form left to right and positive Y direction is
from top to bottom.
There are eight possible directional movements from an
internal nodes (other than boundary nodes): forward,
left-forward, left, left-backward, backward, right-backward,
right and right-forward, each directional movement is
assigned a number on the grid from 1 to 8 respectively as
shown in Figure 2. The movement of robot is restricted to
grid only, therefore the movements on a boundary node are
limited. For example, if the robot is on left boundary then
the directions 6, 7 and 8 are restricted.

108 U. Rajput and M. Kumari
Figure 2 Possible directional movements from an internal node
2.2 Proposed modifications in ACO
The steps of the proposed algorithm are similar to simple
ACO algorithm. We propose to change two major aspects of
ACO approach, probabilistic selection formula and
pheromone updation scheme, to combat the problem of
slower convergence in basic algorithm. The modified
algorithm provides directional movement history to
calculate the probability of selection of next node which
curtails unnecessary moves to substantial level. Pheromones
are updated only on the links of path found; this enhances
the prominence of feasible path over entire grid.
The probabilistic formula in the new approach contains
an essentially important part that is history of recent
movement directions, due to which undesired movements of
robot are avoided and thus faster convergence can be
achieved. The new probabilistic formula with added term
PMij is given as follows
()()
()
()
, if
0, if
F
ij ij ij
ij ik k
kN
jN
τη PM
Pτη
jN
∈
∈
⎧⎛⎞
⎪⎜⎟
∗
⎪⎜⎟
=⎨⎝⎠
⎪
⎪∉
⎩
∑
αβ
αβ
(2)
where
τ
ij and
η
ij are the pheromone and heuristic values
respectively on link (i, j),
α
and
β
are control parameters of
τ
and
η
respectively.
η
ij is the reciprocal of distance of node
j form goal node as in equation (3).
1
(, )
j
ηd j goal
= (3)
The distance considered here is the Euclidean distance
between the two nodes and computed from equation (4)
()( )
22
(, ) j goal j goal
d j goal x x y y=− +− (4)
NF is the set of nodes reachable and adjacent to the current
node i (as explained in section 1).
PM, probability multiplication factor (PMF), is a discrete
vector of 8 dimensions, each dimension corresponds to one
directional movement and value stored in each dimension
represents the influence of previous directional movement
on next directional movement. It fulfils the algorithm’s
requirement of considering the historical data for directional
movement in probabilistic computation for selection of next
node. PMij is PMF in direction from node i to j. Initially the
values in each dimension of 8-tuple is set to 1 and as soon
as the ant changes its direction of movement on grid the
values of PM are updated. The updation is based on empiric
evaluation as follows
1 The value of PM(i) is set 0.1 if i is opposite to the
current directional movement of robot, where i can take
discrete values from 1 to 8.
2 PM(i) is set to 0.3 if i is opposite left or right to the
current directional movement, that is,
‘( 3)mod9’id=+ or ‘( 5)mod9’,id=+ where d is the
value of current directional movement.
3 PM(i) is set to 0.9 if i is opposite to second last or front
left and front right of opposite to second last movement
directions.
4 The value is set to 1 for remaining direction of eight.
5 If any direction is subjected to multiple assignments for
same updation step, minimum value of the two is
considered.
Consider the movement in Figure 3. Vector PM at point 1,
the starting state, is <1, 1, 1, 1, 1, 1, 1, 1>, at point 2 it is
reset to <1, 1, 1, 1, 1, 0.3, 0.1, 0.3> and at point 3 it is again
reset to <1, 1, 1, 0.3, 0.1, 0.3, 0.9, 0.9>.
In order to increase the significance of feasible path, we
propose another major change in ACO approach as a new
pheromone updation scheme. In simple ACO, pheromone
evaporation for each link is cumbersome and increases the
time with great extent. In the modified approach, each time
an ant finds a solution, the pheromone deposition and
evaporation takes place concurrently on the links of path
found. The pheromone levels are updated in such a way and
the optimal path links have a slightly higher pheromone
values than any other link on the grid. It ensures the faster
convergence and avoidance of local minima. The updation
is governed by applying the following formula
(1 ) Δ
ij ij ij
τρττ=− + (5)
where
ρ
is the evaporation factor, 0 ≤
ρ
≤ 1. Δ
τ
ij is the
pheromone value deposited by the ant on link from node
i to j. Δ
τ
ij is dependent on the path length and number of
turns on the path. In the current implementation value of
Δ
τ
ij is determined by equation (6)
_
Δ___
ij Min length
τPath length Number of turns
=∗ (6)
where Min_length is the minimum possible length of path
on the grid without obstacles, Path_length is the length of
path found in the current iteration and Number_of_turns is
the number of turns on the path. The steps of the proposed
algorithm are explained in the flowchart in Figure 5(a). The
stored results of this part of the algorithm are used in next
phase.

Mobile robot path planning with modified ant colony optimisation 109
Figure 3 (a) Movement of robot on grid (b) PMFs at point 1
(c) PMFs at point 1 (d) PMFs at point 1 (see online
version for colours)
(a)
(b)
(c)
(d)
2.3 Path smoothing
The path found in the first phase of the algorithms, the
modified ACO approach, is optimal but there are
possibilities of refinement to reduce the effort employed by
the robot. If the number of turns on the path is high and
other routes with same length with less number of turns are
available then path smoothing phase pick one of these
available paths. This method works by traversing the path
that has been found in the previous phase and removes
unnecessary turnings of this path. Time elapsed in this
phase of the algorithm is negligible as compared to previous
phase since it has to traverse just the solution that is very
small in comparison of the whole grid. Figure 4 shows two
paths that are of similar length but the effort required by the
robot is different for path in Figures 4(a) and 4(b) because
of turnings. Path in Figure 4(b), which is the result
of applying path smoothing phase, is preferred over
Figure 4(a), which is the result of previous phase.
Figure 4 (a) Result of ACO approach (b) After applying path
smoothing (see online version for colours)
(a)
(b)
The flowchart in Figure 5(b) explains the complete
algorithmic steps of the path smoothing phase. Input to this
phase is output of previous phase of implementation. The
complete algorithm proposed in this paper comprises two
parts explained in previous two sections to achieve overall
efficiency and robustness towards robot path planning.
3 Simulation and results
In order to evaluate the performance of the proposed
approach, we conducted several experiments on grids of
different dimensions and with varying obstacle positions.
The experiments are conducted on MATLAB. In this
simulation, the dynamic environment has been elicited by
introducing new obstacles or changing the obstacle
orientations and positions while the ant is finding path to its
goal. The navigation grid is implemented in the form of a
matrix of size n × n, whose each element can be accessed
randomly in unit time. A value 0 in the matrix represents the
corresponding grid cell acquired by some obstacle and a
value 1 is the free space on grid. An instance of such
implementation is shown in Figure 6 for square grid of size
6 × 6.

110 U. Rajput and M. Kumari
Several simulations have been performed to compare the
results of the currents implementation with SACOdm, as
explained in Garcia et al. (2009). On the empty grids of
various sizes (30 × 30, 40 × 40 and 100 × 100), single ant
finds the optimal solution within just one iteration. A
simulation of the algorithm on 40 × 40 grid is shown in
Figure 7. Even when the obstacles of the different sizes and
complex distributions are introduced on the grid the time
(and iterations) needed to find optimal path increases
almost linearly and not drastically. The results are shown in
Table 1.
Figure 5 Flowchart of algorithm, (a) first (modified ACO) phase
(b) second (path smoothing) phase (see online version
for colours)
(a)
Figure 5 Flowchart of algorithm, (a) first (modified ACO) phase
(b) second (path smoothing) phase (continued)
(see online version for colours)
(b)
Figure 6 (a) Grid with obstacles (b) Matrix representation of the
grid in (a) (see online version for colours)
(a) (b)

Mobile robot path planning with modified ant colony optimisation 111
Figure 7 Path from node 1 to 700 on a grid of 40 × 40
(see online version for colours)
In order to check the robustness of proposed scheme
extensive experiments have been performed with various
value combinations of parameters. Result of one such
experiment is depicted by the graph in Figure 8. As shown
in Figure 8, the value of
ρ
, the evaporation rate, changes
from 0.1 to 0.9, while
α
= 0.556 and
β
= 0.553. Graph is
plotted for ten different values of
ρ
versus the number of
iterations needed to find the optimal path and optimal
iterations are obtained for a value of
ρ
= 0.18. Another
experiment, Figure 9 shows the variation of number of turns
on the optimal path found in previous phase with respect to
progress of smoothing phase. As iterations in the smoothing
phase advance, the number of turns is substantially reduced
to a constant value. Table 1 compares the results of
proposed modified ACO and ACO implementation given in
0Garcia et al. (2009). The result given in the table clearly
indicates the proposed scheme performs approximately four
times better than SACOdm (Garcia et al., 2009).
Figure 8 Number of Iterations for various values of
ρ
(evaporation factor) (see online version for colours)
Figure 9 Number of turns on path as smoothing phase progresses (see online version for colours)

112 U. Rajput and M. Kumari
Table 1 Comparative results of basic and modified ACO approaches
Grid size Epochs Time (sec.)
SACOdm
50 × 50 20 0.5 2 1 12.08
Modified ACO
30 × 30 27 0.18
0.556 0.553 2.18
50 × 50 38 0.18
0.556 0.553 3.13
100 × 100 63 0.18
0.556 0.553 4.01
Source: Garcia et al. (2009)
Figure 10 (a) Initially the grid was empty, robot avoids the
obstacle and finds the new path when obstacle are
added dynamically (b) Another obstacle was added
while robot was moving on the second path found
(c) Robot finds final updated optimal path (see online
version for colours)
(a)
(b)
(c)
In order to verify the aptness of modified ACO approach in
dynamic environment, we conducted several experiments.
Figure 10 shows the circumstances on a 100 × 100 grid
when new obstacles are added dynamically. Ant also
updates the path globally after reaching the goal for some
later movements, as in Figure 10(c). The state of the
environment shown in Figure 10(c) is reached in 79 epochs
and 4.32 seconds, which is not much of the overhead for
adaptive solution for dynamic environments.
4 Conclusions
This paper is an effort to match the complexity of robot path
planning and navigation in dynamic unknown environment
by exploiting the local information-based heuristic. We
have proposed a modified ACO-based approach for path
planning and to further refine the near optimal solution with
respect to robot’s moments we have used path smoothing.
The major modification proposed in this paper are the
introduction of PMF in ACO technique, which induces the
effect of recent directional movement history, and the
pheromone updation scheme, that reduces the computation
to a great extent by just updating the pheromone values on
path link and not on the entire grid. Path smoothing simply
reduces number of undue turning of robot on found path.
The inclusion of PMF in the probabilistic path selection
formula in ACO proved to be beneficial for avoiding
unnecessary and exhaustive searches on grid. It constraints
the exploration space available to robot to the feasible
solutions without inducing much complexity in the
algorithm. With proposed new pheromone updation scheme,
a novel way of updating the pheromones is presented that
does not update the pheromone levels on the entire grid but
only on the links of path found. The next phase of
algorithm, path smoothing module reduces the physical
effort of robot, which is considered to be a significant factor
for efficiency in real world implementation, by reducing the
number of turns and thus finding and alternate smoother
path. The proposed scheme provides substantial amount of
adaptation to the changing environment which is shown by
results.

Mobile robot path planning with modified ant colony optimisation 113
The evaluation of the algorithm in various simulations
proved to be almost four times faster than the previously
known efficient implementation (Garcia et al., 2009). The
proposed algorithm can be further extended towards the
improvement in considering the directional movement
history, like the updation of PMF values can be
probabilistic instead of empirical learned values. It is yet to
be seen the extension and application of the given scheme in
multi robot domain.
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