This document compares three popular path planning algorithms: A*, greedy best first search, and jump point search. It implements the algorithms in MATLAB using grid-based maps with random start/goal points and static obstacles. The algorithms are evaluated based on computational complexity, time complexity, and space complexity. Jump point search generally has the best performance out of the three algorithms as it can make long jumps along straight lines in the grid, exploring fewer nodes than A*.

1. COMPARISION OF VARIOUS POPULAR PATH PLANNING ALGORITHMS
1Koyya Shiva Karthik Reddy, 2Vishnunandan Venkatesh
Department of Electrical and Electronics Engineering
Rochester institute of Technology
ABSTARCT
Path planning is a complex task where usually the
robot has to consider many conditions in the
environment apart from just following a map to reach
the desired destination/goal. In the current project
various popular path planning algorithms are compared
in terms of their complexities of time and space. The
algorithms were implemented in a known environment
based upon grid based maps in MATLAB with random
goal, start and obstacles as nodes of the matrix. Three
algorithms were choose, A* algorithm as the baseline
which was then compared against greedy best first
search and joint point search.
Keywords: A*, Greedy best first search, Jump point
search,path planning
INTRODUCTION
The paper is divided into IV section the I section talks
about the previous work and related research in this
field, the second section will talk about all 3 algorithm
we are implementing , the III section will talk about the
future work that needs to be done and IV section will
discuss the result of the work achieved.
Before talking about the implementation of the
algorithms the following assumptions are made by us
towards solving our problem:
 Point Robot with Ideal Localization 
 Workspace is bounded and known 
 Static source, goal 
 Number of obstacles are finite and static 
Our path planning algorithms implement grid based
maps. Grid-based approaches overlay a grid on
configuration space, and assume each configuration is
identified with a grid point.
I. PREVIOUS RESEARCH IN THE FIELD
1. Hierarchical A-Star Algorithm for Big Map
Navigation in Special Areas
This paper addresses the use of A* in the case
for path planning of a large map. The paper
talks about a variation of A* called the
hierarchical A* algorithm where it basically
divides large maps into layers of smaller maps
and then applies the A* algorithm to the
smaller maps individually to find the shortest
path. Then all the shortest paths of the smaller
maps are arranged in hierarchy to obtain the
best path for the entire map. This method is
useful when the map is a country or a state etc.
In our case we don't have a very large map. Our
map is limited to an indoor environment as we
plan to implement the system to a mobile robot.
So we don't need to implement hierarchical A*.
Apart from this crucial point the algorithm we
plan to implement end of the day is the Jump
Point Search which would be much efficient
than the A*.
2. Path Planning of Automated Guided
Vehicles Based on Improved A-Star
Algorithm
The motive behind this paper is to implement
A* in Automated Guided Vehicles. The
improvement over regular A* in the paper is
the removal of diagonal paths. An obstacle
avoidance technique is also implemented where
the AGV (Automated Guided Vehicle) avoids
collision with obstacles. Technically the
improved algorithm is the A* without diagonal
movements.
Our Base algorithm is very similar to this case
where since we look to implement the path
planning algorithm in a mobile robot we also
excluded diagonal paths (i.e. paths are only in
the left, right, up, down directions and don’t
move diagonally across nodes in the map.). Our
algorithm also avoids obstacles. The advantage
we plan to present is that we will implement
the Jump point search which will be much
efficient than regular A* algorithm.

2. 3. Path finding of 2D & 3D Game Real-Time
Strategy with Depth Direction A*Algorithm
for Multi-Layer
A comparison of all the various path planning
algorithms such as A*, Depth First Search,
Iterative Deepening, Breadth First Search,
Dijkstra’s Algorithm, Best First Search, A-Star
Algorithm (A*), Iterative Deepening A*.
Besides, the paper proposes Depth Direction
A*.
Depth Direction A* is very similar to our
proposed Jump Point Search and with the help
of this paper we see proof that Depth Direction
A* is faster than a* although it evaluates more
nodes. This is also a proof that Jump Point
Search is faster than A* as it is very similar to
Depth Direction A*.
4. Path Planning for Virtual Human Motion
Using Improved A* Algorithm
This paper utilises weights to reduce search
steps and to ignore nodes that have obstacles.
This in turn reduces the time. The
improvement is the adding of weights.
This concept of using weights to ignore nodes
with obstacles is similar to how we ignore
obstacles when we calculate the value of
F=G+H and thereby we save time. We do this
by giving all our obstacles a value of infinity in
the map. During the search whenever any node
in the map has a value of infinity the obstacle is
detected in the map. Thus it is ignored with
logical conditions. The method implemented in
the above paper is also similarly implemented
in ours.
5. Optimization using Boundary Lookup
Jump Point Search
One of the crucial information that significantly
differentiates our project and the above paper is
that in the paper above the obstacles are
dynamic in the map. The search method used is
Jump point search. Since obstacles are dynamic
for every instance of real time, the path
planning algorithm is implemented with the
map being updated at those instances of real
time. Hence when a map is stored in memory
during one implementation of the Jump Point
Search then at the next instance of time the
current map is deleted from the cache and a
new map is made and the algorithm is
implemented again.
In our implementation of the project the map
consists of static obstacles. There may be real
time obstacles that are dynamic along the path
but these obstacles don’t change the map. Only
the static obstacles are taken in the map . A
simple obstacle avoider is used in the execution
avoiding real time dynamic obstacles without
making any changes to the map.
6. Sensor-Based Path-Planning Algorithms
for a Nonholonomic Mobile Robot
A nonholonomic system in physics and
mathematics is a system whose state depends
on the path taken in order to achieve it. Thus it
is basically a path planning system. In this
paper depth first search and best first search are
used to implement path planning for a mobile
robot. Sensors are used to avoid obstacles along
the path. Depth first search and greedy best
first search are okay to implement when the
map is an indoor based map and is not very
complex. In cases where the map is complex
the algorithm takes a lot of time to find the path
Our proposed project will be very fast when
compared to the above paper's proposed system
as we use a much efficient path planning
algorithm which is the Jump Point Search.
II. ALGORITHMS EXPLANATION
A. A* algorithm: A* is graph search algorithm
that finds the least-cost path from a given
initial node to one goal node (out of one or
more possible goals). It uses a distance-
plus-cost heuristic function (usually
denoted f(x)) to determine the order in
which the search visits nodes in the tree.
The f(x) is the sum of the h(x) heuristic
which is the distance of any current node
from the goal and g(x) which is the
distance of the current node from the
start.
A-Star Algorithm Pseudo Code
Create Start Node with Current
Position Add Start Node to
Queue
While Queue Not Empty
Sort Node Queue by f(N) Value in Ascending
Get First Node From Queue call Node “N”
If N is Goal Then Found and Exit
Loop Else

3. Mark N Node as Visited Expand each reachable Node
from N call Node
“Next N” f(Next N) = g(Next N) + h(Next N) Loop
FIGURE 1 A*:
B. Greedy best first search: The Best-First-Search
algorithm works in a similar way, except that it
has some estimate or called a heuristic of how
far from the goal any vertex is. Instead of
selecting the vertex closest to the starting point,
it selects the vertex closest to the goal.
Best First Search Pseudo Code
Create Start Node with Current Position
Add Start Node to Queue
While Queue Not Empty
Sort Node Queue by Cost Value in Ascending
Get First Node From Queue call Node “N”
If N is Goal Then Found and Exit Loop
Else
Mark N Node as Visited
Expand each reachable Node from N call Node “Next N”
Loop
FIGURE 2 GREEDY
C. Jump point search: Jump point search is an
optimization to the A* search algorithm path
finding algorithm for uniform-cost grids. It
reduces symmetries in the search procedure by
means of graph pruning, eliminating certain
nodes in the grid based on assumptions that can
be made about the current node's neighbours, as
long as certain conditions relating to the grid
are satisfied. As a result, the algorithm can
consider long jumps along straight (horizontal,
vertical and diagonal) lines in the grid , rather
than the small steps from one grid position to
the next as in A*.
FIGURE 3 JUMP POINT SEARCH
III. RESULTS
The results of any path planning algorithm
can be compared in terms of the 3 factors
1. Computational complexity:
Computational complexity of any
algorithm is described in terms of
number of resources the algorithm used
to reach the desired result the resources
can be CPU time or memory or other
resources.
2. Time complexity: time complexity is
defined as the time taken by the
algorithm to find the path between the
start and the goal.
3. Space complexity: space complexity is
the amount of nodes or units it had to
explore before reaching the goal, more
the nodes explored more the memory
utilization.
For the obstacle course as shown in figure
1, 2 and 3 all the three algorithms were
compared in a 7x7 grid the size 7x7 was
choose so that the path can easily be
visualized . The table 1 below shows the
results for all three algorithms.

4. FIGURE1
The algorithms were also compared for
maps as large 5000x5000 so as to test the
limits, the algorithms worked fine in those
maps as well, even with random obstacle
path.
A thing that should be noted here is that the
results in the table show that the jump point
search has the best result but it may not be
the case every time in a few special cases
greedy and A* might overpower jump
point search.
Appendix 1 shows the results of the
implementations.
IV. FUTURE WORK
Path planning is not a new technology it
has been extensively researched for more
than past 30 years but the recent
development are mainly focused to
improve the computational complexity of
these algorithms. As a future extension of
this project the algorithms can be further
optimised for better performance and be
can tested on a mobile robot in a real
environment with dynamic obstacle course.
Real time implementation and tackling of
problems like SLAM will be a good future
prospect for this project.
V. REFRENCES
[1]. Haifeng Wang; Jiawei Zhou; Guifeng
Zheng; Yun Liang, "HAS: Hierarchical A-
Star Algorithm for Big Map Navigation in
Special Areas," in Digital Home (ICDH),
2014 5th International Conference on ,
vol., no., pp.222-225, 28-30 Nov. 2014
[2]. Chunbao Wang; Lin Wang; Jian Qin;
Zhengzhi Wu; Lihong Duan; Zhongqiu Li;
Mequn Cao; Xicui Ou; Xia Su; Weiguang
Li; Zhijiang Lu; Mengjie Li; Yulong
Wang; Jianjun Long; Meiling Huang;
Yinghong Li; Qiuhong Wang, "Path
planning of automated guided vehicles
based on improved A-Star algorithm,"
in Information and Automation, 2015 IEEE
International Conference on , vol., no.,
pp.2071-2076, 8-10 Aug. 2015
[3]. Khantanapoka, K.; Chinnasarn, K.,
"Pathfinding of 2D & 3D game real-time
strategy with depth direction A∗ algorithm
for multi-layer," in Natural Language
Processing, 2009. SNLP '09. Eighth
International Symposium on , vol., no.,
pp.184-188, 20-22 Oct. 2009
[4]. Junfeng Yao; Chao Lin; Xiaobiao Xie;
Wang, A.J.; Chih-Cheng Hung, "Path
Planning for Virtual Human Motion Using
Improved A* Star Algorithm,"
in Information Technology: New
Generations (ITNG), 2010 Seventh
International Conference on , vol., no.,
pp.1154-1158, 12-14 April 2010
[5]. Traish, J.; Tulip, J.; Moore, W.,
"Optimization using Boundary Lookup
Jump Point Search," in Computational
Intelligence and AI in Games, IEEE
Transactions on ,vol.PP,no.99, pp.1-1

5. APPENDIX 1