P1254325976lsUjI

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Singapore Robotics Games 04 Symposium Title An
Efficient Maze Solving Algorithm for a
Micromouse Presented by Mr. Hui Tin Fat
htf_at_np.edu.sg Alpha Centre Ngee Ann Polytechnic
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1. Abstract In a competition, the performance
of a micromouse is largely dependent on two
factors. They are the maze searching ability and
the maximum maze cruising speed of a micromouse.
The maze searching ability of a micromouse
reflects on the elapsed time for it to reach the
goal and the elapsed time for it to finalize the
dash path. The dash path is crucial for a
micromouse to score its fastest runtime. This
paper demonstrates a method of using a simple
expert algorithm to complement the Bellman
flooding algorithm to tackle a maze-solving
problem. Considerations are given to a limited
on-board processing power and memory space.
Results from implementation and simulation of the
algorithm using for a competing micromouse are
presented.
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2. How to describe a Maze? A maze is formed by
a group of alleyways arranged in longitude and
transverse directions in an enclosed square
platform. The maximum length of a alleyway is 16
units and the minimum length is 1 unit. In a
maze, the alleyways will form the junctions when
the transverse and longitude meets, the dead ends
when the alleyway closes in one end, the loops
when a alleyway joins at the begin and end. All
the alleyways are assembled from walls and poles.
They are either made in plywood or plastics.
The maze starts at one of the four corner
squares and it finishes at one of the center 4
squares.
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3. A Sample Maze
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4. How to define the complexity of a maze? For
Human Brain The characteristics of human brain
is the sense of direction and the sense of
position are not strong. The brain is easily
confused by the similar environments. It is
difficult to identify the same location and
orientation. Therefore if a maze comprises of
many junctions, dead ends and loops. The maze is
considered a complex one for people. For
Micromouse Brain The micro-controller is able
to remember the orientation and position
correctly. This is due to the ability of software
algorithm and the retrieval from memory storage.
Therefore a maze with many junctions, dead
ends and loops is no longer difficult for the
micromouse to solve.
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5. How to define the complexity of a maze for a
micromouse to solve? When a maze comprises of
many long dead ends, it is considered as a
complex maze because the micromouse requires
extra-efforts to reach the goal and locates the
dash path between the start and goal. We can
evaluate the performance of a maze solving
algorithm by the number of backtracks carried
out by the micromouse. If there is less
backtrancks, it shows the algorithm more
efficient. In micromouse competition, the
performance does not only judge on how soon the
robot reached the goal but also how much time to
spend for locating the dash path. By counting the
number of backtracks carried out in both tasks,
we can judge whether the algorithm is good or
not.
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7. Bellman Flooding Algorithm Bellman flooding
algorithm is a common maze solver using by the
contestants. The standard Bellman algorithm
solves a given maze for the shortest route but
this is not always the fastest. Many contestants
modify the algorithm which floods with time
instead of distance. There will be different
time constants assigned to the flooding array
according to the movement to reach the new square
such as a straight, a 900 turn or a 1800 turn.
The Modified Bellman Flooding Algorithm is
implemented as following a) There is only
boundary walls along the outside perimeter. No
internal walls. b) The target square is number
0. The squares joining the target square(s), -
front, right and left with no separating walls,
are numbered by the time constant taken to travel
there from the target square.
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7. Bellman Flooding Algorithm (continued) c)
The squares, front, right and left joining the
above squares, with no separating walls, are also
numbered by the time constant taken to travel
there from the target square. d) The c) process
will be continued until the flooding stops when
the square being renumbered is the current mouse
square. e) The mouse makes the fastest move from
the current mouse square by selecting the lowest
flooding number. f) If the flooding encounters a
situation where there are two possible routes,
with the same Bellman number, then the mouse will
select the route with the following priority as
straight first. Otherwise, the algorithm chooses
the route with lower flooding number.
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7. Bellman Flooding Algorithm (continued)
30
27
24
21
24
25
00
33
26
23
18
15
28
01
34
37
20
17
12
09
02
43
40
43
14
11
06
03
46
41
52
49
08
07
04
47
42
45
46
47
48
05
S
43
52
49
10
09
06
Bellman Flooding Array
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7. Bellman Flooding Algorithm (continued)
E
E
S
S
W
W
N
N
E
S
E
S
N
N
N
W
E
S
E
S
N
E
N
W
E
S
E
N
N
N
E
S
E
E
N
N
N
W
W
W
W
N
S
N
E
N
E
E
N
Bellman Direction Array
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7. Bellman Flooding Algorithm (continued)
Determine next square for micromouse
B
Instruct the micromouse to move to new square
Update wall information on move
Wait for micromouse to reach new square
A
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7. Bellman Flooding Algorithm (continued)
A
Has wall information Changed?
Yes
No
Re-calculate Bellman Flooding Array
Check Flooding direction
B
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8. Does Bellman Flooding Algorithm Work
Well? From the Bellman flow-chart, it is easily
to point out that every new wall information
update, the algorithm has to re-calculate again.
It may cause too much CPU time for a high speed
micormouse. To overcome this, a suggestion is
to re-calculate the flooding array only when it
really needs such as to obtain a back-track path
or a dash path. A simple expert algorithm is
proposed to resolve the micromouse movement when
it reaches a new square. An expert rule array is
used to determine the next move, front, right or
left. Since no calculation involved, this
algorithm only requires the minimum CPU time. It
is very effective for a fast speed micromouse.
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9. A Simple Expert Maze Solving Algorithm The
algorithm assumes each square in the maze is a
junction. A pre-determined rule will be assigned
to the square. If the micromouse reaches this
square, the rule will be draw from the expert
rule assay of this square to decide the next
move. The expert rules are derived from the
movement, front, right, back and left.according
to the priority of checking the openings in the
square. There are total 24 rules. They are
North-East-South-West, North-East-West-South,
North-South-East-West, North-South-West-East,
North-West-East-South, North-West-South-East, and
etc. The assignment of the top priority of
expert rules to each square can be done according
to the design of past competition mazes. The
second and third priorities are assigned either
according to the outcome of the movement that
leads to the goal or starting square.
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9. A Simple Expert Maze Solving Algorithm
(continued)
2
3
4
1
5
North
0
6
7
Expert rules assignment for the Algorithm
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9. A Simple Expert Maze Solving Algorithm
(continued)
Determine next square for micromouse
B
Instruct the micromouse to move to new square
Update wall information on move
Wait for micromouse to reach new square
A
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9. A Simple Expert Maze Solving Algorithm
(continued)
A
Has wall information Changed?
Yes
Yes
Re-calculate Bellman Flooding Array
Back-track or dash run
No
No
Check Flooding direction
Check expert rule direction
B
B
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10. Conclusion The Expert Rule Maze Solving
Algorithm is applied in the school micromouse kit
that performs outstandingly. It reduces the
paused time whenever the micromouse reaches new
junction square. The values of time constants
assigned for the flooding array are reduced to 1
for the diagonal dash path. But it requires a
software to covert the dash path from curve turns
to diagonal turns. My experience in the
micromouse project is the speed of micromouse
playing a vital role beside the maze-solving
algorithm for winning the championship title in a
competition.
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Thank You!