International Journal of Computer Applications (0975 – 8887) Volume 56– No.5, October 2012

Design and Implementation of a Robot for Maze-Solving using Flood-Fill Algorithm Ibrahim Elshamarka

Abu Bakar Sayuti Saman

Department of Electrical and Electronic Engineering Universiti Teknologi PETRONAS 31750 Seri Iskandar Malaysia

Department of Electrical and Electronic Engineering Universiti Teknologi PETRONAS 31750 Seri Iskandar Malaysia

ABSTRACT

2. RELATED WORKS

Autonomous navigation is an important feature that allows a mobile robot to independently move from a point to another without an intervention from a human operator. Autonomous navigation within an unknown area requires the robot to explore, localize and map its surrounding. By solving a maze, the pertaining algorithms and behavior of the robot can be studied and improved upon. This paper describes an implementation of a maze-solving robot designed to solve a maze based on the flood-fill algorithm. Detection of walls and opening in the maze were done using ultrasonic range-finders. Algorithm for straight-line correction was based on PI(D) controller. The robot was able to learn the maze, find all possible routes and solve it using the shortest one.

General Terms Autonomous navigation, maze-solving, flood-fill algorithm, ultrasonic sensor, PI(D) controller.

Keywords Mobile robot, obstacle avoidance, microcontroller.

1. INTRODUCTION In mobile robotics, autonomous navigation is an important feature because it allows the robot to independently move from a point to another without a tele-operator. Numerous techniques and algorithms have been developed for this purpose, each having their own merits and shortcomings [13,8]. Maze-solving – although artificial in terms of the confine that the robot it subjected to – is a structured technique and controlled implementation of autonomous navigation which is sometimes preferable in studying specific aspect of the problem [1]. This paper discusses an implementation of a small size mobile robot designed to solve a maze based on the flood-fill algorithm. The maze-solving task is similar to the ones in the MicroMouse competition where robots compete on solving a maze in the least time possible and using the most efficient way. A robot must navigate from a corner of a maze to the center as quickly as possible. It knows where the starting location is and where the target location is, but it does not have any information about the obstacles between the two. The maze is normally composed of 256 square cells, where the size each cell is about 18 cm × 18cm. The cells are arranged to form a 16 row × 16 column maze. The starting location of the maze is on one of the cells at its corners, and the target location is formed by four cells at the center of the maze. Only one cell is opened for entrance. The requirements of maze walls and support platform are provided in the IEEE standard [2,3].

Dang and Song proposed “An Efficient Algorithm for Robot Maze-Solving” which was based on flood-fill algorithm but improved by reducing some steps not needed in certain cases. As there are channels in the maze where the robot is forced to go only straight forward, when the robot is inside these channels, it does not need to perform all four steps of mazesolving which is updating the wall, flooding the maze, determining which turn to be taken and moving to the next cell. To reduce execution time, it only flood the maze when there is a turn [4]. “Partition-central Algorithm” is another maze-solving algorithm where the standard 16×16 unit maze is virtually divided into twelve partitions. The robot uses data such as its direction and its current location to change between exploring rules to save more time and optimize the solving process. A simulation was developed to verify the algorithm. Test results show that partition–central algorithm has higher average efficiency when compared to other algorithms [5]. In another study, the discretely assigned potential levels were discussed. Using these potential levels, the robot can effectively make autonomous decisions to reach the goal. It demonstrates the method of assigning and controlling these artificial potentials to provide the most optimized path choices while keeping the integrity of the potentials. The basic algorithm is improved by saving information from previous decisions that have been made [6].

3. THE MAZE AND THE ROBOT The maze designed for the robot to solve is of the size of 6×6 cells as shown in Figure 1. The actual maze constructed, as shown in Figure 2, has a physical size of about 2.25 m2. The maze was designed so that it will have two paths in order for it to be solved. One of the paths is longer than the other. The robot (Figure 3) must decide which one of the paths is shorter and solve the maze through that path.

Fig 1: Design of the maze

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International Journal of Computer Applications (0975 – 8887) Volume 56– No.5, October 2012 4.2 Updating The Wall Data Before the robot decides where it wants to move to, it has to check if it is surrounded by any walls in any of the three directions: right, left and front. The robot reads the distance of any obstacle at each direction and check if the distance in each is more than 20 cm. The ones that exceed 20 cm are updated as “wall” on their respective side. This is illustrated by the flow chart in Figure 5. For the robot to update the correct wall data, it has to know first which direction it is facing. There are four orientations for the robot to be facing: north, south, east or west, as shown in Figure 6. Initial orientation was set at start and the robot keeps tracking of any changes. Let Ultrasonic_Right = 0, Ultrasonic_Left = 0, Ultrasonic_Front = 0

Fig 2: The maze Read Ultrasonic_Right, Ultrasonic_Left, Ultrasonic_Front

Is Ultrasonic_Right less than 20 cm

Yes

Update Wall to the Right

Yes

Update Wall to the Left

No

Is Ultrasonic_Left less than 20 cm

No

Fig 3: The robot

Is Ultrasonic_Front less than 20 cm

Yes

Update Wall Infront

No

4. ALGORITHM Choosing an algorithm for the maze robot is critical in solving the maze. In this exercise, flood-fill algorithm was chosen to solve the maze due to its balance in efficiency and complexity. There are four main steps in the algorithm: Mapping, Flooding, Updating and Turning [2, 6-7]; which are described in the following sub-sections.

Done Updating Walls

Fig 5: Flowchart for updating wall location at each cell

4.1 Mapping The Maze For the robot to be able to solve the maze, it has to know how big the maze is and virtually divides them into certain number of cells that can be used later in calculating the shortest path to the destination. In this project, a maze of 6×6 cells is used. Between two cells there can be a wall. Thus, in a row of six cells, there are five walls in between them. In total, in a row, there are eleven units of cells or walls. This information is stored in an 11×11 array, as shown in Figure 4. The white units are the cells which the robot can be placed inside. The orange units are the locations for potential walls. The black units indicate wall intersections which are ignored by the algorithm. The external borders of the maze are also ignored as they are fixed boundaries of the maze. Both cells (white) and walls (orange) are set to zero in as their initial conditions.

Fig 6: Change in array locations to update the wall based on robot orientation

4.3 Flooding The Maze After updating the wall information for the current cell, the robot starts to flood the matrix to find the shortest path to the goal [6]. The flow chart in Figure 7 shows how the robot floods the matrix and makes decision by checking one cell at a time. It does the same for all the cells and keeps repeating for several times until a path between the robot and the goal is found. The algorithm assigns a value to each cell based on how far it is from the destination cell. Based on that, the goal cell gets a value of 1. If the robot is standing on a cell with a value of 4, it means it will take the robot 3 steps (3 cells) to reach the destination cell. The algorithm assumes that the robot can’t move diagonally and it only can make 90 degree turns.

Fig 4: Maze-mapping Array

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International Journal of Computer Applications (0975 – 8887) Volume 56– No.5, October 2012 Define location of Goal cell and set it to = 1 x and y start from 0 to 10 with increment of 2 x is row number and y is column number

If Cell (x,y) is not a Wall AND not a Goal

5.1 Control board Processing power is provided by an Arduino board. The board is powered by ATmega328 which is a microcontroller with 32 KB flash memory for storing the code. The microcontroller can be programmed by Clanguage-like “processing programming language.”

Yes

5.2 Obstacle Sensors

Check cells at north, south, east, and west of cell (x,y)

Three ultrasonic distance sensors were placed on the right, the left and in front of the robot. Each ultrasonic sensor measures the distance between the robot and any obstacle in millimeters.

No

If boundary node has a number in it and cell (x,y) is robot location

No

Yes path found! find the boundary node with the smallest number return that direction to robot controller

If boundry node has a number in it

Yes No Cell (x,y) = number inside boundary node + 1

END

Fig 7: Flowchart for flooding the maze and finding the path

5.3 Wheel Rotation Encoder Each wheel is equipped with a sensor which is basically a pair of infra-red transmitter and receiver. By counting the holes in the wheel and knowing the wheel diameter, the robot can encode the distance traveled. In this case, there are eight holes in the wheel and the wheel diameter is 7.9 cm. That means the distanced traveled is 24.8 cm (7.9×π) when the wheel rotates a full cycle. Figure 9 shows the counting based on one of the wheel rotation sensors. High sensor reading is set to one and low reading is set to zero. The frame in black represent a detection of one cell moved, which is 16 toggles between ones and zeros.

4.4 Checking for Turns

Degrees 0 90 180 270

Turn needed No turn Turn Right Turn back Turn left

5. HARDWARE DESIGN The robot has a length of 22 cm, a width of 15 cm and a height of 15 cm. As illustrated in Fig 1, the robot is equipped with three ultrasonic distance sensors facing front, left and right to scan the area ahead for obstacles and specifically to detect for walls. A wheel rotation encoder is placed near each wheel so that the extend of how much the wheel is rotating can be detected. With the diameter of the wheel is known, the rotation can converted into distance traveled.

Encoder Mapping

700

1.2

600

1

500 0.8 400 0.6 300 0.4

200 0.2 100

0

0 0

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100

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350 -0.2

Time

Encoder Mapping 1 or 0

Table 1. Values returned by the algorithm and its respective turn

Encoder Input and Mapping Encoder Detection

Amount of IR detected

After the robot has decided which direction it will go next, it returns the amount of degrees it needs to turn in order to go to the cell intended (Table 1). After turning the robot, the algorithm updates the new orientation of the robot, i.e. facing north, south, east or west.

Fig 2: Wheel Rotation Detection Curve

5.4 Motor Drive The two wheels are driven by a pair of servo motors which are interfaced to the Arduino board through an L293D dual Hbridge. An L293D can drive two servo motors or two DC motors -- which can be controlled in both clockwise and counter clockwise direction. It has output current of 600 mA and peak output current of 1.2A per channel. The in-built diodes protect the circuit from back EMF (Electro Magnetic Force) at the outputs. Supply voltage range vary from 4.5 V to 36 V, making L293D a flexible choice for a motor driver.

6. ERROR DETECTION AND CORRECTION 6.1 Moving in a Straight Line with a PI(D) Controller

Fig 1: The robot design

Due to the fact that the motors spin at slightly different speed even when they have been calibrated, the robot tends to drift to one side when it moves. For the robot to stay in the middle of the corridor inside the maze, a PI controller was used to fix the errors based on the inputs from the ultrasonic sensors. By applying Ziegler-Nichols tuning method on the difference between the distance detected by the left and right sensors [8]. With P-control, the ultimate gain, Ku = 4 and the ultimate

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International Journal of Computer Applications (0975 – 8887) Volume 56– No.5, October 2012

Table 1. Closed-Loop Calculations of Kp, Ti, Td

600 500

Kp

Ti

Td

P control

2

-

-

PI control

1.818

0.7445

-

PID control

2.353

0.4467

0.11167

400

300 200

100

After testing each controller and manually tuning the gain parameters, PI controller was chosen for its smooth and fast response with Kp= 1.818 and Ti = 0.4.

40

50

20 40

0

30

-20 -40

20

-60 10 -80 0 0

20

40

60

80

100

120

140

160

0 1

501

1001

1501

2001

2501

3001

Time Fig 5: Wheel rotation encoder readings for 360º

6.3 Ultrasonic Sensor Readings

Output

180

200 -100

-10

PWM PI Output

Input - Difference between right and left sensor in mm

PI controller with P= 1.818 I = 4 Input

360 Degrees Rotaion 700

Encoder analogue reading

period, Pu = 0.893. Table 1 shows the pertinent values derived for P, PI and PID controls.

-120

-20

-140

Fig 3: PI controller response

6.1.1 Choosing input for the PI(D) controller At any one cell, relative to the walls surrounding the robot, there are four cases. The robot can be either between two walls, one wall on the right side, one wall on the left side or no wall on both sides This is illustrated in Fig 4. For all cases, the PI controller tries to keep the robot in the middle. When the robot is in the middle, it is approximately 8 cm away from each wall. In case the robot does not detect a wall on its right or left side, the robot uses the wheel rotation encoder reading to move in straight line. It counts the number of toggles in both right and left encoder and compares them with each other.

As the ultrasonic sensors were exhibiting some irregular behavior when the distance detected is below 2 cm, extra tests were done to find the range of the correct readings. The robot was set to move straight with the PI controller and the readings of both left and right sensors were recorded. As shown in Fig 6, 1680 readings were recorded with neglecting the readings that occurred less than 30 times. The highest occurrence was the value of 161 millimeters which occurred 1344 times. Based on that, the value of each sensor was chosen to be 80 mm for the robot to be in the middle between the two walls. Another set of tests were done to find the accurate range for each sensor alone. The robot was randomly moved away from and close to a wall. 3680 readings were recorded with neglecting the readings that occurred less than 30 times. Fig 7 shows that most of the occurrences happened at the values of 34 and 127. Based on that, the accepted range of readings is set between 34 and 127. Any value outside this range is neglected.

Fig 4: Controller input in the three cases

6.2 Turning Left or Right Using Wheel Rotation Encoders There are three types of turning that the robot can make. It can either turn 90 degrees to the right, 90 degrees to the left or 180 degrees to the rear. A few tests were conducted to measure how many toggles the encoder will count before the robot turns 360 degrees with both wheels having the same speed and opposite direction of rotation. Based on the results it was determined that a 90 degrees turn would equal to 5 or 6 toggles counted and a 180 degree turn would be equal to 11 toggles.

Fig 6: Sensor readings for the summation of right and left sensors

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International Journal of Computer Applications (0975 – 8887) Volume 56– No.5, October 2012

7.2 Second Run After reaching the target cell in its first run, the robot starts heading back to its original starting point. It explores the whole maze while continue mapping it by updating the wall data and the distance each cell is from the target. Steps 1 to 9 and 19 to 22 are illustrated in Fig 9. It takes the robot 22 steps to reach the starting point while seeking for an alternative route so that the whole mapping matrix can be updated. Finished Wavefront: 1 Finished Wavefront: 2 Finished Wavefront: 3 . W. . W. . W. 6 W7 8 W. . W. 6 W7 8 W11 12 W15 . . . 5 W6 W. . Finished W. . Wavefront: 5 W6 W9 10 1 Finished W. . Wavefront: 5 W6 W9 10 1 W13 14 M M . MW. . W6 . M 5 . M 6 . MW. . W6 . M 5 . M 6 M 4 5 WR . . . W. 4 5 W.. 11 12 W 13 4 5 W. 15 . . . . 14 W13 x

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Fig 7: Sensor readings of the right sensor

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19 Finished Wavefront: W. . W. . W. . . . . W. W. . W. M M M W. . . WR . . . . . W. . . . . W. . . . M . . . W. . . . . . . . . . . . . . . W. . . . . . . x

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2 Finished Wavefront: 3 1 Finished Wavefront: 6 . . . . 3 . 4 . 5 . 6 . . . . 3 . 4 . 5 . 6 . . . . . . . . . . . . . 5 . . 3 . 2 . 3 . 4 . 5 . . 3 . 2 . 3 . 4 . 5 . . . . . . . . . . . . . 4 3 . 2 . G . 2 . 3 . 4 3 . 2 . G . 2 . 3 . 4 . . . . . . . . . . . . 5 4 . 3 . 2 . 3 . 4 . 5 R W3 . 2 . 3 . 4 . 5 . . . . . . . . . . . 6 R W4 . 3 . 4 . 5 . 6 . W4 . 3 . 4 . 5 . 6 . . . . . . . . . . . 7 . W5 . 4 . 5 . 6 . 7 . W5 . 4 . 5 . 6 . 7 4 Finished Wavefront: 5 Finished Wavefront: 6 6 . . . . 3 . 4 . 5 . 6 . . 4 . 3 . 4 . 5 . 6 . . . . . . . . . . . . 5 . . 3 . 2 . 3 . 4 . 5 . WR W2 . 3 . 4 . 5 . . . . . . . . . 4 . R WG . 2 . 3 . 4 . . WG . 2 . 3 . 4 . . . . . . . . . 5 . W. . 2 . 3 . 4 . 5 . W3 . 2 . 3 . 4 . 5 . . . . . . . . . . . 6 . W. . 3 . 4 . 5 . 6 . W4 . 3 . 4 . 5 . 6 . . . . . . . . . . . 7 . W. . 4 . 5 . 6 . 7 . W5 . 4 . 5 . 6 . 7

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.W.2 .. 3R3 ..W4 5 . .. 6 W5 W3 2 ... 3R5 3 ...W4 4 ... 55 5 . .. 6 W5 W3 .W.2 .. 3R3 ..W4 5 . 6 . W4 44 ... 55 . W4 46 . W4 44 ... 55 ..W.4 7 .. W3 W5 . M ..3 W6 .. W. ... ... W13 . .12 M ..3 W6 .. W. ... ... W13 . .12 M ..3 W6 .. W. ... ... WR . M M M .. W4 .WG 3 ... 42 4. ... 5M 5 ... M 6 . .. M W4 .WG 3 ... 42 4. ... 5M 5 ... M 6 . .. M W4 .WG 3 ... 42 4. ... 5M 5 ... M 6 . M . W5 6 7 . W5 6 7 . W5 6 71 4 3 4 4 3 4 4 3 4 Finished Wavefront: Wavefront: Wavefront: 1 Finished . .11 .2 W7 1 Finished . .11 .2 W7 . ..2 W7 .. . ..8 . 9.. . 10 .. . ..8 . 9.. . 10 .. . ..8 . 9.. . 10 . . . . . . . . . . . . . . . W5 4 .. .3 5 W6 . 6 .. 55 7 . .. 6 W3 W5 4 .. .3 5 W6 . 6 .. 55 7 . .. 6 W3 W5 4 .. .3 5 W6 . 6 .. 55 7 . 6. . W. . W. . W. .. W3 .. 2 .. 2 .. 2 Finished G W8 .. 49 .. 10 . 11 G W8 .. 49 .. 10 . 11 G W8 .. 49 .. 10 .. Wavefront: .1. Finished . ...12 Wavefront: .1. Finished . ...12 Wavefront: .1. . 11 . . . . . . . . . . . W.. W5Finished . W6 . Wavefront: 5 . 6 . . 5 W.. 7W5Finished . W6 . Wavefront: 5 . 6 . . 5 W.. 8W5Finished . W6 . Wavefront: 5 . 6 . 5 .. W4 . 3 W. . 4 . R5. W4 . 6. .. W4 . 3 W. . 4 . R5. W4 . 6. .. W4 . 3 W. . 4 . R5. W4 . 6. M M . . M M . . M M . .. W. W. . .. W. .. .W.5. . . W5 . .. W. .. .W.5. . . W5 . .6 W7 .8 .W.5. . W5 R. .W4 R. .W4 R. .W4 . .W.44. WG . .W.44. WG . .W.44. WG 37 . 4 . W5 5 . 26. .. 37. . . 4 W5 . M 5 . 26. .. 37. .Finished . 4 W5 . M 5 . 26. .. 10 M5 .W6 M M M . Wavefront: W. . W. . . W. W. . W. . 5 W6 W9 1 W. . . . . . . . . . . . . . WG .. 22 .. 3M 3 .. M WG .. 22 .. 3M 3 .. M WG 3 ... M 4 . M .4 W3 44 . . M 5 .4 W3 44 . .. M 5 W..4 W3 22 ... 3M 46 5 . ..W6 5 ..4 ..5 W. .. .. .. W. ..4 ..5 W. .. .. . .. W. ..4 ..5 W. ... ... .. . W3 . 2 .. 33 .. 44 .. 55 . . 6 W3 . 2 .. 33 .. 44 .. 55 . .. 6 W5 W3 .W.2 .. 3R3 ..W4 5 . 6 . W4 . W4 . W4 44 ... 55 W. W. . .. 3 W6 .. W. .. .. W.. . R ..3 W6 .. W. .. .. W.. . . M .. 3 W6 . . . . .. .. . M . W4 . 3 .. 44. .. 5M 5 .. M . 3 .. 44. .. 5M 5 .. M .WG 3 ... 42 4. ... 5M 5 ... M 6 . M . W5 66 . . M 71W4 . W5 66 . .. M 71W4 .4RW5 64 7 3 Finished Wavefront: Finished Wavefront: . .11 .2 W7 . .2 W7 . . .8 . 9. . 10 . . .8 . 9. . 10 . ..2 W7 .. . ..8 . 9.. WR . . . . . . . . . . . . M . W5 . 4 . .5 W6 . 6 .. 57 . . 6 W5 . 4 . .5 W6 . 6 .. 57 . .. 6 W3 W5 . 2 4 .. 3 5 . 6 . 5 7 . W. . W. Finished G W8 . 9 . 10 . .. . . . Wavefront: G W8 .. 49 .. 10 1 . 11 . Wavefront: .1 . 11 . .. 12 G W. . . . .. Finished . .. W6. . 5. . 6. . W.. W5. W. W6 . R5 W4 . 6 . 5 . W5 W. R W4 . .. 5 W. W4 . 3 . 4 . 5. . 6. . M M. .. . M M . .. . . W5 W.. R. W4. . 5. . W.4 WGR .W4 2 .. 35 . 4 . 4 WG . 2 . 3 . .. 4 W5 W5 . M 4 . M 5 . 6. . 7. M M . .. .. . . . . . . WG .. 22 .. 33 .. 44 . 5 . W3 . 2 . 3 . 4 . . 5 4 WG . 2 . 3 . 4 .4 W3 .. .. .. .. . . . . . . . . . . . W3 . 2 .. 33 .. 44 .. 55 . 6 . W4 . 3 . 4 . 5 . . 6 W3 . 2 . 3 . 4 . 5 . W4 . .. .. .. .. . . . . . . . . . . . . W4 . 3 .. 44 .. 55 .. 66 . 7 . W5 . 4 . 5 . 6 . . 7 W4 . 3 . 4 . 5 . 6 . W5 . . . . . . . . . . . W5 . 4 . 5 . 6 . 7 . W5 . 4 . 5 . 6 . 7 x x

In its first run, the robot discovers the maze, map the walls and find the target location. Each time it moves to a new cell, its mapping matrix is updated with new information about the existence of walls and the distance the cell is located from the target. The distance is indicated by the number of steps needed to move from a particular cells to the target. The first 6 steps and steps 19 & 20 are illustrated in Fig 8. Twenty steps are required to reach the target cell. All cell and wall data along the way are updated.

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7. RESULTS AND DISCUSSION 7.1 First Run

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. W5 . W. R W4 . 10 5 . W512W.3 W6 R W4 . R5 W13 Wavefront: 3 W6 . 7 . 8 Finished W. 1 W. M3 W6 M. WR . . M M W.. M . M . . . . MW. . .W6 . M 5 .. 4 6. . M 4 WG . 2. . M . 4 WG 2 . 3 Finished Wavefront: Wavefront: Wavefront: 2 W7 . 8 . 9 . .10 1 Finished . 11 2 W7 . .8 . 9. . 10 1 Finished . 11 2 W7 . 38 .. 4 9 . 10 1 . .. .. .. . .. .. . . . . . . . . . W. . W6 . 5 .Finished . W. .R3 W6 . 55 . . 6 W3 . W.2 . .3 W6 . 55. . 6. W5 5 .. 6 W3 .W.2G .W8 .W4 Finished G W8 . 9 . 10 . 49 ... 10 1 Finished . 11 .. 12. Wavefront: G W8 .. 49 .. 10 1 . 11 . Wavefront: .1 . 11 . ...12 Wavefront: . . . . M M .. W6 . . 5.. . 6.. . W.. .. W6. . 5. . 6. . W.. W5Finished . W. W6 . Wavefront: . 6 . .. 5 W..4 4W5 Finished R5 W4 R3 . 5W5 R5 W4 .. 2 .. 4 . W4 .WG 3 W. 4 .. Wavefront: 5 W4 6 . . 5 W4 . Finished 3 W. . 4 . Wavefront: . 6 . 5 . M M.8 W11 .. . 12 . W M.. M...8 W11 .... . 12 . W. M M..8 W.... .. 6 W7 15 ..6 W7 6 W7 . . . W5 W5 W.42. WG R3 ..W4 . 35 5 . . 4 W5 W.4.. WGR. .W4 . 35 . 4 . W.4. WGR .W4 2 .. 35 . ... 4 W3 . 2 . . 2 . . . 4 . W5 . Wavefront: 4 . M 5 . 6. . 10 7. Finished . W5 . Wavefront: 4 . M 5 . 6. . 10 7. M5 W6 M . . M M Finished Wavefront: 10 Finished W9 1 W 13 14 5 W6 W9 1 W 13 14 5 W6 W9 1 W. . . . . . .. .. .. . . . . . . WG 3 ... M 4 . .. M 2 ... 3M 3 ... M 4 . .. M WG 3 ... M 4 . M 22 ... 3M 46 5 W. .4 W3 24 46 5 W..4 W3 22 ... 3M 46 5 W4 .WG 3. ...W6 .. W..4 W3 . ..W6 5 5 . ..W6 5 ..4 ..5 W. ... .R.. . 14 . W ... ... . R . W13 ..4 ..5 W. ... ... .. .13 ...4 ...5 W. . x

Finished Wavefront: . . . . 3 . 4 . 5 . x . x . x . x . . . 3 . 2 . 3 . 4 . x . x . x . x . 3 . 2 . G . 2 . 3 . x . x . x . x . 4 . 3 . 2 . 3 . 4 . x . x . x . x . 5 . 4 . 3 . 4 . 5 x . x . x . x . R W5 . 4 . 5 . 6 Finished Wavefront: . . . . 3 . 4 . 5 . . . . . . . 3 . 2 . 3 . 4 . . . . R 2 . G . 2 . 3 . . . . . W3 . 2 . 3 . 4 . . . . . W4 . 3 . 4 . 5 . . . . . W5 . 4 . 5 . 6

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Finished Wavefront: 19 Finished Wavefront: 20 Finished Wavefront: 21 . W. . W. . W. . W. . W. . W. . W. . W. . W. . . . . W. W. . W. . . W. W. . W. . . W. W. . W. . M M M M M M M M M R . W. . . W. . . W. . . W. . . W. . . W. x

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3 W. W. . W. . R W. W. . W. M M M M M M 2 W. . . . W. . 2 W. . . . W. M M M M M M G W. . . . . G W. . . . Finished Wavefront: 22 . W. . W. . W. . . W. W. . W. . M M M . . W. . . W.

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Fig 9: Return to start in second run requires 22 steps

7.3 Third run When the maze is fully mapped, the robot navigates the maze to reach the goal through the shortest route using this data. When deciding to move the next cell, it chooses the cell that hold the smallest value. This is repeated until the target is reached. This is illustrated in Fig 10.

Fig 8: Mapping in first run requires 20 steps

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International Journal of Computer Applications (0975 – 8887) Volume 56– No.5, October 2012 Finished Wavefront:

1 Finished Wavefront:

2 Finished Wavefront:

Finished Wavefront: 10 Finished 10 Finished 10 9 . W14 13 W1 9 W8 Wavefront: . W14 13 W1 9 W8 Wavefront: . W14 13 W1 . W. .. W6 . 5 . 6 . W. .. W6 . 5 . 6 . W. .. W6 . 5 . 6 . W15 W12 7 . W15 W12 7 . W15 W12 . . 11 . W8 . . 11 . W8 . . 11 . W8 M. M M M. M M M. M M . W5 W.15 14 R W4 5 R W4 5 R W4 5 2 . 3W5 W6 W.15 14 2 . 3W5 W6 W.15 14 2 3 M M WG . . M M WG . . M M WG . . . 4 WG 2 .W2 3 . 4 . 4 5 WG 2 .W2 3 . 4 . 4 5 WGR .W13 2 .W2 3 . 4 16 .W13 3 W4 16 .W13 3 W4 3 W4 . . .M M . M . . .M M . M . . .M M . M . W3 . 17 2 .W12 3 . 13 4 .. 14 5 W7 . W3 6. 2R .W12 3 . 13 4 .. 14 5 W7 . W3 6. 2. .W12 3 . 13 4 .. 14 5 W7 . . . . M . M . . . . M . M . . . . M . M M M M Finished Wavefront: Wavefront: Wavefront: . W4 . 3R .W11 4 . 10 51 Finished . 6 4 . 10 51 Finished . 6 4 . 10 51 . 6 9 . 8W4 7. 3. .W11 9 . 8W4 7. 3. .W11 9 8 . . . . . . . . . . . . . . . . W. . W6 . 5 . Wavefront: 6 . W. . 4W6 . 5 . Wavefront: 6 . W. . 5W6 . 5 . Wavefront: 6 Finished Finished Finished . W5 . Wavefront: 4 . 5. . 6. .. 10 7 Finished . W5 . Wavefront: 4 . 5. . 6. .. 10 7 Finished . W5 . Wavefront: 4 . 5. . 6. . 10 7 . Finished . W14 13 W1 9 W8 . W. 13 W1 9 W8 . W. . W1 9 . W5 W. R. W4 . 5 . W5 W. R. W4 . 5 . W5 W. R. W4 . 5 . W. . W6. . 5. . 6 . W. . W6. . 5. . 6 . W. . W6. . 5. . 6 M M M7 M M7 M . W15 W12 11 W8 . W. W12 11 W8 . W. W12 11 W8 . . . . . . . . . . 4 WG . 2 . 3 . M 4 . M 4MWG . 2 . 3 . M 4 . M 4MWG . 2 . 3 . M 4 M M . W5. W..R 14 R. W4 . . 5 . W... R.R W4 . . 5 . W... R.. W4 . . 5 WG 2 . 3W5 W6 WG 2 . 3W5 W6 WG 2 3 . . W3 . 2 . M 3 . M 4 . 5. . . W3 . 2 . M 3 . M 4 . 5. . . W3 . 2 . M 3 . M 4 . 5. .. 4. WG . 2 . 3 . 4 . 4 WG . 2 . 3 . 4 . 4 WG . 2 . 3 . W 13 W2 3 W4 5 . W 13 W2 3 W4 5 . WR W2 3 W4 . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . W4 . 3 . 4 . 5 . M 6 . MW4M. 3 . 4 . 5 . M 6 . MW4M. 3 . 4 . 5 . M 6 M M 3. . 13 4. .. 14 5 W7 3. . 13 4. .. 14 5 W7 3. . 13 4. .. 14 5 W7 .. W3. . 2.. .W12 .. W3. 6. 2.. .W12 .. W3. 6. 2.. .W12 . . 5. . 6. . M . .M . W5M. 4. . 5. . 6. . M . .M . W5M. 4. . 5. . 6. . M . M . W5 . 4 7 7 7. M Finished Wavefront: Wavefront: Wavefront: . W4 . 3. .W11 4 . 10 51 Finished . 6 4 . 10 51 Finished . 6 4 . 10 51 . 6 9 . 8W4 7. 3. .W11 9 . 8W4 7. 3. .W11 9 8 . . . . . . . . . . . . . . . . W. . W6 . 5 . Wavefront: 6 . W. . 7W6 . 5 . Wavefront: 6 . W. . 8W6 . 5 . Wavefront: 6 Finished Finished Finished . W5 . Wavefront: 4 . 5. . 6. .. 10 7 . W5 . 4 . 5. . 6. .. 7 . W5 . 4 . 5. . 6. . 7 . Finished . W. . W1 9 W8 . W. . W. 9 W8 . W. . W. . . W5 W. R. W4 . 5 . W5 W. R. W4 . 5 . W5 W. R. W4 . 5 . W. . W6. . 5. . 6 M M . W. W.. 11 W8 M7 M. W.. W.. . W8 M7 M. W.. W.. . W8 . . . 4 WG . 2 . 3 . M 4 . M 4MWG . 2 . 3 . M 4 . M 4MWG . 2 . 3 . M 4 M M . W5. W... R.. W4 . . 5 . .. .. WG . . .. .. WG . WG 2 3 W6 2 3 W6 2 3 . W3 . 2 . M 3 . M 4 . 5. . . W3 . 2 . 3 . 4 . 5 . W3 . 2 . 3 . 4 . 5 .. 4. WG . 2 . 3 . 4 . W. W2 3 W4 5 . W. W2 3 W4 5 . W. W2 3 W4 . . . . . . . . . . . . . . . . . . W4 . 3 . 4 . 5 . M 6 . MW4M. 3 . 4 . 5 . M 6 . MW4M. 3 . 4 . 5 . M 6 M M 3. . 4.. .. 5. W7 .. W3. . 2.. .WR . . 6 .. W.. .. . . W7 . . 6 .. W.. .. . . W7 . . 5. . 6. . M . .M . W5M. 4 . 5 . 6 . M MW5M. 4 . 5 . 6 . M . W5 . 4 7 7 . 7 M M Finished Wavefront: . W4 . 3. .W11 4 . 10 51 Finished . 6 9 8 Wavefront: 7 . WR 10 1 9 8 7 . W. R 9 8 . . 5. . Wavefront: . W. .. W6 6. . . W. .10W6 . 5 . Wavefront: 6 Finished Finished 11 Finished Wavefront: . W5 . 4 . 5. . 6. .. 7 . . . . W. . W. . W. . W. . W. . W. . W. . W. . . W5 W. R. W4 . 5 . W5 W. R. W4 . 5 . M M. W.. W.. . W. M7 M. W.. W.. . W. . . W. W. . W. . 4 WG . 2 . 3 . M 4 . M 4MWG . 2 . 3 . M 4 M M M M M . .. .. WG . . .. .. WG . 2 3 W6 2 3 W6 . . WG 2 3 . W3 . 2 . 3 . 4 . 5 . W3 . 2 . 3 . 4 . 5 3 W4 3 W4 5 . W. W2 3 W4 . . .. W.. W2 . . . 5 .. W.. W2 . M M M . W4 . 3 . 4 . 5 . M 6 . MW4M. 3 . 4 . 5 . M 6 M M . . . W. . . .. W.. .. . . W7 . . 6 .. W.. .. . . W7 6 . W. M M M . W5 . 4 . 5 . 6 . M 7 . MW5M. 4 . 5 . 6 . M 7 M M x

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. W. . R 8 7 . W. . . R 7 . W. . . . R Finished Wavefront: 13 Finished Wavefront: 14 Finished Wavefront: 15 . W. . W. . W. . W. . W. . W. . W. . W. . W. . . . . W. W. . W. . . W. W. . W. . . W. W. . W. . M M M M M M M M M . . WG 2 3 W. . . WG 2 3 W. . . WG 2 3 W. x

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9. REFERENCES [1] Verner, I.M. and D.J. Ahlgren, Robot contest as a laboratory for experiential engineering education. J. Educ. Resour. Comput., 2004. 4(2): p. 2. [2] Mishra, S. and P. Bande. Maze Solving Algorithms for Micro Mouse. in Signal Image Technology and Internet Based Systems, 2008. SITIS '08. IEEE International Conference on. 2008. [3] Willardson, D.M., Analysis of Micromouse Maze Solving Algorithm, in Learning from Data. 2001, Portland State University.

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In order to improve the quality in wall detection and selfcorrection, a better object sensor, such as a laser range finder, can be employed. A laser range finder is much more costly but provides the ability to the robot to scan its surrounding at a wide angle plane instead of limited directional object detection provided by ultrasonic sensors.

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Future works may include but not limited to studying the robot’s maze-solving capability in a bigger and more complex maze, in particular adaptable the robot is. The maze can be designed and built to be reconfigurable so that the robot will be faced with different challenge each time.

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The robot has successfully able to map the maze in the first and second runs. In its third run it reaches its target cell through the shortest route it has mapped in the previous two runs.

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Fig 10: Third run requires 18 steps Compared to the first run where the robot was still learning the maze, in the final run, the robot takes two less steps because it already learned about the whole maze and knows the shortest path to the target cell.

8. CONCLUSION & RECOMMENDATIONS This exercise is a study about the ability to equip a small mobile robot with the ability to learn how to navigate in unknown environment based on its own decisions. The floodfill algorithm was found to be an effective tool for mazesolving of a moderate size. For the robot to make its decisions it relies on inputs from several sensors, namely the ultrasonic range sensors and wheel rotation decoders. The robot is able to correct its orientation errors arising from its physical motion within the maze using a PI controller.

[4] Dang, H., J. Song, and Q. Guo, An Efficient Algorithm for Robot Maze-Solving, in Proceedings of the 2010 Second International Conference on Intelligent HumanMachine Systems and Cybernetics - Volume 02. 2010, IEEE Computer Society. p. 79-82. [5] Cai, J., et al., An Algorithm of Micromouse Maze Solving, in Proceedings of the 2010 10th IEEE International Conference on Computer and Information Technology. 2010, IEEE Computer Society. p. 19952000. [6] Wyard-Scott, L. and Q.H.M. Meng. A potential maze solving algorithm for a micromouse robot. in Communications, Computers, and Signal Processing, 1995. Proceedings., IEEE Pacific Rim Conference on. 1995. [7] Jianping, C., et al. A micromouse maze sovling simulator. in Future Computer and Communication (ICFCC), 2010 2nd International Conference on. 2010. [8] Kendre, S. S., P. V. Mulmule, et al. Navigation of PIC based Mobile Robot using Path Planning Algorithm. International Journal of Computer Applications. 2010 [9] Choudhury, D.R., Process Control System, in Modern Control Engineering. 2004, PHI Learning Pvt. Ltd. p. 323-351.

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