CENTER FIRST ROUTING THEOREM

BY: Ayush Dewan

ABSTRACT

 • Algorithm is developed for Micromouse routing

in maze. • In the algorithm, a Center-First-Theorem is

applied to find out several short roads in maze, then the shortest road can be find out among those roads by comparing with each other.

• In practice, it is proved that this algorithm can reduces error execution and improves efficiency.

MICROMOUSE

IEEE micro-mouse is maze routing competition .

It has a center, which is the destination cell for the Micromouse.

The robot has to search the entire maze and find the path that it can travel in the shortest possible time.

MICROMOUSE RULES

The robot must be completely autonomous.

The robot must reach the center in the least possible time.

No external power source is allowed.

MAZE SPECIFICATIONThe maze in the Micromouse competition consists of multiples of an 18cmx18cm square.

It consists of 16x16unit squares .

The walls of the maze are 5 cm high and 1.2 cm thick

MICROMOUSE HARDWARE

• Chassis• Microcontroller• Sensors: Analog or Digital• EEPROM• Motor: DC or Stepper• Motor Driver• Power Supply• LCD

MICROMOUSE SOFTWARE

The Logic Layer: Consist of logic code that would help the robot decide which cell to move towards on the basis of the sensor data that it received

The Motion Layer: It is comprised of Code that controls the motion of the robot.

CENTER FIRST ROUTING THEOREM ALGORITHM

DETERMINE SEVERAL SHORT PATHS TOWARDS CENTER.

COUNT NUMBER OF STEPS AND STORE COORDINATE INFORMATION FOR EACH PATH IN A MATRIX.

COMPARE EACH PATH AND SELECT THE SHORTEST PATH.

TRAVEL THE SHORTEST PATH WITH FASTEST POSSIBLE SPEED.

MAZE INFORMATION

• FOUR POSSIBLE PATHS ARE:– CUL DE-SAC

– STRAIGHT

– CROSSROAD

– T SHAPED ROAD

– TURNING

MAZE INFORMATION• ONE BYTE IS USED TO STORE MAZE INFORMATION FOR EACH CELL.

BIT 3 2 1 0

DIRECTION NORTH(U) WEST(L) SOUTH(D) EAST(R)

BIT 5 4NO CUL DE- SAC 1 11 CUL DE-SAC 0 12 CUL DE-SAC 1 0

BIT 7 6

1 SIDE TO GO 0 0

T SHAPED ROAD 0 1

CROSS ROAD 1 0

Recording coordinate and information of maze’s cell.

• The information of cell is recorded in a matrix whose name is maze and size is 15×15.

• Register named Dir to recording the direction. DIR DIRECTION

0 NORTH: Y++

1 EAST: X++

2 SOUTH: Y--

3 WEST: Y++

•The original location of micro-mouse is (0, 0), and the routing direction is north.

Recording coordinate and information of maze’s cell.

DIRECTION CALCULATIONLEFT -1RIGHT +1TURNING BACK FROM LEFT -2TURNING BACK FROM RIGHT +2

•VALUE OF DIR IS BETWEEN 0 AND 3.•FORMULA FOR CALCULATING COORDINATE:

CUT CUL DE -SAC• When micro-mouse makes a back turning (means there is a cul-de-sac),

both turning back from left and from right, making a marker in a register whose name is noroad ,with the value of 1 means there is a cul-de-sac while 0 is no.

• Set values of all cells to FFH, which belong to the cul-de-sac between the end of it and the crossing cell nearest to it.

• Then ,marker of this direction of the nearest crossing cell is set to 1 to prevent micro-mouse from selecting this direction when it goes here again.

Implementation Of CFRT

In consideration of the information stored in the register Dir , micro-mouse selects a direction to go.

If it has only one direction to go, it doesn’t make choice but just go by this direction.

For a crossing, it chooses the direction pointing to the end.

CALCULATION OF DIR

Dn-1: Former Cell

Dn= Present cell

Where, m = (-2, -1, 0, 1, 2),

At the same time, it uses a times register named times (original value is 0) to alternate priority of direction x++ and y++ between

Two adjacent road junctions. The value 0 means y++ first and 1 means x++ first.

Dn=dn-1 + m

SHORTEST PATH

• Newroad[]: coordinates of present path.• Short road[]: coordinate of the route searched

out at first time.• Steps are calculated using th formula:

ROUTING BY CFRT

s =25+7× 0.5=28.5

ROUTING BY CFRT

s =23+7 × 0.5=26.5

SPRINT

After we got the shortest road, sprint is the key to win the game.

COMPARISON WITH OTHER ALGORITHMS

  • Left-right-straight algorithm(LRSRT): Left side’s priority is first,

right is secondary, and straight is last.• Left-straight-right algorithm (LSRRT)• Right-left-straight algorithm (RLSRT) • Right-straight left algorithm (RSLRT) • Straight-left-right algorithm(SRLRT) • Straight-right-left algorithm (SLRRT)• Random algorithm (RRT): Each side’s priority is same and

which side to choose is random.

COMPARISON WITH OTHER ALGORITHMS

LRSRT LSRRT RLSRT RSLRT SLRRT

SLRRT SRLRT

CONCLUSION

• By analyzing in theory and carrying it out in practice, we conclude that Center First Routing algorithm can avoid a lot of work in information recording, repairing and managing, and can improve efficiency. At the same time, it makes the

• Programming of route searching become easily and reduces error execution in practice.