Maze Running Robots

EGR106 Project

Spring 2004

Project Goal

Computer control (through a Matlab program) of a Lego robot to:

1. Explore a maze (start to end)

2. Recognize the final room to drop cargo

3. Return the robot to its starting place

START

END

• You will not be assembling the robot, but controlling it

• Basic control will be through a Matlab function

Typical robot circa 2002

Maze Assumptions

• Size is known • Start is at the lower

left corner, robot pointing up/north

• Drop site for the cargo is at the upper right corner

START

END

The Robot Interface

MATLAB function robot.m:

[l,c,r] = robot(command)

• one input value

• three binary outputs

• Value for command (plus the robot always looks around):

0 drive forward one unit (room)1 turn left by 90o 2 turn right by 90o

3 do nothing (just look around)4 play a sound (drop the cargo)≥ 10 initialize and run the simulator

• Three binary output variables:– Returned for all commands – Denote the presence or absence of wall

openings from the current room/orientation– Left, Center, Right walls only – Value = 1 for opening present, 0 for no opening

• Note – result is dependent upon the orientation of the robot.

Output is

[ L, C, R ] = [ 1 0 0 ]

Output is

[ L, C, R ] = [ 1 1 0 ]

Robot Simulator

• Useful for program development – Virtual robot, much faster than the

real thing– Available 24/7 (download file)– Includes multiple practice mazes

to test your programs – maze and robot progress shown in a figure window

Programming Notes

4 parts:1. Search/wander the maze

2. Build a map of what you see

3. Drop the cargo; analyze the map

4. Return to start

1. Search/wander the maze– Make good moves – remember that the goal is

to get to the upper right corner; don’t just make random turns, aim the robot

– Keep track of the robot location – row and column notation makes it easy to recognize the end room

– Orientation determines where the robot goes

2. Build a map of what you see– At the beginning you know nothing of the

maze; for each new room visited, you learn a bit more

– Use the map to help the exploration (i.e. recognize areas/directions to be ignored, don’t revisit rooms, …)

– One idea on mapping is …..

A map “matrix” for a M by N maze: – Number the rooms 1 to M*N– The (m,n) and (n,m) entries (identical) describe

the connection between rooms m and n using 3 values:• connection unknown• no direct connection • a direct connection

Example Map1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

Legend:

white = not adjacent

red = closed wall green = open wall

1 2 3

1 0 119

65

1 2

7 8

4

3. Drop the cargo; analyze the map– Identify the end room by beeping – Use the map matrix to find a short path back

to start – While many ideas could be tried, one simple

analysis tool is Bellman’s flooding algorithm…..

Bellman’s flooding algorithm:– Start analysis at the “end” room– Assign costs to each room of going from that

room to the end– Sequentially expand to connected adjacent

rooms– Stop when you hit “start”

0

0

1

2

2

0

1

2

2

3

34

0

1

0

1

2

2

3

3

0

1

2

2

3

345

5

67

6

• Path identified by tracing from “start” to “end” following decreasing costs

• Result: room path

1, 2, 6, 10, 11, 7, 8, 12

0

1

2

2

3

345

5

67

6

1 2 3

1 0 119

65

1 2

7 8

4

forward

4. Return to start– Convert reverse

path to robot commands

12, 8, 7, 11, 10, 6, 2, 1

1 2 3

1 0 119

65

1 2

7 8

4

3

1

2

3

2

04

56

5

67

reverse

12 8 7 11 10 6 2 1

robot(1)robot(1)robot(0)

robot(2)robot(0)

robot(2)robot(0)

robot(1)robot(0)

robot(1)robot(0)

robot(0) robot(2)robot(0)

1 2 3

1 0 119

65

1 2

7 8

4

Team Deliverables• Working program(s):

– electronic copy for testing

– written description (with examples)

• Written report:

– details of format later

• Oral Presentation to class:

– each person describes an aspect of the work

• Due May 4 (final class day)

Scoring in the Demonstration

• Sum of two parts (a lower score is better):– 1 point per forward movement while searching – 2 points per forward movement while returning

• Must: – Drop the cargo in the “end” room– Return to “start”– Not cross walls

Schedule

• Today:– meet your team (Preassigned)– brainstorm issues and ideas, ask questions

• Homework (due this Thursday):– team name

Schedule (continued)

• April 15, 20, 22, 27 & 29– in-class work time– Quiz 3 on the 20th – weekly reviews with me (5 minute schedule per

team)

• May 4: – Presentations including maze running demos