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Maze-Solving Mindstorms NXT Robot. Peter Dempsey Pericles Kariotis Adam Procter. Our Mission. Investigate the capabilities of the NXT robot Explore development options Build something interesting!. Problem Outline. Robot is placed in a “grid” of same-sized squares
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Maze-Solving Mindstorms NXT Robot Peter Dempsey Pericles Kariotis Adam Procter
Our Mission • Investigate the capabilities of the NXT robot • Explore development options • Build something interesting!
Problem Outline • Robot is placed in a “grid” of same-sized squares • (Due to obscure and annoying technical limitations, the robot always starts at the “southwest” corner of the maze, facing “north”) • Each square can be blocked on 0-4 sides (we just used note cards!) • Maze is rectangularly bounded • One square is a “goal” square (we indicate this by covering the floor of the goal square in white note cards ) • The robot has to get to the goal square
Robot Design • Uses basic “driving base” from NXT building guide, plus two light sensors (pointed downwards) and one ultrasonic distance sensor (pointed forwards) • The light sensors are used to detect the goal square, and the distance sensor is used to detect walls
Robot Design, cont’d Ultrasonic Sensor LightSensors
Search Algorithm • Simple Depth-First Search • Robot scans each cell for walls and constructs a DFS tree rooted at the START cell • As the DFS tree is constructed, it indicates which cells have been explored and provides paths for backtracking • The DFS halts when the GOAL cell is found
DFS Tree Data Structure • Two-Dimensional Array Cell maze[MAX_HEIGHT][MAX_WIDTH] typedef struct { bool isExplored; (= false) Direction parentDirection; (= NO_DIRECTION) WallStatus[4] wallStatus; (= {UNKNOWN}) } Cell; • Actually implemented as parallel arrays due to RobotC limitations
DFS Algorithm while (true) { if robot is at GOAL cell victoryDance(); if there is an unexplored, unobstructed neighbor Mark parent of neighbor as current cell; Proceed to the neighbor; else if robot is not in START cell Backtrack; else return; //No GOAL cell exists, so we exit }
Example 3x3 maze GOAL
We start out at (0,0) – the “southwest” corner of the maze Location of goal is unknown
So we go forward; the red arrow indicates that (0,0) is (1,0)’s predecessor.
We sense a wall here too, so we’re gonna have to look north.
…so we go forward. “When you come to a fork in the road, take it.”–Yogi Berra on depth-first search
We already know that the wall on the right is blocked, so we try turning left instead.
Wall here too! Now there are no unexplored neighboring squares that we can get to. So, we backtrack! (Retrace the red arrow)
…and go forward. Now we’ve backtracked to a square that might have an unexplored neighbor. Let’s check!
What luck! Here’s the goal. Final step: Execute victory dance.
Movement and Sensing • The search algorithm above requires five basic movement/sensing operations: • “Move forward” to the square we’re facing • “Turn left” 90 degrees • “Turn right” 90 degrees • “Sense wall” in front of us • “Sense goal” in the current square
Movement and Sensing, cont’d • Sensing turns out not to be such a big problem • If the ultrasonic sensor returns less than a certain distance, there’s a wall in front of us; otherwise there’s not • Goal sensing is similar (if the floor is “bright enough”, we’re at the goal)
Movement and Sensing, cont’d • The motion operations are a major challenge, however • Imagine trying to drive a car, straight ahead, exactly ten feet, with your eyes closed. That’s more or less what “move forward” is supposed to do – at least ideally. • In the current implementation, we just make our best estimate by turning the wheels a certain fixed number of degrees, and make no attempt to correct for error. • We’ll talk about other options later
