Question

Your goal is to navigate a robot out of a maze. The robot starts in the center of the maze facing north. You can turn the robot to face north, east, south, or west. You can direct the robot to move forward a certain distance, although it will stop before hitting a wall.

1. Formulate this problem. How large is the state space?
2. In navigating a maze, the only place we need to turn is at the intersection of two or more corridors. Reformulate this problem using this observation. How large is the state space now

for aritficial intelligence

Answer 1

a) Initial State:

                     At( (0,0) ), Facing( (0,1) ).

Successor Function( At(x), Facing(y) ):

                      <Turn(North), {At(x),Facing( (0,1) )} >

                     <Turn(East), {At(x),Facing( (1,0) )} >

                     <Turn(South), {At(x),Facing( (0,-1) )} >

                     <Turn(West), {At(x),Facing( (-1,0) )} >

                     <Move( k blocks), {At(x + y min(k, Dmax(x, y))), Facing(y)}> where Dmax(x, y) is the maximum distance the robot can move in direction y from point x without

hitting a wall.

Goal State:

                   At(x), x ∈ G, where G is the set of locations outside the maze.If the maze is comprized of S blocks, then the total number of states is 4S.

b)

The successor function remains the same for intersections,and for locations x which are straight corridors:

Successor Function( At(x), Facing(y) ):

             <Move( k blocks), {At(x + y min(k, Dmax(x, y))), Facing(y)}>

Thus if the maze has I intersection blocks then the size of the state space is 4I + 2(S − I).