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  The wall-hugging Robot, Finite State Machines

The wall-hugging robot:

Program a toy robot to follow a wall. The figure shown below describes the assumptions. In a simplified version of ‘turtle geometry’, the robot’s world is a grid; any square is either free or occupied by the ‘wall’. The robot, shown as a triangle, is positioned on a free square facing in one of four possible directions. The robot consists of two binary sensors: h (‘head’, a touch sensitive bumper) signals whether the square is in front of the robot is free (0) or occupied by the wall (1); r (right)  gives the same  information  for  the square to the right of the robot. Robot is capable of two primitive actions: R turns right by 90° whereas remaining on the same square; F (forward) advances one square in the robot’s present direction.

247_wall hugging robot.jpg
Figure: i) The city wall and ii) the predicate ‘wall to the rear-right’.

The  robot should  be  programmed  to  find  out a  piece  of wall,  then  endlessly cycle all along within the wall, hugging it with right side. The given finite state machine, represented in tabular form, resolves the problem.

Seek: precondition = true, post-condition = ‘wall to the rear-right’

r     h     Actions     Next state
1     -                     Track
-     1     RRR          Track
0     0     F              Seek

Track: precondition = post-condition = ‘wall to the rear-right’

r     h     Actions     Next state
0     -     RF            Track
1     0     F             Track
1     1     RRR         Track

The robot begins in state Seek, not knowing anything regarding its position, as stated by the vacuous assertion “precondition = true”. Function of this state is to bring about the post-condition ‘wall to the rear-right’, described in figure above: There is a piece of wall to the right of robot, or diagonally to the rear-right, or both. As long as robot hasn’t sensed any piece of wall (r = 0, h = 0) it moves forward with F. When it senses a wall, either ahead or to the right, it positions itself so as to fulfill the post-condition ‘wall to the rear-right’. With the ‘don’t care’ notation “-” we follow the design principle ‘specify behavior just as far as required’ and make the robot non-deterministic.

The mathematically inclined reader might find it instructive to confirm the program correct by checking that the state Track maintains the invariant ‘wall to the rear-right’, and that, in each and every transition, the robot progresses in his march all along the wall. Here we just point out how some basic ideas of the theory of computation, of algorithms and programs can be described in a simple, playful setting whose rules are rapidly understood.

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