Symbolic Driving

A passenger in a taxi may instruct the driver to “turn left,” “go straight,” or “turn right.” These terms have no geometrical meanings but are symbols. Each of these symbols specifies a path segment connected to an intersection depending on the current car’s frame (position and direction).

[1] Symbolic Driving in a Block World

A user’s mouse clicks navigate
the car in this block world.

An approximate direction, left, right, up, or down, relative to the current car frame matters, but not the exact position of the mouse click.

[2] Symbolic Driving in a Maze

The Swan robot solves a maze
using a left-handed rule
that selects the left-most path-section
at each T intersection.

The Swan robot solves a maze
using a right-handed rule
that selects the right-most path-section
at each T intersection.

In both maze solutions, the Swan robot uses a special U-turn in the omega mode. In the mode, a motion is created by a pair, (translation velocity, rotation velocity) = (v, ω).  For a short while,  v = 0 and ω ≠ 0, and the motion produces an extremely small fingerprint. The Swan can make a motion either in the curvature mode or in the omega mode; an automobile can move only in the curvature mode.