  A nonholonomic under-actuated robot with a bounded control range travels
inside an unknown and unstructured 3D tunnel bounded by a generic 2D surface.
The robot has access to the nearest point of the surface and measures the
distance to the surface along any ray from a narrow beam emitted from the robot
around the direction to the nearest point. The paper presents some mathematical
facts underlying justification of the convergence and performance of a new
navigation law that ensures constant advancement of the robot through the
tunnel, along with respecting a given safety margin to its surface, driving the
robot to the desired distance to it, and subsequently maintaining this
distance.
