  A single nonholonomic under-actuated mobile robot with a bounded control
range travels in a 3D workspace. This workspace also hosts a compact unknown
domain with a smooth boundary. The robot has access to the horizontal distance
to this domain and to a certain direction (typically, vertical) in the space,
along with its coordinate (typically, altitude) in this direction. We present a
new navigation law that drives the robot to the desired distance to the domain
and ensures subsequent full scan of its surface within a desired range of
"altitudes". The proposed strategy is computationally inexpensive and achieves
full scan at the lowest control level via generating the current control as a
simple, reflex-like reaction to the current observation. The paper presents and
proves key technical facts underlying mathematically rigorous analysis and
justification of the proposed guidance approach.
