We present a method for guidance of a Dubins-like vehicle to its intended target in a steady simply connected maze-like environment. The vehicle always has access to the relative bearing of the target (even if the target is behind an obstacle or is far from the vehicle) and to the distance to the nearest point of the maze whenever this distance does not exceed the sensing range. The proposed control law is constituted of bio-inspired reflex-level rules. Mathematically rigorous analysis of this law is provided and confirmed by computer simulation and experiments with real robots. (C) 2013 Elsevier Ltd. All rights reserved.