Proofs of the Technical Results Justifying a Biologically Inspired   Algorithm for Reactive Navigation of Nonholonomic Robots in Maze-Like   Environments
  We present technical results justifying a method for guidance of a Dubins-like vehicle with saturated control towards a target in a steady simply connected maze-like environment. The vehicle always has access to to the target relative bearing angle and the distance to the nearest point of the maze if it is within the given sensor range. The proposed control law is composed by biologically inspired reflex-level rules. Mathematically rigorous analysis of this law is provided; its convergence and performance are confirmed by computer simulations and experiments with real robots. 
Alexey S. Matveev, Michael C. Hoy, and Andrey V. Savkin
math.OC