Stochastic behavior of robots that navigate by interacting with their environment

This paper reports on the benefit of including boundary interaction behaviors, specifically wall-following, in reducing the position uncertainty of mobile robots with little or no localization capacity. Assuming that the robot has some primitive wall-following capabilities, and can switch its behavior depending on whether it moves in free-space or along obstacle boundaries, the time evolution of its trajectories is modeled by a stochastic differential equation with piece-wise constant drift and diffusion terms. The probability law of this piece-wise linear time-invariant diffusion is matched at any given time instant by that of an appropriately constructed single diffusion, in what is called here a time-weighted convolution. Since the Fokker-Planck associated with the single diffusion can be solved analytically, this matching enables the exact calculation of the position distribution of the stochastic switching vehicle dynamics at any given stopping time.