This article introduces a novel path planning algorithm, called , that reduces the problem of robot path planning to optimisation of a probabilistic finite state automaton. The -algorithm makes use of renormalised measure of regular languages to plan the optimal path for a specified goal. Although the underlying navigation model is probabilistic, the -algorithm yields path plans that can be executed in a deterministic setting with automated optimal trade-off between path length and robustness under dynamic uncertainties. The -algorithm has been experimentally validated on Segway Robotic Mobility Platforms in a laboratory environment.