µ-Planner: A Robot Path Planning Approach Based on Language Measure of Unsupervised Automata

Abstract

This paper proposes a robot path planner based on language measure, µ-planner. Workspace is discretized in a occupancy grid map and we model the system by considering how events, associated to robot's motions, take it to different cells (discrete positions). The calculated language measure values corresponds to a gradient, which the robot can use reach its destination by choosing events that take it to states with higher measure values. Concepts of Lapace's equation and harmonic functions are used to prove that our method guarantees both the existence and monotonicity of language measure. The proposed method is simple and computationally inexpensive and guarantees existence of path from any co-accessible state to the destination. Experiments considering different scenarios have been performed to validate and compare µ-planner with similar methods.