Robot 2D self-localization using range pattern matching via the Discrete Fourier Transform

This article describes a novel method for localization of a robot within a 2D scene given a binary map of the scene and a set of range measurements obtained by the robot from some unknown position and orientation. Theoretically, the algorithm is capable of solving all recognized variants of the robot localization problem: tracking, global localization, and kidnapped robot. This is accomplished by treating each set of range measurements as a unique fingerprint, referred to as a range pattern, that is associated with each potential (x, y, θ) pose of the robot. We provide detailed theoretical analysis and an exact solution for the problem when both the range and angle measurements are constrained to come from a discrete set of possible values. Experimental results are obtained using simulated range data taken from synthetic and real-world maps to provide insight on the robustness of our approach and identify situations where the localization solution obtained is not unique. Our solution to this more-constrained problem has low computational complexity and is exact which makes it appropriate for use in real-time robotic navigation applications. Solutions to this problem are of great importance for successful deployment of autonomous robotic vehicles within a-priori known spaces, e.g., buildings, hospitals, etc.