# Minkowski Operations of Sets with Application to Robot Localization

## TL;DR

This paper introduces a novel approach using separators linked to Minkowski operations to efficiently solve robot localization problems with sonar data in complex environments.

## Contribution

It presents the integration of separators with Minkowski sums and differences to improve robot localization methods.

## Key findings

- Efficient localization in unstructured environments demonstrated.
- Separators facilitate solving the robot localization problem.
- Test-case validates the approach.

## Abstract

This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach.