Introducci\'on a la teor\'ia de complejidad topol\'ogica

TL;DR

This paper reviews the concept of topological complexity and applies it to solve the motion planning problem for a robot navigating in a plane with obstacles, including calculations and algorithm design.

Contribution

It introduces the topological complexity theory and demonstrates its application to robot motion planning with explicit calculations and algorithms.

Findings

Calculated topological complexity for the robot navigation problem.

Designed explicit motion planning algorithms based on topological complexity.

Showed how topological complexity informs robot navigation strategies.

Abstract

In this work we will review the notion of topological complexity, introduced by Michael Farber in 2003. We will use this theory of topological complexity to solve the motion planning problem of a mobile robot that navigates in the Euclidean plane avoiding colliding with an obstacle. Specifically, we calculate topological complexity and design explicit algorithms.