Evolutionary-based global localization and mapping of three dimensional environments

A fully autonomous robot must obtain and interpret information about the environment to execute several tasks. The mobile robot mapping or SLAM problem is closely related to these abilities. It consists of interpreting the information perceived by its sensors in order to build map and localize itself in it. There are many other robot skills that depend on this task; thus, it is one of the most important problems to be solved by a truly autonomous robot. The objective of this work is to design various specific tools related to the mapping problem in order to improve the autonomy of MANFRED-2, which is a mobile robot fully developed by the Robotics Lab research group of the Systems Engineering and Automation Department of the Carlos III University of Madrid. The localization problem in mobile robotics can be defined as the search of the robot's coordinates in a known environment. If there is no information about the initial location, we are talking about global localization. In this work, we have developed an algorithm that solves this problem in a three-dimensional environment using Differential Evolution, which is a particle-based evolutionary algorithm that evolves in time to the solution that yields the cost function lowest value. The proposed method has many features that make it very robust and reliable: thresholding and discarding mechanisms, different cost functions, effective convergence criteria, and so on. The resulting global localization module has been tested in numerous experiments. The high accuracy of the method allows its application in manipulation tasks. If the environment information is given by laser readings, it is essential to correct the local errors between pairs of scans to improve the map quality, which is called registration or scan matching. We have implemented a scan matching algorithm for three-dimensional environments. It is also based on the Differential Evolution method. The high accuracy and computational effi ciency of the proposed method have been demonstrated with experimental results. The last problem addressed here consists of detecting when the robot is navigating through a known place (loop detection). After that, the accumulated error can be minimized to give consistency to the global map (loop closure). We have developed a loop detection method that compares features extracted from two different scans to obtain a loop indicator. This approach allows the introduction of very different characteristics in the descriptor. First, the surface features include the geometric forms of the scan (lines, planes, and spheres). Second, the numerical features describe other several properties (volume, average range, curvature, etc.). The algorithm has been tested with real data to demonstrate its effi ciency. All true loops are correctly detected and no false detections are appreciated when the mobile robot is covering a long trajectory. The results are similar or even better than those obtained by other research groups. In addition, it is a more versatile method because it admits a wide variety of scan properties and different weights in the comparison formula. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Un robot completamente autónomo debe ser capaz de obtener e interpretar la información del entorno para ejecutar diversas tareas. El problema de mapeado o SLAM para robots móviles está estrechamente relacionado con estas habilidades. Consiste en interpretar la infomació percibida por sus sensores para construir un mapa y localizarse. Hay muchas otras tareas que dependen del mapeado, luego este es uno de los problemas más importantes para un robot móvil. El objetivo de este trabajo es el desarrollo de varias herramientas específicas relacionadas con el mapeado de entornos tridimensionales. Con ellas se mejorar a la autonomía del robot manipulador MANFRED-2, que es un robot móvil desarrollado íntegramente en el Robotics Lab del Departamento de Ingeniería de Sistemas y Automática de la Universidad Carlos III de Madrid. El problema de localización para un robot móvil puede ser de nido como la búsqueda de las coordenadas del robot dentro de un entorno conocido. Si no hay información sobre la localización inicial, el problema se denomina localización global. En este trabajo se ha desarrollado un módulo que soluciona este problema para entornos tridimensionales utilizando el algoritmo Differential Evolution, el cual es un filtro evolutivo basado en part culas que evolucionan con el tiempo hacia la solución que tiene asociado un mejor valor para una función de coste dada. El algoritmo desarrollado tiene diversas características que lo hacen muy robusto y fiable: mecanismos de umbralización y descarte, diferentes funciones de coste, criterios de convergencia efectivos, etc. El módulo de localización global se ha probado en m últiples experimentos. La elevada precisión de este método permite que el robot sea utilizado en tareas de manipulación. Si la información del entorno viene dada por barridos de un láser, es muy importante que se pueda corregir el error local entre pares de barridos para mejorar la calidad del mapa. Este proceso se conoce como registro o scan matching. Hemos implementado un algoritmo que resuelve este problema en entornos tridimensionales. Est a tambi en basado en el Differential Evolution. Si se elige la función de forma adecuada es posible resolver el problema de scan matching utilizando este método. La elevada precisión y la eficiencia computacional se han demostrado en los resultados experimentales. El último problema abordado aquí consiste en detectar cuando el robot está navegando por un entorno conocido. Después de esto se podrá minimizar el error acumulado para aumentar la consistencia del mapa. La tarea de detecci on se llama usualmente detección de bucles, mientras que la minimización del error es el cierre del bucle. Se ha desarrollado un algoritmo de detección que extrae las características más importantes de dos barridos del láser para obtener un indicador que es usado como umbral para detectar si el robot está en un lugar que ha visitado previamente. Nuestro método permite tener en cuenta características muy diferentes. Primero, las caractrísticas de superficie permiten incluir las formas geométricas presentes en el barrido (líneas, planos y esferas). Segundo, las características numéricas permiten describir diversas propiedades (volumen, rango medio, curvatura, etc.). El algoritmo ha sido probado con datos reales para demostrar su eficiencia. Todos los bucles son detectados correctamente y no se aprecian falsos positivos cuando el robot está navegando por una trayectoria larga con varios bucles. Los resultados son parecidos o mejores que los que obtienen otros grupos de investigación. Además, este es un m etodo muy versátil pues admite multitud de variables y diferentes pesos en la fórmula de comparación

Two different tools for three-dimensional mapping: DE-based scan matching and feature-based loop detection

An autonomous robot must obtain information about its surroundings to accomplish multiple tasks that are greatly improved when this information is efficiently incorporated into amap. Some examples are navigation, manipulation, localization, etc. This mapping problem has been an important research area in mobile robotics during last decades. It does not have a unique solution and can be divided into multiple sub-problems. Two different aspects of the mobile robot mapping problem are addressed in this work. First, we have developed a Differential Evolution-based scan matching algorithm that operates with high accuracy in three-dimensional environments. The map obtained by an autonomous robot must be consistent after registration. It is basic to detect when the robot is navigating around a previously visited place in order to minimize the accumulated error. This phase, which is called loop detection, is the second aspect studied here. We have developed an algorithm that extracts the most important features from two different three-dimensional laser scans in order to obtain a loop indicator that is used to detect when the robot is visiting a known place. This approach allows the introduction of very different characteristics in the descriptor. First, the surface features include the geometric forms of the scan (lines, planes, and spheres). Second, the numerical features are values that describe several numerical properties of the measurements: volume, average range, curvature, etc. Both algorithms have been tested with real data to demonstrate that these are efficient tools to be used in mapping tasks.Publicad

Robotic Motion using Harmonic Functions and Finite Elements

The harmonic functions have proved to be a powerful technique for motion planning in a known environment. They have two important properties: given an initial point and an objective in a connected domain, a unique path exists between those points. This path is the maximum gradient path of the harmonic function that begins in the initial point and ends in the goal point. The second property is that the harmonic function cannot have local minima in the interior of the domain (the objective point is considered as a border). This paper proposes a new method to solve Laplace's equation. The harmonic function solution with mixed boundary conditions provides paths that verify the smoothness and safety considerations required for mobile robot path planning. The proposed approach uses the Finite Elements Method to solve Laplace's equation, and this allows us to deal with complicated shapes of obstacles and walls. Mixed boundary conditions are applied to the harmonic function to improve the quality of the trajectories. In this way, the trajectories are smooth, avoiding the corners of walls and obstacles, and the potential slope is not too small, avoiding the difficulty of the numerical calculus of the trajectory. Results show that this method is able to deal with moving obstacles, and even for non-holonomic vehicles. The proposed method can be generalized to 3D or more dimensions and it can be used to move robot manipulators

High-accuracy global localization filter for three-dimensional environments

The localization problem in mobile robotics can be defined as the search of the robot's coordinates in a known environment. If there is no information about the initial location, we are talking about global localization. In this work, we have developed an algorithm that solves this problem in a three-dimensional (3D) environment using evolutionary computation concepts. The method has been called RELF-3D and has many features that make it very robust and reliable: thresholding and discarding mechanisms, different cost functions, effective convergence criteria, and so on. The resulting global localization module has been tested in numerous experiments and the most important improvement obtained is the accuracy of the method, allowing its application in manipulation tasksThe localization problem in mobile robotics can be defined as the search of the robot's coordinates in a known environment. If there is no information about the initial location, we are talking about global localization. In this work, we have developed an algorithm that solves this problem in a three-dimensional (3D) environment using evolutionary computation concepts. The method has been called RELF-3D and has many features that make it very robust and reliable: thresholding and discarding mechanisms, different cost functions, effective convergence criteria, and so on. The resulting global localization module has been tested in numerous experiments and the most important improvement obtained is the accuracy of the method, allowing its application in manipulation tasksThis work has been supported by the CAM Project S2009/DPI-1559/ROBOCITY2030 II, developed by the research team RoboticsLab at the University Carlos III of Madrid.Publicad

An anisotropic fast marching method applied to path planning for Mars rovers

This paper presents the application of the Anisotropic Fast Marching Method to the path planning problem of mobile robots moving in outdoors environments, such as Mars. Considering that at any point on a 3D surface there are two main slopes: the maximum, which is the slope of the gradient, and the minimum, the height map of a terrain can be considered as a tensor filed. Using the Anisotropic Fast Marching Method, the resulting trajectory of the path planning takes the tensor field into account so that the slopes in the trajectory are minimized. Numerical simulations are presented to show the advantage of this method over its isotropic version. Besides, the influence of the anisotropic index and the traversability of the resultant paths are analyzed.This work was supported in part by the projects: "RoboCity2030-III-CM project (Robótica aplicada a la mejora de la calidad de vida de los ciudadanos. fase III; S2013/MIT-2748), in part by Programas de Actividades I+D en la Comunidad de Madrid and cofunded by Structural Funds of the EU" and in part by "Investigación para la mejora competitiva del ciclo de perforación y voladura en minería y obras subterráneas, mediante la concepción de nuevas técnicas de ingeniería, explosivos, prototipos y herramientas avanzadas (TUÑEL)"

Fast marching subjected to a vector field-path planning method for mars rovers

Path planning is an essential tool for the robots that explore the surface of Mars or other celestial bodies such as dwarf planets, asteroids, or moons. These vehicles require expert and intelligent systems to adopt the best decisions in order to survive in a hostile environment. The planning module has to take into account multiple factors such as the obstacles, the slope of the terrain, the surface roughness, the type of ground (presence of sand), or the information uncertainty. This paper presents a path planning system for rovers based on an improved version of the Fast Marching (FM) method. Scalar and vectorial properties are considered when computing the potential field which is the basis of the proposed technique. Each position in the map of the environment has a cost value (potential) that is used to include different types of variables. The scalar properties can be introduced in a component of the cost function that can represent characteristics such as difficulty, slowness, viscosity, refraction index, or incertitude. The cost value can be computed in different ways depending on the information extracted from the surface and the sensor data of the rover. In this paper, the surface roughness, the slope of the terrain, and the changes in height have been chosen according to the available information. When the robot is navigating sandy terrain with a certain slope, there is a landslide that has to be considered and corrected in the path calculation. This landslide is similar to a lateral current or vector field in the direction of the negative gradient of the surface. Our technique is able to compensate this vector field by introducing the influence of this variable in the cost function. Because of this modification, the new method has been called Fast Marching (subjected to a) vector field (FMVF). Different experiments have been carried out in simulated and real maps to test the method performance.Publicad

Differential evolution Markov chain filter for global localization

A key challenge for an autonomous mobile robot is to estimate its location according to the available information. A particular aspect of this task is the global localization problem. In our previous work, we developed an algorithm based on the Differential Evolution method that solves this problem in 2D and 3D environments. The robot’s pose is represented by a set of possible location estimates weighted by a fitness function. The Markov Chain Monte Carlo algorithms have been successfully applied to multiple fields such as econometrics or computing science. It has been demonstrated that they can be combined with the Differential Evolution method to solve efficiently many optimization problems. In this work, we have combined both approaches to develop a global localization filter. The algorithm performance has been tested in simulated and real maps. The population requirements have been reduced when compared to the previous version.The research leading to these results has received funding from the RoboCity2030-III-CM project (Robotica aplicada a la mejora de la calidad de vida de los ciudadanos. fase III; S2013/MIT-2748), funded by Programas de Actividades I+D en la Comunidad de Madrid and cofunded by Structural Funds of the EU.Publicad

Design of Fractional Order Controllers Using the PM Diagram

This article belongs to the Special Issue Fractional Calculus and Nonlinear SystemsThis work presents a modeling and controller tuning method for non-rational systems. First, a graphical tool is proposed where transfer functions are represented in a four-dimensional space. The magnitude is represented in decibels as the third dimension and a color code is applied to represent the phase in a fourth dimension. This tool, which is called Phase Magnitude (PM) diagram, allows the user to visually obtain the phase and the magnitude that have to be added to a system to meet some control design specifications. The application of the PM diagram to systems with non-rational transfer functions is discussed in this paper. A fractional order Proportional Integral Derivative (PID) controller is computed to control different non-rational systems. The tuning method, based on evolutionary computation concepts, relies on a cost function that defines the behavior in the frequency domain. The cost value is read in the PM diagram to estimate the optimum controller. To validate the contribution of this research, four different non-rational reference systems have been considered. The method proposed here contributes first to a simpler and graphical modeling of these complex systems, and second to provide an effective tool to face the unsolved control problem of these systems

Kullback-Leibler divergence-based differential eEvolution Markov chain filter for global localization of mobile robots

One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot's pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area.The research leading to these results has received funding from the RoboCity2030-III-CM project (Robótica aplicada a la mejora de la calidad de vida de los ciudadanos, fase III; S2013/MIT-2748),funded by Programas de Actividades I+Den la Comunidad de Madrid and cofunded by the Structural Funds of the EU

DE-based tuning of PIλDμ controllers

A new method that relies on evolutionary computation concepts is proposed in this paper to tune the parameters of fractional order PIlambdaDmu controllers, in which the orders of the integral and derivative parts, lambda and mu, respectively, are fractional. The main advantage of the fractional order controllers is that the increase in the number of parameters in the controller allows an increase in the number of control specifications that can be met. A Differential Evolution (DE) algorithm is proposed to make the controlled system fulfill different design specifications in time and frequency domains. This method is based on the minimization of a fitness function. Experiments have been carried out in simulation and in a real DC motor platform. The results illustrate the effectiveness of this method.Publicad