GPS raw data (control points and ground control points) from the Liguria Region, Borghetto Santo Spirito, Italy

Monitoring the impact of sea storms on coastal areas is fundamental to study beach evolution and the vulnerability of low-lying coasts to erosion and flooding. Modelling wave runup on a beach is possible, but it requires accurate topographic data and model tuning, that can be done comparing observed and modeled runup. In this study we collected aerial photos using an Unmanned Aerial Vehicle after two different swells on the same study area. We merged the point cloud obtained with photogrammetry with multibeam data, in order to obtain a complete beach topography. Then, on each set of rectified and georeferenced UAV orthophotos, we identified the maximum wave runup for both events recognizing the wet area left by the waves. We then used our topography and numerical models to simulate the wave runup and compare the model results to observed values during the two events. Our results highlight the potential of the methodology presented, which integrates UAV platforms, photogrammetry and Geographic Information Systems to provide faster and cheaper information on beach topography and geomorphology compared with traditional techniques without losing in accuracy. We use the results obtained from this technique as a topographic base for a model that calculates runup for the two swells. The observed and modeled runups are consistent, and open new directions for future research.

Aerodynamic study of airfoils geometric imperfections at low Reynolds number

The interest of this study is based on the observation that some manufacturing processes of various vehicles wings, such as unmanned aerial vehicle (UAV), or blades, such as wind turbine blades, or other devices that use aerodynamic profiles, produce imperfections in the leading edge or open trailing edge with bigger thickness than original airfoil, because, for example, they are manufactured in two parts, top surface and bottom surface and subsequently joined. In this last step might appear a sliding between the top surface and the bottom surface having a small step on the leading edge or a small thickness gain can occur on the trailing edge. Normally these imperfections are corrected through a refill and/or sanding processes using many hours of manual labor. Therefore the initial objective of this research is to determine the level of influence in the aerodynamic characteristics at low Reynolds numbers (Lissaman, 1981, Carmichael, 1981, Nagamatsu and Cuche, 1981, Schmitz, 1957, Cebeci, 1989, Mueller and Batill, 1982) of these imperfections in the manufacture, and determine whether there may be a value for which it would not be necessary to correct them

Biomechanics of smart wings in a bat robot: morphing wings using SMA actuators

This paper presents the design of a bat-like micro aerial vehicle with actuated morphing wings. NiTi shape memory alloys (SMAs) acting as artificial biceps and triceps muscles are used for mimicking the morphing wing mechanism of the bat flight apparatus. Our objective is twofold. Firstly, we have implemented a control architecture that allows an accurate and fast SMA actuation. This control makes use of the electrical resistance measurements of SMAs to adjust morphing wing motions. Secondly, the feasibility of using SMA actuation technology is evaluated for the application at hand. To this purpose, experiments are conducted to analyze the control performance in terms of nominal and overloaded operation modes of the SMAs. This analysis includes: (i) inertial forces regarding the stretchable wing membrane and aerodynamic loads, and (ii) uncertainties due to impact of airflow conditions over the resistance–motion relationship of SMAs. With the proposed control, morphing actuation speed can be increased up to 2.5 Hz, being sufficient to generate lift forces at a cruising speed of 5ms−1.

Towards a ground navigation system based in visual feedback provided by a mini UAV

This paper addresses initial efforts to develop a navigation system for ground vehicles supported by visual feedback from a mini aerial vehicle. A visual-based algorithm computes the ground vehicle pose in the world frame, as well as possible obstacles within the ground vehicle pathway. Relying on that information, a navigation and obstacle avoidance system is used to re-plan the ground vehicle trajectory, ensuring an optimal detour. Finally, some experiments are presented employing a unmanned ground vehicle (UGV) and a low cost mini unmanned aerial vehicle (UAV).

See-and-avoid quadcopter using fuzzy control optimized by cross-entropy

In this work we present an optimized fuzzy visual servoing system for obstacle avoidance using an unmanned aerial vehicle. The cross-entropy theory is used to optimise the gains of our controllers. The optimization process was made using the ROS-Gazebo 3D simulation with purposeful extensions developed for our experiments. Visual servoing is achieved through an image processing front-end that uses the Camshift algorithm to detect and track objects in the scene. Experimental flight trials using a small quadrotor were performed to validate the parameters estimated from simulation. The integration of crossentropy methods is a straightforward way to estimate optimal gains achieving excellent results when tested in real flights.

Fusion of probabilistic knowledge-based classification rules and learning automata for automatic recognition of digital images

In this paper, the fusion of probabilistic knowledge-based classification rules and learning automata theory is proposed and as a result we present a set of probabilistic classification rules with self-learning capability. The probabilities of the classification rules change dynamically guided by a supervised reinforcement process aimed at obtaining an optimum classification accuracy. This novel classifier is applied to the automatic recognition of digital images corresponding to visual landmarks for the autonomous navigation of an unmanned aerial vehicle (UAV) developed by the authors. The classification accuracy of the proposed classifier and its comparison with well-established pattern recognition methods is finally reported.

Arquitectura cognitiva híbrida para la navegación autónoma de UAVs mediante mapas topológicos visuales

El objetivo fundamental de la presente tesis doctoral es el diseño de una arquitectura cognitiva, que pueda ser empleada para la navegación autónoma de vehículos aéreos no tripulados conocidos como UAV (Unmanned Aerial Vehicle). Dicha arquitectura cognitiva se apoya en la definición de una librería de comportamientos, que aportarán la inteligencia necesaria al UAV para alcanzar los objetivos establecidos, en base a la información sensorial recopilada del entorno de operación. La navegación autónoma del UAV se apoyará en la utilización de un mapa topológico visual, consistente en la definición de un grafo que engloba mediante nodos los diferentes landmarks ubicados en el entorno, y que le servirán al UAV de guía para alcanzar su objetivo. Los arcos establecidos entre los nodos del mapa topológico, le proporcionarán de la información necesaria para establecer el rumbo más adecuado para alcanzar el siguiente landmark a visitar, siguiendo siempre una secuencia lógica de navegación, basada en la distancia entre un determinado landmark con respecto al objetivo final ó landmark destino. La arquitectura define un mecanismo híbrido de control, el cual puede conmutar entre dos diferentes modos de navegación. El primero es el denominado como Search Mode, el cual se activará cuando el UAV se encuentre en un estado desconocido dentro del entorno, para lo cual hará uso de cálculos basado en la entropía para la búsqueda de posibles landmarks. Se empleará como estrategia novedosa la idea de que la entropía de una imagen tiene una correlación directa con respecto a la probabilidad de que dicha imagen contenga uno ó varios landmarks. De esta forma, la estrategia para la búsqueda de nuevos landmarks en el entorno, se basará en un proceso continuo de maximización de la entropía. Si por el contrario el UAV identifica la existencia de un posible landmark entre los definidos en su mapa topológico, se considerará que está sobre un estado conocido, por lo que se conmutará al segundo modo de navegación denominado como Homing Mode, el cual se encargará de calcular señales de control para la aproximación del UAV al landmark localizado. Éste último modo implementa un control dual basado en dos tipos de controladores (FeedForward/FeedBack) que mediante su combinación, aportarán al UAV señales de control cada vez más óptimas, además de llevar a cabo un entrenamiento continuo y en tiempo real. Para cumplir con los requisitos de ejecución y aprendizaje en tiempo real de la arquitectura, se han tomado como principales referencias dos paradigmas empleados en diferentes estudios dentro del área de la robótica, como son el paradigma de robots de desarrollo (developmental robots) basado en un aprendizaje del robot en tiempo real y de forma adaptativa con su entorno, así como del paradigma de modelos internos (internal models) basado en los resultados obtenidos a partir de estudios neurocientíficos del cerebelo humano; dicho modelo interno sirve de base para la construcción del control dual de la arquitectura. Se presentarán los detalles de diseño e implementación de los diferentes módulos que componen la arquitectura cognitiva híbrida, y posteriormente, los diferentes resultados obtenidos a partir de las pruebas experimentales ejecutadas, empleando como UAV la plataforma robótica aérea de AR.Drone. Como resultado final se ha obtenido una validación completa de la arquitectura cognitiva híbrida objetivo de la tesis, cumplimento con la totalidad de requisitos especificados y garantizando su viabilidad como aplicación operativa en el mundo real. Finalmente, se muestran las distintas conclusiones a las cuales se ha llegado a partir de los resultados experimentales, y se presentan las diferentes líneas de investigación futuras que podrán ser ejecutadas.

New generation of human machine interfaces for controlling UAV through depth based gesture recognition

New forms of natural interactions between human operators and UAVs (Unmanned Aerial Vehicle) are demanded by the military industry to achieve a better balance of the UAV control and the burden of the human operator. In this work, a human machine interface (HMI) based on a novel gesture recognition system using depth imagery is proposed for the control of UAVs. Hand gesture recognition based on depth imagery is a promising approach for HMIs because it is more intuitive, natural, and non-intrusive than other alternatives using complex controllers. The proposed system is based on a Support Vector Machine (SVM) classifier that uses spatio-temporal depth descriptors as input features. The designed descriptor is based on a variation of the Local Binary Pattern (LBP) technique to efficiently work with depth video sequences. Other major consideration is the especial hand sign language used for the UAV control. A tradeoff between the use of natural hand signs and the minimization of the inter-sign interference has been established. Promising results have been achieved in a depth based database of hand gestures especially developed for the validation of the proposed system.

Sistema de soporte al desarrollo de un planificador de misiones en un vehículo aéreo no tripulado

En esta memoria se describe el trabajo de construcción de una arquitectura software diseñada para facilitar el desarrollo un planificador de misión de un vehículo aéreo no tripulado (UAV), con el fin de que éste alcance los objetivos marcados en la competición internacional de robótica IARC (séptima edición). A lo largo de la memoria, se describe en primer lugar, una revisión de técnicas de robótica inteligente aplicadas a la construcción de vehículos aéreos no tripulados, en el que se ven los diferentes paradigmas de programación de la robótica inteligente y la clasificación de dichos robots aéreos, dependiendo de su autonomía. Este descripción finaliza con la presentación del problema correspondiente a la competición IARC. A continuación se describe el diseño realizado para soporte al desarrollo de un planificador de misiones de UAVs, con simulación de comportamiento de vehículos robóticos y visualización 3D con movimiento. Finalmente, se muestran las pruebas que se han realizado para validar la construcción de dicha arquitectura software. ---ABSTRACT---In this report it is presented the construction of a software architecture, designed to facilitate the development of a mission planner for an unmanned aerial vehicle (UAV), so that it reaches the goals set in the International Aerial Robotics Competition - IARC (seventh edition). Throughout this report, it is described first, a review of intelligent robotics techniques applied to the construction of unmanned aerial vehicles, where different paradigms of intelligent robotics are seen, along with a classification of such aerial robots, depending on their autonomy. Description ends with the presentation of the problem corresponding to the IARC competition. Following, it is described the design made to satisfy the support to the development of a mission planner for UAV´s, with a simulation of the robotics vehicles’ behaviours and a 3D display with motion. Finally, we will deal with the tests that have been conducted to validate the construction of the software architecture.

Control reactivo de vehículo aéreo no tripulado para la competición internacional IARC

El trabajo está centrado en la construcción de una simulación y en el desarrollo de un control reactivo para un vehículo aéreo no tripulado con fin de participar en la séptima edición de la competición internacional IARC. Para cumplir los objetivos de la competición se van a estudiar técnicas existentes de inteligencia artificial aplicadas al control de vehículos aéreos no tripulados, así como las técnicas para la elaboración de un modelo de simulación realista sobre el que realizar las distintas pruebas. Por último, se explica el trabajo realizado para crear un controlador reactivo que satisface las reglas de la competición y permite al vehículo aéreo no tripulado operar de forma autónoma en el ambiente de la simulación. Para validar el comportamiento, se realizan casos de prueba y un estudio de los resultados.---ABSTRACT---This report is focused on the construction of a simulation and the development of a reactive control for an unmanned aerial vehicle in order to participate in the seventh edition of the international competition IARC. Artificial intelligence techniques applied to the control of unmanned aerial vehicles are going to be studied to meet the objectives of the competition, as well as techniques for developing a realistic simulation model on which to perform the different tests. Finally, the last part of the report explains the work accomplished to create a reactive controller that meets the rules of the competition and allows the unmanned aerial vehicle to operate autonomously in the simulation environment. Test cases and a study of the results is performed to validate the behavior.

Vision-Based Tracking, Odometry and Control for UAV Autonomy

El principal objetivo de este trabajo es proporcionar una solución en tiempo real basada en visión estéreo o monocular precisa y robusta para que un vehículo aéreo no tripulado (UAV) sea autónomo en varios tipos de aplicaciones UAV, especialmente en entornos abarrotados sin señal GPS. Este trabajo principalmente consiste en tres temas de investigación de UAV basados en técnicas de visión por computador: (I) visual tracking, proporciona soluciones efectivas para localizar visualmente objetos de interés estáticos o en movimiento durante el tiempo que dura el vuelo del UAV mediante una aproximación adaptativa online y una estrategia de múltiple resolución, de este modo superamos los problemas generados por las diferentes situaciones desafiantes, tales como cambios significativos de aspecto, iluminación del entorno variante, fondo del tracking embarullado, oclusión parcial o total de objetos, variaciones rápidas de posición y vibraciones mecánicas a bordo. La solución ha sido utilizada en aterrizajes autónomos, inspección de plataformas mar adentro o tracking de aviones en pleno vuelo para su detección y evasión; (II) odometría visual: proporciona una solución eficiente al UAV para estimar la posición con 6 grados de libertad (6D) usando únicamente la entrada de una cámara estéreo a bordo del UAV. Un método Semi-Global Blocking Matching (SGBM) eficiente basado en una estrategia grueso-a-fino ha sido implementada para una rápida y profunda estimación del plano. Además, la solución toma provecho eficazmente de la información 2D y 3D para estimar la posición 6D, resolviendo de esta manera la limitación de un punto de referencia fijo en la cámara estéreo. Una robusta aproximación volumétrica de mapping basada en el framework Octomap ha sido utilizada para reconstruir entornos cerrados y al aire libre bastante abarrotados en 3D con memoria y errores correlacionados espacialmente o temporalmente; (III) visual control, ofrece soluciones de control prácticas para la navegación de un UAV usando Fuzzy Logic Controller (FLC) con la estimación visual. Y el framework de Cross-Entropy Optimization (CEO) ha sido usado para optimizar el factor de escala y la función de pertenencia en FLC. Todas las soluciones basadas en visión en este trabajo han sido probadas en test reales. Y los conjuntos de datos de imágenes reales grabados en estos test o disponibles para la comunidad pública han sido utilizados para evaluar el rendimiento de estas soluciones basadas en visión con ground truth. Además, las soluciones de visión presentadas han sido comparadas con algoritmos de visión del estado del arte. Los test reales y los resultados de evaluación muestran que las soluciones basadas en visión proporcionadas han obtenido rendimientos en tiempo real precisos y robustos, o han alcanzado un mejor rendimiento que aquellos algoritmos del estado del arte. La estimación basada en visión ha ganado un rol muy importante en controlar un UAV típico para alcanzar autonomía en aplicaciones UAV. ABSTRACT The main objective of this dissertation is providing real-time accurate robust monocular or stereo vision-based solution for Unmanned Aerial Vehicle (UAV) to achieve the autonomy in various types of UAV applications, especially in GPS-denied dynamic cluttered environments. This dissertation mainly consists of three UAV research topics based on computer vision technique: (I) visual tracking, it supplys effective solutions to visually locate interesting static or moving object over time during UAV flight with on-line adaptivity approach and multiple-resolution strategy, thereby overcoming the problems generated by the different challenging situations, such as significant appearance change, variant surrounding illumination, cluttered tracking background, partial or full object occlusion, rapid pose variation and onboard mechanical vibration. The solutions have been utilized in autonomous landing, offshore floating platform inspection and midair aircraft tracking for sense-and-avoid; (II) visual odometry: it provides the efficient solution for UAV to estimate the 6 Degree-of-freedom (6D) pose using only the input of stereo camera onboard UAV. An efficient Semi-Global Blocking Matching (SGBM) method based on a coarse-to-fine strategy has been implemented for fast depth map estimation. In addition, the solution effectively takes advantage of both 2D and 3D information to estimate the 6D pose, thereby solving the limitation of a fixed small baseline in the stereo camera. A robust volumetric occupancy mapping approach based on the Octomap framework has been utilized to reconstruct indoor and outdoor large-scale cluttered environments in 3D with less temporally or spatially correlated measurement errors and memory; (III) visual control, it offers practical control solutions to navigate UAV using Fuzzy Logic Controller (FLC) with the visual estimation. And the Cross-Entropy Optimization (CEO) framework has been used to optimize the scaling factor and the membership function in FLC. All the vision-based solutions in this dissertation have been tested in real tests. And the real image datasets recorded from these tests or available from public community have been utilized to evaluate the performance of these vision-based solutions with ground truth. Additionally, the presented vision solutions have compared with the state-of-art visual algorithms. Real tests and evaluation results show that the provided vision-based solutions have obtained real-time accurate robust performances, or gained better performance than those state-of-art visual algorithms. The vision-based estimation has played a critically important role for controlling a typical UAV to achieve autonomy in the UAV application.

Estudio, ensamblaje, caracterización y ensayos de dos modelos reales de RPA

Un dron o un RPA (del inglés, Remote Piloted Aircraft) es un vehículo aéreo no tripulado capaz de despegar, volar y aterrizar de forma autónoma, semiautónoma o manual, siempre con control remoto. Además, toda aeronave de estas características debe ser capaz de mantener un nivel de vuelo controlado y sostenido. A lo largo de los años, estos aparatos han ido evolución tanto en aplicaciones como en su estética y características físicas, siempre impulsado por los requerimientos militares en cada momento. Gracias a este desarrollo, hoy en día los drones son uno más en la sociedad y desempeñan tareas que para cualquier ser humano serían peligrosas o difíciles de llevar a cabo. Debido a la reciente proliferación de los RPA, los gobiernos de los distintos países se han visto obligados a redactar nuevas leyes y/o modificar las ya existentes en relación a los diferentes usos del espacio aéreo para promover la convivencia de estas aeronaves con el resto de vehículos aéreos. El objeto principal de este proyecto es ensamblar, caracterizar y configurar dos modelos reales de dron: el DJI F450 y el TAROT t810. Para conseguir un montaje apropiado a las aplicaciones posteriores que se les va a dar, antes de su construcción se ha realizado un estudio individualizado en detalle de cada una de las partes y módulos que componen estos vehículos. Adicionalmente, se ha investigado acerca de los distintos tipos de sistemas de transmisión de control remoto, vídeo y telemetría, sin dejar de lado las baterías que impulsarán al aparato durante sus vuelos. De este modo, es sabido que los RPA están compuestos por distintos módulos operativos: los principales, todo aquel módulo para que el aparato pueda volar, y los complementarios, que son aquellos que dotan a cada aeronave de características adicionales y personalizadas que lo hacen apto para diferentes usos. A lo largo de este proyecto se han instalado y probado diferentes módulos adicionales en cada uno de los drones, además de estar ambos constituidos por distintos bloques principales, incluyendo el controlador principal: NAZA-M Lite instalado en el dron DJI F450 y NAZA-M V2 incorporado en el TAROT t810. De esta forma se ha podido establecer una comparativa real acerca del comportamiento de éstos, tanto de forma conjunta como de ambos controladores individualmente. Tras la evaluación experimental obtenida tras diversas pruebas de vuelo, se puede concluir que ambos modelos de controladores se ajustan a las necesidades demandadas por el proyecto y sus futuras aplicaciones, siendo más apropiada la elección del modelo M Lite por motivos estrictamente económicos, ya que su comportamiento en entornos recreativos es similar al modelo M V2. ABSTRACT. A drone or RPA (Remote Piloted Aircraft) is an unmanned aerial vehicle that is able to take off, to fly and to land autonomously, semi-autonomously or manually, always connected via remote control. In addition, these aircrafts must be able to keep a controlled and sustained flight level. Over the years, the applications for these devices have evolved as much as their aesthetics and physical features both boosted by the military needs along time. Thanks to this development, nowadays drones are part of our society, executing tasks potentially dangerous or difficult to complete by humans. Due to the recent proliferation of RPA, governments worldwide have been forced to draft legislation and/or modify the existing ones about the different uses of the aerial space to promote the cohabitation of these aircrafts with the rest of the aerial vehicles. The main objective of this project is to assemble, to characterize and to set-up two real drone models: DJI F450 and TAROT t810. Before constructing the vehicles, a detailed study of each part and module that composes them has been carried out, in order to get an appropriate structure for their expected uses. Additionally, the different kinds of remote control, video and telemetry transmission systems have been investigated, including the batteries that will power the aircrafts during their flights. RPA are made of several operative modules: main modules, i.e. those which make the aircraft fly, and complementary modules, that customize each aircraft and equip them with additional features, making them suitable for a particular use. Along this project, several complementary modules for each drone have been installed and tested. Furthermore, both are built from different main units, including the main controller: NAZA-M Lite installed on DJI F450 and NAZA-M V2 on board of TAROT t810. This way, it has been possible to establish an accurate comparison, related to the performance of both models, not only jointly but individually as well. After several flight tests and an experimental evaluation, it can be concluded that both main controller models are suitable for the requirements fixed for the project and the future applications, being more appropriate to choose the M Lite model strictly due to economic reasons, as its performance in recreational environment is similar to the M V2.

Utilização de veículo aéreo não tripulado de asa fixa no monitoramento e coleta de imagem de animais e ambientes em propriedades rurais

Este trabalho tem por finalidade mostrar a aplicação e a utilização de um aeromodelo elétrico de asa fixa, também conhecido como veículo aéreo não tripulado (VANT), com controle manual ou automático, para coleta de dados e imagens em propriedades rurais, com a premissa de auxiliar os gestores no processo de gestão e tomada de decisão. A metodologia utilizada para a realização das coletas foi feita por meio de voos programados em dias e condições diferentes, para verificação e análise de desempenho do aeromodelo. Os resultados obtidos com os voos foram acima do esperado, gerando excelentes imagens e dados confiáveis. Sendo assim, pôde-se concluir que a utilização de VANTs, em coletas de dados e imagens em propriedades rurais foi satisfatória e auxiliou os gestores no processo de gerenciamento e rotacionamento de animais no pasto, uma vez que as imagens permitiram uma boa visualização e o aeromodelo desenvolvido cumpriu o seu objetivo com bom desempenho e agilidade.

Criação de zonas de alta permeabilidade em fraturas: modelagem numérica do Lajedo de Soledade, Formação Jandaíra, Bacia Potiguar

The fracturing in carbonate rocks has been attracting increasingly attention due to new oil discoveries in carbonate reservoirs. This study investigates how the fractures (faults and joints) behave when subjected to different stress fields and how their behavior may be associated with the generation of karst and consequently to increased secondary porosity in these rocks. In this study I used satellite imagery and unmanned aerial vehicle UAV images and field data to identify and map faults and joints in a carbonate outcrop, which I consider a good analogue of carbonate reservoir. The outcrop comprises rocks of the Jandaíra Formation, Potiguar Basin. Field data were modeled using the TECTOS software, which uses finite element analysis for 2D fracture modeling. I identified three sets of fractures were identified: NS, EW and NW-SE. They correspond to faults that reactivate joint sets. The Ratio of Failure by Stress (RFS) represents stress concentration and how close the rock is to failure and reach the Mohr-Coulomb envelopment. The results indicate that the tectonic stresses are concentrated in preferred structural zones, which are ideal places for carbonate dissolution. Dissolution was observed along sedimentary bedding and fractures throughout the outcrop. However, I observed that the highest values of RFS occur in fracture intersections and terminations. These are site of karst concentration. I finally suggest that there is a relationship between stress concentration and location of karst dissolution in carbonate rocks.

Criação de zonas de alta permeabilidade em fraturas: modelagem numérica do Lajedo de Soledade, Formação Jandaíra, Bacia Potiguar

The fracturing in carbonate rocks has been attracting increasingly attention due to new oil discoveries in carbonate reservoirs. This study investigates how the fractures (faults and joints) behave when subjected to different stress fields and how their behavior may be associated with the generation of karst and consequently to increased secondary porosity in these rocks. In this study I used satellite imagery and unmanned aerial vehicle UAV images and field data to identify and map faults and joints in a carbonate outcrop, which I consider a good analogue of carbonate reservoir. The outcrop comprises rocks of the Jandaíra Formation, Potiguar Basin. Field data were modeled using the TECTOS software, which uses finite element analysis for 2D fracture modeling. I identified three sets of fractures were identified: NS, EW and NW-SE. They correspond to faults that reactivate joint sets. The Ratio of Failure by Stress (RFS) represents stress concentration and how close the rock is to failure and reach the Mohr-Coulomb envelopment. The results indicate that the tectonic stresses are concentrated in preferred structural zones, which are ideal places for carbonate dissolution. Dissolution was observed along sedimentary bedding and fractures throughout the outcrop. However, I observed that the highest values of RFS occur in fracture intersections and terminations. These are site of karst concentration. I finally suggest that there is a relationship between stress concentration and location of karst dissolution in carbonate rocks.