Skeletal representations of orthogonal shapes

Skeletal representations are important shape descriptors which encode topological and geometrical properties of shapes and reduce their dimension. Skeletons are used in several fields of science and attract the attention of many researchers. In the biocad field, the analysis of structural properties such as porosity of biomaterials requires the previous computation of a skeleton. As the size of three-dimensional images become larger, efficient and robust algorithms that extract simple skeletal structures are required. The most popular and prominent skeletal representation is the medial axis, defined as the shape points which have at least two closest points on the shape boundary. Unfortunately, the medial axis is highly sensitive to noise and perturbations of the shape boundary. That is, a small change of the shape boundary may involve a considerable change of its medial axis. Moreover, the exact computation of the medial axis is only possible for a few classes of shapes. For example, the medial axis of polyhedra is composed of non planar surfaces, and its accurate and robust computation is difficult. These problems led to the emergence of approximate medial axis representations. There exists two main approximation methods: the shape is approximated with another shape class or the Euclidean metric is approximated with another metric. The main contribution of this thesis is the combination of a specific shape and metric simplification. The input shape is approximated with an orthogonal shape, which are polygons or polyhedra enclosed by axis-aligned edges or faces, respectively. In the same vein, the Euclidean metric is replaced by the L infinity or Chebyshev metric. Despite the simpler structure of orthogonal shapes, there are few works on skeletal representations applied to orthogonal shapes. Much of the efforts have been devoted to binary images and volumes, which are a subset of orthogonal shapes. Two new skeletal representations based on this paradigm are introduced: the cube skeleton and the scale cube skeleton. The cube skeleton is shown to be composed of straight line segments or planar faces and to be homotopical equivalent to the input shape. The scale cube skeleton is based upon the cube skeleton, and introduces a family of skeletons that are more stable to shape noise and perturbations. In addition, the necessary algorithms to compute the cube skeleton of polygons and polyhedra and the scale cube skeleton of polygons are presented. Several experimental results confirm the efficiency, robustness and practical use of all the presented methods

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Distributed framework for a multi-purpose household robotic arm

Projecte final de carrera fet en col.laboració amb l'Institut de Robòtica i Informàtica IndustrialThe concept of household robotic servants has been in our mind for ages, and domestic appliances are far more robotised than they used to be. At present, manufacturers are starting to introduce small, household human-interactive robots to the market. Any human-interactive device has safety, endurability and simplicity constraints, which are especially strict when it comes to robots. Indeed, we are still far from a multi-purpose intelligent household robot, but human-interactive robots and arti cial intelligence research has evolved considerably, demonstration prototypes are a proof of what can be done. This project contributes to the research in humaninteractive robots, as the robotic arm and hand used are specially designed for human-interactive applications. The present study provides a distributed framework for an arm and a hand devices based on the robotics YARP protocol using the WAMTM arm and the BarrettHandTM as well as a basic modular client application complemented with vision. Firstly, two device drivers and a network interface are designed and implemented to control the WAMTM arm and the BarrettHandTM from the network. The drivers allow abstract access to each device, providing three ports: command requests port, state requests port and asynchronous replies port. Secondly, each driver is then encapsulated by YARP devices publishing realtime monitoring feedback and motion control to the network through what is called a Network wrapper. In particular, the network wrapper for the WAMTM arm and BarrettHandTM provides a state port, command port, Remote Procedure Call (RPC) port and an asynchronous noti cations port. The state port provides the WAMTM position and orientation feedback at 50 Hz, which represents a maximum blindness of one centimetre. This rst part of the project sets the foundations of a distributed, complete robot, whose design enables processing and power payload to be shared by di erent workstations. Moreover, users are able to work with the robot remotely over Ethernet and Wireless through a clear, understandable local interface within YARP. In addition to the distributed robotic framework provided, a client software framework with vision is also supplied. The client framework establishes a general software shell for further development and is organized in the basic, separate robotic branches: control, vision and plani cation. The vision module supports distributed image grabbing on mobile robotics, and shared-memory for xed, local vision. In order to incorporate environment interaction and robot autonomy with the planner, hand-eye transformation matrices have been obtained to perform object grasping and manipulation. The image processing is based on OpenCV libraries and provides object recognition with Scale Invariant Feature Transform (SIFT) features matching, Hough transform and polygon approximation algorithms. Grasping and path planning use pre-de ned grasps which take into account the size, shape and orientation of the target objects. The proof-of-concept applications feature a household robotic arm with the ability to tidy randomly distributed common kitchen objects to speci ed locations, with robot real-time monitoring and basic control. The device modularity introduced in this project philosophy of decoupling communication, device local access and the components, was successful. Thanks to the abstract access and decoupling, the demonstration applications provided were easily deployed to test the arm's performance and its remote control and monitorization. Moreover, both resultant frameworks are arm-independent and the design is currently being adopted by other projects' devices within the IRI

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

Learning Probabilistic Generative Models For Fast Sampling-Based Planning

Due to their simplicity and efficiency in high dimensional space, sampling-based motion planners have been gaining interest for robotic manipulation in recent years. We present several new learning approaches using probabilistic generative models for fast sampling-based planning. First, we propose fast collision detection in high dimensional configuration spaces based on Gaussian Mixture Models (GMMs) for Rapidly-exploring Random Trees (RRT). In addition, we introduce a new probabilistically safe local steering primitive based on the probabilistic model. Our local steering procedure is based on a new notion of a convex probabilistically safety corridor that is constructed around a configuration using tangent hyperplanes of confidence ellipsoids of GMMs learned from prior collision history. For efficient sampling, we suggest a sampling method with a learned Q-function with linear function approximation based on feature representations such as Radial Basis Functions. This sampling method chooses the optimal node from which to extend the search tree via the softmax function of learned state values. We also discuss a novel constrained sampling-based motion planning method for grasp and transport tasks with redundant robotic manipulators, which allows the best grasp configuration and approach direction to be automatically determined. Since these approaches with the learned probabilistic models require large size data and time for training, it is essential that they are able to be adapted to environmental change in an online manner. The suggested online learning approach with the Dirichlet Process Mixture Model (DPMM) can adapt the complexity to the data and learn new Gaussian clusters with streaming data in newly explored areas without batch learning. We have applied these approaches in a number of robot arm planning scenarios and have shown their utility and effectiveness in simulation and on a physical 7-DoF robot manipulator

Conference on Intelligent Robotics in Field, Factory, Service, and Space (CIRFFSS 1994), volume 1

The AIAA/NASA Conference on Intelligent Robotics in Field, Factory, Service, and Space (CIRFFSS '94) was originally proposed because of the strong belief that America's problems of global economic competitiveness and job creation and preservation can partly be solved by the use of intelligent robotics, which are also required for human space exploration missions. Individual sessions addressed nuclear industry, agile manufacturing, security/building monitoring, on-orbit applications, vision and sensing technologies, situated control and low-level control, robotic systems architecture, environmental restoration and waste management, robotic remanufacturing, and healthcare applications

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Chemical Kinetics

Chemical Kinetics relates to the rates of chemical reactions and factors such as concentration and temperature, which affects the rates of chemical reactions. Such studies are important in providing essential evidence as to the mechanisms of chemical processes. The book is designed to help the reader, particularly students and researchers of physical science, understand the chemical kinetics mechanics and chemical reactions. The selection of topics addressed and the examples, tables and graphs used to illustrate them are governed, to a large extent, by the fact that this book is aimed primarily at physical science (mainly chemistry) technologists. Undoubtedly, this book contains "must read" materials for students, engineers, and researchers working in the chemistry and chemical kinetics area. This book provides valuable insight into the mechanisms and chemical reactions. It is written in concise, self-explanatory and informative manner by a world class scientists in the field