A Fibonacci control system with application to hyper-redundant manipulators

We study a robot snake model based on a discrete linear control system involving Fibonacci sequence and closely related to the theory of expansions in non-integer bases. The present paper includes an investigation of the reachable workspace, a more general analysis of the control system underlying the model, its reachability and local controllability properties and the relation with expansions in non-integer bases and with iterated function systems

Basis expansions in applied mathematics

Basis expansions are an extremely useful tool in applied mathematics. By using them, we can express a function representing a physical quantity as a linear combination of simpler ``modules'' with well-known properties. They are particularly useful for the applications described in this thesis. Perhaps the best known expansion of this type is the Fourier series of a periodic function, as decomposition into the infinite sum of simple sinusoidal and cosinusoidal elements, originally proposed by Fourier to study heat transfer. This dissertation employs some mathematical tools on problems taken from various areas of Engineering, exploiting their expansion properties: 1) Non-integer bases, which are applied to mathematical models in Robotics (Chapter 2). In this Chapter we study, in particular, a model for snake-like robots based on the Fibonacci sequence. It includes an investigation of the reachableworkspace, a more general analysis of the control system underlying the model, its reachability and local controllability properties. 2) Orthonormal bases, Riesz bases: exponential and cardinal Riesz basis with perturbations (Chapter 3). In this Chapter we obtain also a stability result for cardinal Riesz basis in the case of complex perturbations of the integers. We also consider a mathematical model for energy of the signal at the output of an ideal DAC, in presence of sampling clock jitter. When sampling clock jitter occurs, the energy of the signal at the output of ideal DAC does not satisfies a Parseval identity. Nevertheless, an estimation of the signal energy is here shown by a direct method involving cardinal series. 3) Orthogonal polynomials (Chapter 4). In this Chapter we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev polynomials of the first and second kind. We discuss some relations between zeros of Lucas-Lehmer polynomials and Gray code. We study nested square roots of 2 applying a "binary code" that associates bits 0 and 1 to + and - signs in the nested form. This gives the possibility to obtain an ordering for the zeros of Lucas-Lehmer polynomials, which take the form of nested square roots of 2. These zeros are used to obtain two new formulas for Pi

Modular soft pneumatic actuator system design for compliance matching

The future of robotics is personal. Never before has technology been as pervasive as it is today, with advanced mobile electronics hardware and multi-level network connectivity pushing âsmartâ devices deeper into our daily lives through home automation systems, virtual assistants, and wearable activity monitoring. As the suite of personal technology around us continues to grow in this way, augmenting and offloading the burden of routine activities of daily living, the notion that this trend will extend to robotics seems inevitable. Transitioning robots from their current principal domain of industrial factory settings to domestic, workplace, or public environments is not simply a matter of relocation or reprogramming, however. The key differences between âtraditionalâ types of robots and those which would best serve personal, proximal, human interactive applications demand a new approach to their design. Chief among these are requirements for safety, adaptability, reliability, reconfigurability, and to a more practical extent, usability. These properties frame the context and objectives of my thesis work, which seeks to provide solutions and answers to not only how these features might be achieved in personal robotic systems, but as well what benefits they can afford. I approach the investigation of these questions from a perspective of compliance matching of hardware systems to their applications, by providing methods to achieve mechanical attributes complimentary to their environment and end-use. These features are fundamental to the burgeoning field of Soft Robotics, wherein flexible, compliant materials are used as the basis for the structure, actuation, sensing, and control of complete robotic systems. Combined with pressurized air as a power source, soft pneumatic actuator (SPA) based systems offers new and novel methods of exploiting the intrinsic compliance of soft material components in robotic systems. While this strategy seems to answer many of the needs for human-safe robotic applications, it also brings new questions and challenges: What are the needs and applications personal robots may best serve? Are soft pneumatic actuators capable of these tasks, or âusefulâ work output and performance? How can SPA based systems be applied to provide complex functionality needed for operation in diverse, real-world environments? What are the theoretical and practical challenges in implementing scalable, multiple degrees of freedom systems, and how can they be overcome? I present solutions to these problems in my thesis work, elucidated through scientific design, testing and evaluation of robotic prototypes which leverage and demonstrate three key features: 1) Intrinsic compliance: provided by passive elastic and flexible component material properties, 2) Extrinsic compliance: rendered through high number of independent, controllable degrees of freedom, and 3) Complementary design: exhibited by modular, plug and play architectures which combine both attributes to achieve compliant systems. Through these core projects and others listed below I have been engaged in soft robotic technology, its application, and solutions to the challenges which are critical to providing a path forward within the soft robotics field, as well as for the future of personal robotics as a whole toward creating a better society

Fast Marching Methods in path and motion planning: improvements and high-level applications

Mención Internacional en el título de doctorPath planning is defined as the process to establish the sequence of states a system must go through in order to reach a desired state. Additionally, motion planning (or trajectory planning) aims to compute the sequence of motions (or actions) to take the system from one state to another. In robotics path planning can refer for instance to the waypoints a robot should follow through a maze or the sequence of points a robotic arm has to follow in order to grasp an object. Motion planning is considered a more general problem, since it includes kinodynamic constraints. As motion planning is a more complex problem, it is often solved in a two-level approach: path planning in the first level and then a control layer tries to drive the system along the specified path. However, it is hard to guarantee that the final trajectory will keep the initial characteristics. The objective of this work is to solve different path and motion planning problems under a common framework in order to facilitate the integration of the different algorithms that can be required during the nominal operation of a mobile robot. Also, other related areas such as motion learning are explored using this framework. In order to achieve this, a simple but powerful algorithm called Fast Marching will be used. Originally, it was proposed to solve optimal control problems. However, it has became very useful to other related problems such as path and motion planning. Since Fast Marching was initially proposed, many different alternative approaches have been proposed. Therefore, the first step is to formulate all these methods within a common framework and carry out an exhaustive comparison in order to give a final answer to: which algorithm is the best under which situations? This Thesis shows that the different versions of Fast Marching Methods become useful when applied to motion and path planning problems. Usually, high-level problems as motion learning or robot formation planning are solved with completely different algorithms, as the problem formulation are mixed. Under a common framework, task integration becomes much easier bringing robots closer to everyday applications. The Fast Marching Method has also inspired modern probabilistic methodologies, where computational cost is enormously improved at the cost of bounded, stochastic variations on the resulting paths and trajectories. This Thesis also explores these novel algorithms and their performance.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Carlos Balaguer Bernaldo de Quirós.- Secretario: Antonio Giménez Fernández.- Vocal: Isabel Lobato de Faria Ribeir

ABACUS - A Branch-And-CUt System, Version 2.0, User's Guide and Reference Manual

ABACUS is a C++ framework for the implementation of branch-and-cut algorithms, branch-and-price algorithms, and their combination for linear mixed integer and combinatorial optimization problems. This manual explains the installation, the design, and the usage of the framework. Both the basic steps and advanced features are discussed. The reference manual describes all classes together with all members that are relevant for the user

Extending functional databases for use in text-intensive applications

This thesis continues research exploring the benefits of using functional databases based around the functional data model for advanced database applications-particularly those supporting investigative systems. This is a growing generic application domain covering areas such as criminal and military intelligence, which are characterised by significant data complexity, large data sets and the need for high performance, interactive use. An experimental functional database language was developed to provide the requisite semantic richness. However, heavy use in a practical context has shown that language extensions and implementation improvements are required-especially in the crucial areas of string matching and graph traversal. In addition, an implementation on multiprocessor, parallel architectures is essential to meet the performance needs arising from existing and projected database sizes in the chosen application area. [Continues.

Algèbres hypercomplexes pour le Calcul

Dans les domaines mathématique ou applicatif, la multiplication de nombres possède un rôle clef pour le Calcul. En Science et en Ingénierie, la nonlinéarité offre de grands défis de modélisation mais aussi de résolution. Notre approche vise, via la multiplication, l'étude de certains phénomènes non linéaires que l'on retrouve fréquemment dans le domaine de la Science et de l'Industrie. Pour cela, nous étudions dans cette thèse la multiplication de nombres multidimensionnels, associée à des structures algébriques en dimension finie appelées algèbres hypercomplexes. Nous utilisons la multiplication comme lien entre les divisions apparentes des différents domaines théorique et pratique que nous abordons par une approche transdisciplinaire. Nous effectuons une analyse comparative entre les algèbres hypercomplexes et les principaux outils de Calcul, approche qui n’est pas développée dans la littérature existante. Nous présentons une synthèse des applications existantes (par ex. robotique, modélisation 3D, électromagnétisme) et des principaux avantages des algèbres hypercomplexes, pour la Science et l’Ingénierie. A partir des conséquences de l’utilisation des structures alternatives (autres que réelles ou complexes), nous proposons une extension nouvelle de la théorie spectrale présentée sous le nom de couplage spectral. Grâce aux algèbres hypercomplexes et à la théorie du couplage spectral, nous présentons des applications inédites à la mécanique et à la chimie ainsi que des perspectives pour le domaine du calcul quantique. Pour les domaines d’applications présentés, existants ou inédits, nous étudions les aspects de modélisation théorique et aussi d’analyse numérique. Nous montrons que suivant les cas d'étude, les aspects numériques avantageux découlent d'un choix judicieux des modèles et des algèbres hypercomplexes associées. Ces avantages sont principalement dus à la manière de définir la multiplication dans les algèbres concernées. Dans les domaines applicatifs abordés, une grande partie des modèles théoriques et numériques repose actuellement sur l’utilisation des nombres réels ou complexes ainsi que sur l’algèbre linéaire. Nous montrons dans cette thèse que les algèbres hypercomplexes sont complémentaires des outils algébriques actuellement utilisés et possèdent un vaste potentiel théorique et pratique, grandement sous-exploité pour le Calcul

An Approach for the Development of Complex Systems Archetypes

The purpose of this research is to explore the principles and concepts of systems theory in pursuit of a collection of complex systems archetypes that can be used for system exploration and diagnostics. The study begins with an examination of the archetypes and classification systems that already exist in the domain of systems theory. This review includes a critique of their purpose, structure, and general applicability. The research then develops and employs a new approach to grounded theory, using a visual coding model to explore the origins, relationships, and meanings of the principles of systems theory. The goal of the visual grounded theory approach is to identity underlying, recurrent imagery in the systems literature that will form the basis for the archetypes. Using coding models derived from the literature, the study then examines the interrelationships between system principles. These relationships are used to clearly define the environment where the archetypes are found in terms of energy, entropy and time. A collection of complex system archetypes is then derived which are firmly rooted in the literature, as well as being demonstrably manifested in the real world. The definitions of the emerging complex systems archetypes are consistent with the environmental definition and are governed by the system’s behavior related to energy collection, entropy displacement, and the pursuit of viability. Once the archetypes have been identified, this study examines the similarities and differences that distinguish them. The individual system principles that either define or differentiate each of the archetypes are described, and real-world manifestations of the archetypes are discussed. The collection of archetypes is then examined as a continuum, where they are related to one another in terms of energy use, entropy accumulation, self-modification and external-modification. To illustrate the applicability of these archetypes, a case study is undertaken which examines a medium-sized organization with multiple departments in an industrial setting. The individual departments are discussed in detail, and their archetypical forms are identified and described. Finally, the study examines future applications for the archetypes and other research that might enhance their utility for complex systems governance