Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

Strength prediction of single- and double-lap joints by standard and extended finite element modelling

The structural integrity of multi-component structures is usually determined by the strength and durability of their unions. Adhesive bonding is often chosen over welding, riveting and bolting, due to the reduction of stress concentrations, reduced weight penalty and easy manufacturing, amongst other issues. In the past decades, the Finite Element Method (FEM) has been used for the simulation and strength prediction of bonded structures, by strength of materials or fracture mechanics-based criteria. Cohesive-zone models (CZMs) have already proved to be an effective tool in modelling damage growth, surpassing a few limitations of the aforementioned techniques. Despite this fact, they still suffer from the restriction of damage growth only at predefined growth paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the FEM, developed to allow the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom with special displacement functions, thus overcoming the main restriction of CZMs. These two techniques were tested to simulate adhesively bonded single- and double-lap joints. The comparative evaluation of the two methods showed their capabilities and/or limitations for this specific purpose.

Sistema de modelização tridimensional de galerias subterrâneas

A presente dissertação apresenta uma solução para o problema de modelização tridimensional de galerias subterrâneas. O trabalho desenvolvido emprega técnicas provenientes da área da robótica móvel para obtenção um sistema autónomo móvel de modelização, capaz de operar em ambientes não estruturados sem acesso a sistemas de posicionamento global, designadamente GPS. Um sistema de modelização móvel e autónomo pode ser bastante vantajoso, pois constitui um método rápido e simples de monitorização das estruturas e criação de representações virtuais das galerias com um elevado nível de detalhe. O sistema de modelização desloca-se no interior dos túneis para recolher informações sensoriais sobre a geometria da estrutura. A tarefa de organização destes dados com vista _a construção de um modelo coerente, exige um conhecimento exacto do percurso praticado pelo sistema, logo o problema de localização da plataforma sensorial tem que ser resolvido. A formulação de um sistema de localização autónoma tem que superar obstáculos que se manifestam vincadamente nos ambientes underground, tais como a monotonia estrutural e a já referida ausência de sistemas de posicionamento global. Neste contexto, foi abordado o conceito de SLAM (Simultaneous Loacalization and Mapping) para determinação da localização da plataforma sensorial em seis graus de liberdade. Seguindo a abordagem tradicional, o núcleo do algoritmo de SLAM consiste no filtro de Kalman estendido (EKF { Extended Kalman Filter ). O sistema proposto incorpora métodos avançados do estado da arte, designadamente a parametrização em profundidade inversa (Inverse Depth Parametrization) e o método de rejeição de outliers 1-Point RANSAC. A contribuição mais importante do método por nós proposto para o avanço do estado da arte foi a fusão da informação visual com a informação inercial. O algoritmo de localização foi testado com base em dados reais, adquiridos no interior de um túnel rodoviário. Os resultados obtidos permitem concluir que, ao fundir medidas inerciais com informações visuais, conseguimos evitar o fenómeno de degeneração do factor de escala, comum nas aplicações de localização através de sistemas puramente monoculares. Provámos simultaneamente que a correcção de um sistema de localização inercial através da consideração de informações visuais é eficaz, pois permite suprimir os desvios de trajectória que caracterizam os sistemas de dead reckoning. O algoritmo de modelização, com base na localização estimada, organiza no espaço tridimensional os dados geométricos adquiridos, resultando deste processo um modelo em nuvem de pontos, que posteriormente _e convertido numa malha triangular, atingindo-se assim uma representação mais realista do cenário original.

Assigning real-time tasks on heterogeneous multiprocessors with two types of processors

Consider the problem of scheduling a set of implicitdeadline sporadic tasks on a heterogeneous multiprocessor so as to meet all deadlines. Tasks cannot migrate and the platform is restricted in that each processor is either of type-1 or type-2 (with each task characterized by a different speed of execution upon each type of processor). We present an algorithm for this problem with a timecomplexity of O(n·m), where n is the number of tasks and m is the number of processors. It offers the guarantee that if a task set can be scheduled by any non-migrative algorithm to meet deadlines then our algorithm meets deadlines as well if given processors twice as fast. Although this result is proven for only a restricted heterogeneous multiprocessor, we consider it significant for being the first realtime scheduling algorithm to use a low-complexity binpacking approach to schedule tasks on a heterogeneous multiprocessor with provably good performance.

Feasibility of the extended finite element method for the simulation of composite bonded joints

Adhesive-bonding for the unions in multi-component structures is gaining momentum over welding, riveting and fastening. It is vital for the design of bonded structures the availability of accurate damage models, to minimize design costs and time to market. Cohesive Zone Models (CZM’s) have been used for fracture prediction in structures. The eXtended Finite Element Method (XFEM) is a recent improvement of the Finite Element Method (FEM) that relies on traction-separation laws similar to those of CZM’s but it allows the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom. This work proposes and validates a damage law to model crack propagation in a thin layer of a structural epoxy adhesive using the XFEM. The fracture toughness in pure mode I (GIc) and tensile cohesive strength (sn0) were defined by Double-Cantilever Beam (DCB) and bulk tensile tests, respectively, which permitted to build the damage law. The XFEM simulations of the DCB tests accurately matched the experimental load-displacement (P-d) curves, which validated the analysis procedure.

Multi-criteria optimization manipulator trajectory planning

In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control, system identification, robotics, planning and scheduling, image processing, and pattern and speech recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance and manipulator structure design considering a single criteria has been solved using several techniques (Alander, 2003). Most engineering applications require the optimization of several criteria simultaneously. Often the problems are complex, include discrete and continuous variables and there is no prior knowledge about the search space. These kind of problems are very more complex, since they consider multiple design criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective) optimization, that has been addressed successfully through GAs (Deb, 2001). The overall aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible and iii) to achieve a Pareto front uniformly spread. Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area. In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA) (Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello, 1998). In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ), ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance, end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at destination point. Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development of an algorithm to find a continuous motion that takes the manipulator from a given starting configuration up to a desired end position without colliding with any obstacle in the workspace. The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches proposed in the literature. Section 3 formulates the problem, namely the representation adopted to solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links) when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for the 3R redundant manipulator with five goals and for other complementary experiments are described, respectively. Finally, section 8 draws the main conclusions.

Manipulator trajectory planning using a MOEA

Generating manipulator trajectories considering multiple objectives and obstacle avoidance is a non-trivial optimization problem. In this paper a multi-objective genetic algorithm based technique is proposed to address this problem. Multiple criteria are optimized considering up to five simultaneous objectives. Simulation results are presented for robots with two and three degrees of freedom, considering two and five objectives optimization. A subsequent analysis of the spread and solutions distribution along the converged non-dominated Pareto front is carried out, in terms of the achieved diversity.

Comparison of internet usage habits in two generations of higher education students: a case study

Posters

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Simple Kinematic Design for Evading the Forced Oscillation of a Car-Wheel Suspension System

An adaptive control damping the forced vibration of a car while passing along a bumpy road is investigated. It is based on a simple kinematic description of the desired behavior of the damped system. A modified PID controller containing an approximation of Caputo’s fractional derivative suppresses the high-frequency components related to the bumps and dips, while the low frequency part of passing hills/valleys are strictly traced. Neither a complete dynamic model of the car nor ’a priori’ information on the surface of the road is needed. The adaptive control realizes this kinematic design in spite of the existence of dynamically coupled, excitable internal degrees of freedom. The method is investigated via Scicos-based simulation in the case of a paradigm. It was found that both adaptivity and fractional order derivatives are essential parts of the control that can keep the vibration of the load at bay without directly controlling its motion.