José António Tenreiro Machado

Fractional Dynamics and Control

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Analysis and Visualization of Seismic Data Using Mutual Information

Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.

A Survey of Technologies for Climbing Robots Adhesion to Surfaces

Climbing robots are being developed for applications ranging from cleaning to inspection of difficult to reach constructions. These machines should be capable of travelling on different types of surfaces (such as floors, walls, ceilings) and to walk between such surfaces. Furthermore, these machines should adapt and reconfigure for various environment conditions and should be self-contained. Regarding the adhesion to the surface, they should be able to produce a secure gripping force using a light-weight mechanism. Bearing these facts in mind, this paper presents a survey of different technologies used for climbing robots adhesion to surfaces.

Goal-oriented biped walking based on force interaction control

Addresses the problem of modelling and control of a biped robot by combining Cartesian-based position and force control algorithms. The walking cycle is divided in two phases: single support, in which one leg is in contact with the ground and the other leg swings forward, and double support, in which the forward leg absorbs the impact and gradually accepts the robots weight. The contact of the foot with the constrained surface is modelled through linear and nonlinear spring-damper systems. The proposed control approach is based on simple motion goals taking into account the reaction forces between the feet and the ground. The control algorithm is tested through several experiments and its effectiveness and robustness is discussed.

Dynamical Stability and Predictability of Football Players: The Study of One Match

The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match.

A statistical and harmonic model for robot manipulators

A new approach to the analysis and design of robot manipulators is presented. The novel feature resides on a non-standard formulation to the modelling problem. Usually, system descriptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyse. These facts motivate the need of alternative models based on different mathematical concepts. The proposed statistical approach to the Fourier modelling gives clear guidelines towards the optimisation of the robot kinematics and points out structural characteristics of the trajectory planning algorithms.

Position/force control of biped walking robots

The paper addresses the problem of modelling and control of a biped robot by combining Cartesian based position and force control algorithms. The complete walking cycle is divided into two phases: i) single support, in which is studied the trajectory controllability based on simple motion goals and ii) exchange of support, in which the forward leg absorbs the impact and then gradually accepts the robots weight. The contact of the foot with the constrained surface is modelled through linear spring-damper systems. The systems controllability is enhanced through the insertion of a dynamic selection matrix that modifies the actuating profile in each phase. The control algorithms are simulated and their effectiveness and robustness are discussed.

Kinematic aspects of robotic biped locomotion systems

This paper presents the kinematic study of robotic biped locomotion systems. The main purpose is to determine the kinematic characteristics and the system performance during walking. For that objective, the prescribed motion of the biped is completely characterised in terms of five locomotion variables: step length, hip height, maximum hip ripple, maximum foot clearance and link lengths. In this work, we propose three methods to quantitatively measure the performance of the walking robot: locomobility measure, perturbation analysis and low-pass frequency response. These performance measures are discussed and compared in determining the robustness and effectiveness of the resulting locomotion.