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- On statistical modelling of mechanical manipulatorsPublication . Galhano, Alexandra; Tenreiro Machado, J. A.; Carvalho, J. L. Martins deA novel approach to the modelling of robot manipulators is presented. System descriptions based on a set of differential equations may lead to very precise results and strategies but, in general, require laborious conputations. This motivates the need of alternative methods based on other mathematical concepts. The proposed statistical model gives clear quidelines towards the robot kinematic and dynamic optimization and the definition of rest and active manipulation regions. Furthermore, the results point out ideal properties for the actuators namely as "position and acceleration" devices instead of "velocity" machines. This observation is of utmost importance as it gives a basis to new mechanical robot manipulator structures, with performances close to biomechanical systems.
- Towards the real-time control of robotic systemsPublication . Tenreiro Machado, J. A.; Carvalho, J. L. Martins de; Galhano, AlexandraIn the last decades robot control has been an area of active research and development. Mechanical manipulators have a complex dynamics which makes difficult the design efficient controllers. Linear PID algorithms are still used in industrial robotics however, they are inappropriate for high performances. The limited efficiency of these systems motivated the development of controllers based on different concepts Dubwsky and DesForges (1), Luh e tal. (2), Freund (3). Nevertheless, the high computational load posed by many of the modern algorithms precludes its industrial application using present day microcomputers. In fact, the use of powerful monoprocessor computers is expensive while, on the other hand, multi-microprocessor architectures Luh and Lin (4), Binder and Herzog (5), Watanabe et al. (6) are still in a research stage. This situation can be overcome through the development of control strategies more adapted to the microcomputer. In this line of thought, this article compares the computational capabilities of several computers and introduces techniques capable of rendering more efficient practical implementations. It is organized as follows. In section two we evaluate the computational load posed by different operations to several computer systems. Based on the results, in section three, we present general techniques amenable to robot control implementation. Finally, in section four conclusions are drawn.
- Statistical modelling of robot manipulatorsPublication . Galhano, Alexandra; Tenreiro Machado, J. A.; Carvalho, J. L. Martins deRobotics is an area encompassing a wide range of industrial, technological and scientific applications. Still, many of them pose challenging issues to the available industrial manipulators. The superior performances of the human arm induced an extensive research towards better mechanical structures. In this line of thought, considerable research has been done either on the kinematics Tsai and Soni (1), Asada (2) or the dynamics Yoshikawa (3,4), Youcef-Toumi and Asada (5). However, a simple optimization criterion comprising both the kinematics and the dynamics is still lacking. In the present paper we address this problem, and our presentation is organized as follows. In section two the robot manipulator model and the associated optimization criterion are discussed. In section three a new model leading to natural optimization criterion is formulated and applied to a 2R robot manipulator. Finally, in section four conclusions are drawn.
- Some Applications of Fractional Calculus in EngineeringPublication . Tenreiro Machado, J. A.; Silva, Manuel; Barbosa, Ramiro; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria G.; Galhano, AlexandraFractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.
- Microcomputer evaluation in robot controlPublication . Tenreiro Machado, J. A.; Carvalho, J. L. Martins de; Galhano, AlexandraThe high computational burden posed by modern control algorithms preclude its industrial application using present day microcomputers. In this paper we evaluate the computational load of different logical and arithmetic operations and the capabilities of several computing systems (software and hardware). This study reveals that real-time limitations ca be alleviated through the adoptation of general techniques associated with the data representation. Such techniques achieve not only a more efficient management of the computational resources but also provide a deeper insight on developments towards future real-time control architectures.
- Towards the statistical modelling of robotic manipulatorsPublication . Galhano, Alexandra; Carvalho, J. L. Martins de; Tenreiro Machado, J. A.A novel approach to the modelling of robot manipulators is presented. Usually, system descriptions are based on a set of differential equations which, due to their nature, lead to very precise results and strategies. However, they need laborious computations and, therefore, methods based on alternative mathematical concepts are required. The proposed statistical model overcomes thes problems and gives clear guidelines towards the optimization of the robot performances.
- Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomenaPublication . Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Galhano, AlexandraThe development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.
- Fractional order inductive phenomena based on the skin effectPublication . Machado, J. A. Tenreiro; Galhano, AlexandraThe Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.
- Fractional dynamics and MDS visualization of earthquake phenomenaPublication . Lopes, António M.; Machado, J.A.Tenreiro; Pinto, Carla M.A.; Galhano, AlexandraThis paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.
- Cálculo diferencial e integral: exercíciosPublication . Machado, J. A. Tenreiro; Galhano, Alexandra; Ferreira, Flávio; Ferreira, Fernanda A.