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- Fractional-order harmonics in the trajectory control of redundant manipulatorsPublication . Duarte, Fernando B. M.; Marcos, Maria da Graça; Tenreiro Machado, J. A.Redundant manipulators are superior to classical arms because they allow the trajectory optimization, the obstacle avoidance, and the resolution of singularities. For this type of manipulators, the kinematic control algorithms adopt generalized inverse matrices that may lead to unpredictable responses. Motivated by these problems this paper studies the complexity revealed by the trajectory planning scheme when controlling redundant manipulators. The result reveals a chaotic phenomenon and the existence of fractional order sub-harmonics in the robot signals.
- Applications of fractional calculus in electrical and computer engineeringPublication . Tenreiro Machado, J. A.; Silva, Manuel; Barbosa, Ramiro; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria da Graça; M. Afonso, Luís; Lima, Miguel F. M.; Pires, E. J. Solteiro; Ferreira, N. M. FonsecaFractional 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 a FC perspective in the study of the dynamics and control of several systems. This article illustrates several applications of fractional calculus in science and engineering. It has been recognized the advantageous use of this mathematical tool in the modeling and control of many dynamical systems. In this perspective, this paper investigates the use of FC in the fields of controller tuning, electrical systems, digital circuit synthesis, evolutionary computing, redundant robots, legged robots, robotic manipulators, nonlinear friction and financial modeling.
- An evolutionary approach to the trajectory planning of redundant robotsPublication . Marcos, Maria da Graça; Tenreiro Machado, J. A.; Azevedo-Perdicoúlis, T. P.Several kinematic techniques for the trajectory optimization of redundant manipulators control the gripper using the pseudoinverse of the Jacobian. Nevertheless, these algorithms lead to a kind of chaotic motion with unpredictable arm configurations. This paper presents a new technique for solving the inverse kinematics problem for redundant manipulators that combines the closed-loop pseudoinverse method with genetic algorithms.
- Matemática IPublication . Marcos, Maria da Graça; Oliveira, Marisa João Guerra Pereira de; Barreiras, Alcinda Maria de SousaEste livro pretende ser um contributo para as unidades curriculares de Matemática 1 ou Análise Matemática, focando aspetos considerados essenciais para os estudantes de engenharia e de ciências em geral de forma a fornecer conhecimentos base necessários para outras unidades curriculares. Os seus conteúdos resultam em grande parte da experiência das autoras no ensino destas unidades curriculares nos vários cursos de Engenharia que são ministrados no Instituto Superior de Engenharia do Porto (ISEP) e incluem o cálculo diferencial, o cálculo integral, as séries numéricas e séries de funções.
- Towards the application of fractional calculus in engineering sciencesPublication . Tenreiro Machado, J. A.; Barbosa, Ramiro; Jesus, Isabel S.; Silva, Manuel; Reis, Cecília; M. Afonso, Luís; Marcos, Maria da Graça; Lima, Miguel F. M.; Pires, Eduardo S.This article illustrates several applications of Fractional Calculus (FC) in engineering sciences. This mathematical tool will be used here to model, analyze and control various dynamical systems, such as the Van der Pol oscillator, legged robots, electrical systems, digital circuit synthesis, evolutionary computing, redundant robots and financial modelling. Their effectiveness and utility will be demonstrated.
- Fractional order dynamical systems and its applicationsPublication . Tenreiro Machado, J. A.; Barbosa, Ramiro; Jesus, Isabel S.; Silva, Manuel; Figueiredo, Lino; Reis, Cecília; Marcos, Maria da Graça; M. Afonso, Luís; Galhano, Alexandra; Duarte, Fernando B.; Lima, Miguel L.; Pires, Eduardo S.; Ferreira, Nuno M. FonsecaThis article illustrates several applications of fractional calculus (FC) in science and engineering. It has been recognized the advantageous use of this mathematical tool in the modeling and control of many dynamical systems. In this perspective, this paper investigates the use of FC in the following fields: Controller tuning; Electrical systems; Traffic systems; Digital circuit synthesis; Evolutionary computing; Redundant robots; Legged robots; Robotic manipulators; Nonlinear friction; Financial modeling.
- Some applications of fractional calculus in engineeringPublication . Tenreiro Machado, J. A.; Silva, Manuel; Barbosa, Ramiro; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria da Graça; 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.