Ensino da matemática para a vida: criação de cenários de aprendizagem com recurso a robots

A Matemática para a Vida é uma disciplina dos Currículos Específicos Individuais que pretende ajudar os alunos com Necessidades Educativas Especiais a desenvolver aptidões que aumentem as suas competências pessoais e sociais e que facilitem a sua integração na sociedade. A matriz curricular visa a promoção da autonomia de modo a termos alunos capazes de enfrentar o dia a dia sozinhos. A presente investigação procurou conhecer mais sobre a forma como alunos com Necessidades Educativas Especiais (NEE) aprendem a Matemática para a Vida, de que forma atribuem significados, o que abrangem esses significados e qual o papel dos robots na construção dessa aprendizagem. Utilizou-se uma abordagem qualitativa com recurso à observação participante. O estudo envolveu a criação de um cenário de aprendizagem composto por um robot e elementos com formas geométricas distintas, tendo como participantes duas alunas com NEE. A recolha de dados foi feita por observação direta, registos áudio e vídeo e análise dos trabalhos desenvolvidos pelas alunas. Da análise dos dados concluiu-se que o uso dos robots permitiu uma aproximação da escola às reais necessidades dos alunos com NEE, proporcionando-lhes novas oportunidades de aprendizagem e momentos de descoberta e partilha. Ao trabalharem com o robot, as alunas adquiriram novas competências e, como consequência das suas pequenas conquistas, ganharam mais autonomia, tornando-se capazes de tomar decisões face aos desafios enfrentados. A utilização do robot contribuiu ainda para o estímulo da criatividade, além de ter permitido a construção do conhecimento de acordo com o ritmo individual das alunas, ao possibilitar novas formas de pensar e de aprender.

Contribuição para o estudo da aprendizagem da matemática e da programação em comunidades virtuais de prática com foco no uso de robots como mediadores da aprendizagem

Contribuição para o Estudo da Aprendizagem da Matemática e da Programação em Comunidades Virtuais de Prática com Foco no Uso de Robots como Mediadores da Aprendizagem O propósito deste estudo, desenvolvido no âmbito de um projeto de investigação que envolveu a utilização de robots na aprendizagem colaborativa da Matemática e da Informática através da Web, é analisar e discutir a noção de participação e o processo de construção do conhecimento em comunidades virtuais de prática. O referido projeto foi desenvolvido em três etapas principais. Na primeira, foram selecionadas as ferramentas de comunicação a serem utilizadas. A segunda etapa envolveu a elaboração e contextualização dos problemas-desafio a serem resolvidos pelos grupos virtuais. A terceira e última etapa do projeto compreendeu o registo e a recolha dos dados e informações obtidos nas reuniões virtuais com grupos de alunos do Ensino Secundário e sua posterior análise, utilizando uma abordagem qualitativa de natureza interpretativa, tendo como referencial teórico a teoria da aprendizagem situada de Lave e Wenger e os conceitos subjacentes às comunidades de prática, objetivando com isto melhor compreender os efeitos das tecnologias sobre tais comunidades, bem como as características da aprendizagem realizada em espaços virtuais. A utilização de robots como mediadores da aprendizagem facilitou a exploração de conceitos abstratos fundamentais relativos às áreas da Matemática e da Informática, permitindo com isto que as tarefas de programação necessárias à resolução dos problemas propostos fizessem mais sentido, pelo facto dos resultados obtidos poderem ser concretizados no mundo real.

Os robots na aprendizagem da trignometria

Este trabalho foi elaborado no âmbito do Mestrado de Ensino de Matemática do 3º Ciclo do Ensino Básico e Secundário da Universidade da Madeira, no ano letivo de 2012/2013. Os grandes objetivos deste estudo são os de analisar qualitativamente uma atividade, para compreender como é que os alunos aprendem trigonometria, utilizando os robots NXT da Lego. De igual modo, se procede também, de forma sucinta, à apresentação do trabalho desenvolvido pelo grupo de estágio, ao longo da Prática de Ensino Supervisionado. Para a realização da investigação, foram recolhidos dados pelo investigador, através de registos audiovisuais do trabalho dos alunos, com câmara e vídeo. Com o fim de melhor estudar o problema aqui apresentado, o mesmo foi dissecado em três questões de investigação: (a) Que aprendizagens os alunos realizam com a montagem, programação e interação com os robots? (b) De que forma é que os alunos aprendem trigonometria, quando utilizam os Robots? (c) Quais as dificuldades manifestadas pelos alunos na resolução de problemas? As questões de investigação iluminaram a análise dos dados. Das conclusões que advêm deste estudo destaca-se o papel essencial da robótica e dos materiais manipuláveis, na construção e concetualização do conhecimento dos alunos.

A survey of control architectures for autonomous mobile robots

MEDEIROS, Adelardo A. D.A survey of control architectures for autonomous mobile robots. J. Braz. Comp. Soc., Campinas, v. 4, n. 3, abr. 1998 .Disponível em: Acesso: 27 set. 2010.

TORP: The Open Robot Project A Framework for Module-Based Robots

The development of robots has shown itself as a very complex interdisciplinary research field. The predominant procedure for these developments in the last decades is based on the assumption that each robot is a fully personalized project, with the direct embedding of hardware and software technologies in robot parts with no level of abstraction. Although this methodology has brought countless benefits to the robotics research, on the other hand, it has imposed major drawbacks: (i) the difficulty to reuse hardware and software parts in new robots or new versions; (ii) the difficulty to compare performance of different robots parts; and (iii) the difficulty to adapt development needs-in hardware and software levels-to local groups expertise. Large advances might be reached, for example, if physical parts of a robot could be reused in a different robot constructed with other technologies by other researcher or group. This paper proposes a framework for robots, TORP (The Open Robot Project), that aims to put forward a standardization in all dimensions (electrical, mechanical and computational) of a robot shared development model. This architecture is based on the dissociation between the robot and its parts, and between the robot parts and their technologies. In this paper, the first specification for a TORP family and the first humanoid robot constructed following the TORP specification set are presented, as well as the advances proposed for their improvement.

Optimal Conditions for Biomass and Recombinant Glycerol Kinase Production Using the Yeast Pichia pastoris

The extracellular glycerol kinase gene from Saccharomyces cerevisiae (GUT]) was cloned into the expression vector pPICZ alpha. A and integrated into the genome of the methylotrophic yeast Pichia pastoris X-33. The presence of the GUT1 insert was confirmed by PCR analysis. Four clones were selected and the functionality of the recombinant enzyme was assayed. Among the tested clones, one exhibited glycerol kinase activity of 0.32 U/mL, with specific activity of 0.025 U/mg of protein. A medium optimized for maximum biomass production by recombinant Pichia pastoris in shaker cultures was initially explored, using 2.31 % (by volume) glycerol as the carbon source. Optimization was carried out by response surface methodology (RSM). In preliminary experiments, following a Plackett-Burman design, glycerol volume fraction (phi(Gly)) and growth time (t) were selected as the most important factors in biomass production. Therefore, subsequent experiments, carried out to optimize biomass production, followed a central composite rotatable design as a function of phi(Gly) and time. Glycerol volume fraction proved to have a significant positive linear effect on biomass production. Also, time was a significant factor (at linear positive and quadratic levels) in biomass production. Experimental data were well fitted by a convex surface representing a second order polynomial model, in which biomass is a function of both factors (R(2)=0.946). Yield and specific activity of glycerol kinase were mainly affected by the additions of glycerol and methanol to the medium. The optimized medium composition for enzyme production was: 1 % yeast extract, 1 % peptone, 100 mM potassium phosphate buffer, pH=6.0, 1.34 % yeast nitrogen base (YNB), 4.10(-5) % biotin, 1 %, methanol and 1 %, glycerol, reaching 0.89 U/mL of glycerol kinase activity and 14.55 g/L of total protein in the medium after 48 h of growth.

Influence of visual information on optimal obstacle crossing

Human motion seems to be guided by some optimal principles. In general, it is assumed that human walking is generated with minimal energy consumption. However, in the presence of disturbances during gait, there is a trade-off between stability (avoiding a fall) and energy-consumption. This work analyses the obstacle-crossing with the leading foot. It was hypothesized that energy-saving mechanisms during obstacle-crossing are modulated by the requirement to avoid a fall using the available sensory information, particularly, by vision. A total of fourteen subjects, seven with no visual impairment and seven blind, walked along a 5 meter flat pathway with an obstacle of 0.26 m height located at 3 m from the starting point. The seven subjects with normal vision crossed the obstacle successfully 30 times in two conditions: blindfolded and with normal vision. The seven blind subjects did the same 30 times. The motion of the leading limb was recorded by video at 60 Hz. There were markers placed on the subject's hip, knee, ankle, rear foot, and forefoot. The motion data were filtered with a fourth order Butterworth filter with a cut-off frequency of 4 Hz. The following variables were calculated: horizontal distance between the leading foot and the obstacle at toe-off prior to (DHPO) and after (DHOP) crossing, minimal vertical height from the foot to the obstacle (DVPO), average step velocity (VELOm). The segmental energies were also calculated and the work consumed by the leading limb during the crossing obstacle was computed for each trial. A statistical analysis repeated-measures ANOVA was conducted on these dependent variables revealing significant differences between the vision and non-vision conditions in healthy subjects. In addition, there were no significant differences between the blind and people with vision blindfolded. These results indicate that vision is crucial to determine the optimal trade-off between energy consumption and avoiding a trip during obstacle crossing.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimal reactive power flow via the modified barrier Lagrangian function approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimal attitude corrections for cylindrical spacecraft

A first order analytical model for optimal small amplitude attitude maneuvers of spacecraft with cylindrical symmetry in an elliptical orbits is presented. The optimization problem is formulated as a Mayer problem with the control torques provided by a power limited propulsion system. The state is defined by Seffet-Andoyer's variables and the control by the components of the propulsive torques. The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Serret-Andoyer's variables and their adjoints. For small amplitude attitude maneuvers, the optimal Hamiltonian function is linearized around a reference attitude. A complete first order analytical solution is obtained by simple quadrature and is expressed through a linear algebraic system involving the initial values of the adjoint variables. A numerical solution is obtained by taking the Euler angles formulation of the problem, solving the two-point boundary problem through the shooting method, and, then, determining the Serret-Andoyer variables through Serret-Andoyer transformation. Numerical results show that the first order solution provides a good approximation to the optimal control law and also that is possible to establish an optimal control law for the artificial satellite's attitude. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

Security constrained optimal active power flow via network model and interior point method

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sub-Optimal Orbital Maneuvers for Artificial Satellites

The determination of a specific orbit and the procedure to calculate orbital maneuvers of artificial satellites are problems of extreme importance in the study of orbital mechanics. Therefore, the transferring problem of a spaceship from one orbit to another, and the attention due to this subject has in increased during the last years. Many applications can be found in several space activities, for example, to put a satellite in a geostationary orbit, to change the position of a spaceship, to maintain a specific satellite's orbit, in the design of an interplanetary mission, and others. The Brazilian Satellite SCD-1 (Data Collecting Satellite) will be used as example in this paper. It is the first satellite developed entirely in Brazil, and it remains in operation to this date. SCD-1 was designed, developed, built, and tested by Brazilian scientists, engineers, and technicians working at INPE (National Institute for Space Research, and in Brazilian Industries. During the lifetime, it might be necessary do some complementary maneuvers, being this one either an orbital transferring, or just to make periodical corrections. The purpose of transferring problem is to change the position, velocity and the satellite's mass to a new pre determined state. This transfer can be totally linked (in the case of "Rendezvous") or partially free (free time, free final velocity, etc). In the global case, the direction, the orientation and the magnitude of the thrust to be applied must be chosen, respecting the equipment's limit. In order to make this transferring, either sub-optimal or optimal maneuvers may be used. In the present study, only the sub-optimal will be shown. Hence, this method will simplify the direction of thrust application, to allow a fast calculation that may be used in real time, with a very fast processing. The thrust application direction to be applied will be assumed small and constant, and the purpose of this paper is to find the time interval that the thrust is applied. This paper is basically divided into three parts: during the first one the sub-optimal maneuver is explained and detailed, the second presents the Satellite SCD-1, and finally the last part shows the results using the sub-optimal maneuver applied to the Brazilian Satellite.

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program. (C) 2002 Elsevier B.V. B.V. All rights reserved.

H-2 and H-infinity-optimal control for the tracking problem with zero variation

The problem of signal tracking, in the presence of a disturbance signal in the plant, is solved using a zero-variation methodology. A state feedback controller is designed in order to minimise the H-2-norm of the closed-loop system, such that the effect of the disturbance is attenuated. Then, a state estimator is designed and the modification of the zeros is used to minimise the H-infinity-norm from the reference input signal to the error signal. The error is taken to be the difference between the reference and the output signals, thereby making it a tracking problem. The design is formulated in a linear matrix inequality framework, such that the optimal solution of the stated control problem is obtained. Practical examples illustrate the effectiveness of the proposed method.

Design of fuzzy regulators with optimal initial conditions compensation

In almost all cases, the goal of the design of automatic control systems is to obtain the parameters of the controllers, which are described by differential equations. In general, the controller is artificially built and it is possible to update its initial conditions. In the design of optimal quadratic regulators, the initial conditions of the controller can be changed in an optimal way and they can improve the performance of the controlled system. Following this idea, a LNU-based design procedure to update the initial conditions of PI controllers, considering the nonlinear plant described by Takagi-Sugeno fuzzy models, is presented. The importance of the proposed method is that it also allows other specifications, such as, the decay rate and constraints on control input and output. The application in the control of an inverted pendulum illustrates the effectively of proposed method.