A presente pesquisa, de cunho quantitativo, tem como propósito responder a seguinte questão: De que modo e em que alcance o trabalho pedagógico articulado com a história, geometria e meio computacional tem refletido sobre posturas e caminhos que levassem os alunos a se envolver com o conhecimento matemático? Desse modo, fizemos uma investigação e análise sobre os efeitos de uma articulação entre o ensino da história da matemática e o uso de ferramentas computacionais como solução para as dificuldades apresentadas no Ensino de Geometria, principalmente no Ensino Médio. Utilizamos a obra de Lakatos e a primeira proposição (do livro 1) de Euclides para realizar a verificação de sua demonstração através de um software de Geometria dinâmica. Os resultados serão utilizados para a construção de um novo software que envolva o ensino e aprendizagem de história da matemática e geometria. Outros objetivos podem ser assim colocados: Refletir sobre as condições e viabilidade da integração de recursos computacionais para o ensino da Matemática no âmbito Ensino Médio em especial a partir do produtos/softwares propostos para a educação matemática; Compreender o potencial de softwares de geometria dinâmica para a educação matemática escolar; Analisar as necessidades matemáticas de uma instrumentação eficaz, a partir da história da Matemática, para compreender a Matemática como um 9 processo em construção, em especial no âmbito das relações geométricas. Para isso foram retiradas vivências do cotidiano das aulas de Matemática para a reflexão sobre a geometria, e os resultados foram que a história da Matemática junto as novas tecnologias podem mudar as concepções de conhecimento da Matemática, pois através do professor ela pode chegar à sala de aula e transformar a prática pedagógica. / The current study focused on quantity, aims to answer the following question: How and to what extent the educational work linked to the story, using computational geometry and has reflected on postures and paths that could lead students to engage with the mathematical knowledge? Thus, we developed a research and analysis on the effects of an articulation between the teaching of mathematics and the use of computational tools as a solution to the problems presented in the Teaching of Geometry, especially in high school. We used the work of Lakatos and the first proposition (Book 1) Euclid to perform the verification of his statement through a dynamic geometry software. Results will be used for the construction of a new software that involves teaching and learning of history of mathematics and geometry. Other goals may be well placed: Reflecting on the conditions and feasibility of integrating computing resources - to the teaching of mathematics in high school - in particular from the product / software proposed for mathematics education; understand the potential of software for geometry dynamic for mathematics education; analyze the needs of a mathematical effective instrumentation, from the history of mathematics, to understand mathematics as an ongoing process, particularly in the context of geometric relationships. For that were withdrawn daily experiences of mathematics lessons to reflect on the geometry and the results 11 were that the history of mathematics with the new technologies may change the concepts of knowledge of mathematics, because through it the teacher can get to the room transform the classroom and practice teaching.

Cada vez mais empilhadeiras robóticas são utilizadas para a tarefa de transporte em indústrias e armazéns. O gerenciamento dessas empilhadeiras é a chave para um sistema de transporte eficiente visando maximizar sua taxa de transferência. Um dos principais problemas na operação desses sistemas é a decisão de roteamento das empilhadeiras dentro dos depósitos. Este trabalho propõe um algoritmo de roteamento com a capacidade de realizar a otimização das rotas em tempo-real. Na computação da rota são considerados o desvio de obstáculos, as dimensões e as propriedades físicas das empilhadeiras, pois uma trajetória calculada deste ponto de referência está livre de colisões durante a execução do roteamento. Para realizar os testes foram utilizados os softwares Player/Stage, os quais permitem que simulações do funcionamento do sistema de roteamento sejam realizadas antes que os algoritmos sejam testados em robôs reais. Através dos testes simulados, analisou-se a capacidade de locomoção das empilhadeiras referente ao calculo da melhor rota no ambiente proposto, com o intuito de melhorar o ganho de performance no planejamento de trajetória. / Forklift robots have been increasingly used in transport tasks in industries and warehouses. The key to an efficient transport system is held by a sound management of these forklifts that aim to maximize the transference rate. One of the main problems faced by the transportation systems is routing decision for forklifts within warehouse. The present paper proposes a routing algorithm to calculate optimal routes in real time. Therefore, its computation takes into account obstacle avoidance, the dimension and physical properties of the forklifts, since the calculated path regarding the routing is conflict-free. Simulations were carried out using the software Player/Stage before the algorithms were tested in a real robot. Simulated tests were analyzed in order to observe the locomotion ability of forklifts regarding calculation of the best route in the environment proposed to improve the trajectory planning performance will be assessed.

In this thesis we consider optimization problems with complementarity constraints in infinite-dimensional spaces. On the one hand, we deal with the general situation, in which the complementarity constraint is governed by a closed convex cone. We use the local decomposition approach, which is known from finite dimensions, to derive first-order necessary optimality conditions of strongly stationary type. In the non-polyhedric case, stronger conditions are obtained by an additional linearization argument. On the other hand, we consider the optimal control of the obstacle problem. This is a classical example for a problem with complementarity constraints in infinite dimensions. We are concerned with the control-constrained case. Due to the lack of surjectivity, a system of strong stationarity is not necessarily satisfied for all local minimizers. We identify assumptions on the data of the optimal control problem under which strong stationarity of local minimizers can be verified. Moreover, without any additional assumptions on the data, we show that a system of M-stationarity is satisfied provided that some sequence of multipliers converges in capacity. Finally, we also discuss the notion of polyhedric sets. These sets have many applications in infinite-dimensional optimization theory. Since the results concerning polyhedricity are scattered in the literature, we provide a review of the known results. Furthermore, we give some new results concerning polyhedricity of intersections and provide counterexamples which demonstrate that intersections of polyhedric sets may fail to be polyhedric. We also prove a new polyhedricity result for sets in vector-valued Sobolev spaces.

Obstacle detection is one of the major focus area on image processing. For mobile robots, obstacle detection and collision avoidance is a notorious problem and is still a part of the modern research. There are already a lot of research have been done so far for obstacle detection and collision avoidance. This thesis evaluates the existing various well-known methods and sensors for collision free navigation of the mobile robot. For moving obstacle detection purpose the frame difference approach is adopted. Robotino® is used as the mobile robot platform and additionally Microsoft Kinect is used as 3D sensor. For getting information from the environment about obstacle, the 9-built-in distance sensor of Robotino® and 3D depth image data from the Kinect is used. The combination is done to get the maximum advantages for obstacles information. The detection of moving object in front of the sensor is a major interest of this work.

Today, there are industries that utilize AGVs to transport goods and materials from one location to another. For smaller scale industries it is costly to have a custom made AGV for their manufacturing unit, so they modify the shape of an AGV to accommodate the necessity of carrying and transporting goods. When the shape of an AGV is modified the built-in sensors will not detect the change in shape of the AGV. Hence, there is a risk that the AGV may collide with objects. Also in some AGVs floor sensors are missing to detect the presence of floor/no floor in front of the AGV, which can be a hazardous situation as there are chances of the AGV falling off from the surface. An example of such an AGV is the Patrolbot which can travel around in an industrial premise wirelessly, but needs addition of such sensors to avoid collisions with the modified structure. A Patrolbot has been used in this thesis work and ultrasonic sensors are utilised for obstacle detection with a modified structure and a built-in laser scanner is studied for mapping purpose. The results of this master thesis was that the ultrasonic sensors were tested under various conditions and results were derived. To obtain the same level of results every time it is required to maintain the conditions on which the ultrasonic sensors rely.

In this thesis, robot navigation using the Particle Filter based FastSLAM approach for obstacle avoidance derived from a modified Velocity Potential Field method was investigated. A switching controller was developed to deal with robot’s efficient turning direction when close to obstacles. The determination of the efficient turning direction is based on the local map robot derived from its on board local sensing. The estimation of local map and robot path was implemented using the FastSLAM approach. A particle filter was utilized to obtain estimated robot path and obstacles (local map). When robot sensed only obstacles, the estimated robot positions was regarding to obstacles based the measurement of the distance between the robot and obstacles. When the robot detected the goal, estimation of robot path will switch to estimation with regard to the goal in order to obtain better estimated robot positions. Both simulation and experimental results illustrated that estimation with regard to the goal performs better than estimation regarding only to obstacles, because when robot travelled close to the goal, the residual error between estimated robot path and the ideal robot path becomes monotonously decreasing. When robot reached the goal, the estimated robot position and the ideal robot position converge. We investigated our proposed approach in two typical robot navigation scenarios. Simulations were accomplished using MATLAB, and experiments were conducted with the help of both MATLAB and LabVIEW. In simulations and experiments, the robot successfully chose efficiently turning direction to avoid obstacles and finally reached the goal.

It is well established that aging is associated with numerous health concerns, including poor balance. Deteriorations in attention demand also place older adults at a greater risk for falls. Emerging experiments have explored the impact of dual-task training programs and have improved dual-tasking in older adults. However, it is unknown whether these performance-related improvements are a function of the intervention itself or the repeated exposure to the testing protocol. Study 1 explored the implications of repeated administration, once per week for 5 weeks, of a protocol involving standing postural sway while concurrently performing reaction time (RT) tasks in older adults. Results revealed that postural sway was stable across testing sessions whereas the difficult RT task gradually improved over time. Study 2 examined the influence of repeated exposure, once per week for 5 weeks, of a protocol involving negotiating a series of obstacles while performing RT tasks in older adults. Participants walked significantly faster with repeated exposure and gradually improved RT. Study 3 investigated the impact of repeated exposure, once per week for 5 weeks, to three functional mobility measures in older adults. It also examined the influence of a 12-week balance and mobility training (BMT) program as well as a 12-week balance and mobility plus cognitive training (BMT+C) program on functional mobility in older adults. Functional mobility served to be stable over time. Both the BMT and BMT+C groups significantly improved functional mobility and sustained these improvements at the 12-week follow-up, while no changes were observed in the control group. No differences between the BMT and BMT+C groups emerged. Experiment 4 examined the influence of BMT and BMT+C on postural sway and RT in older adults. Participants in both training groups significantly improved RT and sustained these improvements at the follow-up, while no changes were observed in the control group. No changes to postural control were shown in any group. No differences between the BMT and BMT+C groups emerged. Experiment 5 examined the influence of BMT and BMT+C on negotiating a series of obstacles while performing RT tasks in older adults. Both the BMT and BMT+C groups significantly improved RT and sustained these improvements at the follow-up, while no changes were observed in the control group. All groups showed faster time to completion of the obstacle series. No differences between the BMT and BMT+C groups emerged. Collectively, these findings suggest that BMT and BMT+C significantly improve functional mobility and divided attention, and sustain these improvements over time. Although some improvements were observed after repeated exposure over 5 weeks, no changes in the control group were observed. Therefore, the improvements exhibited from BMT and BMT+C are likely not a function of repeated exposure to the testing protocol, as participants may be more susceptible to performance-related improvements when the testing sessions are close in proximity. Altogether, these findings propose that, whether or not cognitive training is included, attention demanding dual-task training not only improves functional mobility and RT, but also sustains these improvements over time in older adults. These results may be used to improve the prescription of exercise in older adults.

La marche est un mécanisme complexe impliquant l’élaboration de trajectoires dans des milieux divers et variés et la réalisation des mouvements segmentaires qui permettent de les parcourir. Elle est alors dépendante de l’environnement, des obstacles et autres individus qui le peuplent mais également des capacités physiques du corps humain. De part cette complexité, l’étude de la marche est généralement compartimentée en deux niveaux : la génération de trajectoires locomotrices d’une part et les mouvements des membres d’autre part. Ce travail vise à proposer un processus complet d’analyse de la marche, en s’intéressant au lien unissant les trajectoires locomotrices aux mouvements segmentaires. Dans un premier temps nous nous intéressons à la génération de trajectoires. Plus particulièrement, nous nous focalisons sur une situation de croisement entre deux piétons et sur les stratégies mises en place pour éviter la collision. Puis, nous portons notre attention sur la manière dont les endroits de pose de pieds sont influencés par la trajectoire. Cette analyse nous conduit à proposer un modèle de génération d’empreintes de pas. Enfin, nous nous intéressons à la générations des trajectoires articulaires menant au mouvement de marche. Par l’utilisation de la méthode de linéarisation locale nous proposons une nouvelle méthodologie pour la simulation de la marche à partir d’une entrée unique : la prochaine empreinte pas / Walking is a complex mecanism involving trajectories generation in various environments and motion generation in order to follow the path. Then, it is dependent on environment, obstacles and peoples moving around but also on body capabilities. This complexity lead scientits to split walking analysis in two levels : trajectory generation in one hand, and motion generation in the othe hand. This work aim to provide a global walking analysis processus by linking trajectorires and motion generation. First, we explore walking trajectories throw a particular situation : pedestrians crossing. Here we take interest in trajectories and speed adaptations. Then, we sink for the link between trajectory and heelstrike. It lead us to develop a model for heelstrike generation based on trajectory. Finally, we take interest in walking motion simulation. By the use of local linearization, we provide a new methodology for joints joints angles generation

A drone is an unmanned aerial vehicle with multiple forms of usage. Drones can be programmed to fly with different degrees of autonomous flight. Autonomous controlled flight makes it possible for the drone to fly without human involvement and it is then controlled solely by software. The goal of this project is to program the micro drone Crazyflie 2.1 to autonomously fly through an obstacle course in the shortest amount of time and a predetermined direction. The nature and placement of the obstacles are unknown beforehand. The obstacles are detected and avoided by using the obstacle detection sensor Multi- ranger. To achieve autonomous flight two possible navigation systems were tested, the Loco Positioning System and Flow deck. Flying the Crazyflie while using Flow deck as positioning system performed best, managing to fly through the obstacle course avoiding all obstacles.

abstract: One potential application of multi-robot systems is collective transport, a task in which multiple mobile robots collaboratively transport a payload that is too large or heavy to be carried by a single robot. Numerous control schemes have been proposed for collective transport in environments where robots can localize themselves (e.g., using GPS) and communicate with one another, have information about the payload's geometric and dynamical properties, and follow predefined robot and/or payload trajectories. However, these approaches cannot be applied in uncertain environments where robots do not have reliable communication and GPS and lack information about the payload. These conditions characterize a variety of applications, including construction, mining, assembly in space and underwater, search-and-rescue, and disaster response. Toward this end, this thesis presents decentralized control strategies for collective transport by robots that regulate their actions using only their local sensor measurements and minimal prior information. These strategies can be implemented on robots that have limited or absent localization capabilities, do not explicitly exchange information, and are not assigned predefined trajectories. The controllers are developed for collective transport over planar surfaces, but can be extended to three-dimensional environments. This thesis addresses the above problem for two control objectives. First, decentralized controllers are proposed for velocity control of collective transport, in which the robots must transport a payload at a constant velocity through an unbounded domain that may contain strictly convex obstacles. The robots are provided only with the target transport velocity, and they do not have global localization or prior information about any obstacles in the environment. Second, decentralized controllers are proposed for position control of collective transport, in which the robots must transport a payload to a target position through a bounded or unbounded domain that may contain convex obstacles. The robots are subject to the same constraints as in the velocity control scenario, except that they are assumed to have global localization. Theoretical guarantees for successful execution of the task are derived using techniques from nonlinear control theory, and it is shown through simulations and physical robot experiments that the transport objectives are achieved with the proposed controllers. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2020