Submitted by ALINE DE FREITAS MORONI null (ali-moroni@hotmail.com) on 2016-05-17T15:39:59Z No. of bitstreams: 1 Rotações no espaço tridimensional por meio de produtos quaterniônicos..pdf: 761793 bytes, checksum: 0d00cba6c4297a34f603a3b61904efc4 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-05-19T13:44:08Z (GMT) No. of bitstreams: 1 moroni_af_me_rcla.pdf: 761793 bytes, checksum: 0d00cba6c4297a34f603a3b61904efc4 (MD5) / Made available in DSpace on 2016-05-19T13:44:08Z (GMT). No. of bitstreams: 1 moroni_af_me_rcla.pdf: 761793 bytes, checksum: 0d00cba6c4297a34f603a3b61904efc4 (MD5) Previous issue date: 2016-04-20 / Neste trabalho pretendemos descrever o processo de construção da álgebra dos quatérnios, e a interpretação da multiplicação desses objetos via rotações no espaço. Para isto, vimos a necessidade de iniciar com conceitos que formam a base da álgebra, listando axiomas para o sistema de números reais e complexos. / The aim of this work is to describe the construction of the quaternion algebra and to interpret the multiplication operation via tridimensional rotations. For that we begin with basic algebraic concepts, and we list the axioms for the real and complex number systems.

This thesis deals with a design of 9DOF module for the evaluation of orientation in space. The thesis includes a theoretical description of sensors, mathematical apparatus for rotating and the Kalman filter. The practical part deals with the design of hardware, firmware and software, whereby the mathematical formulas set out in the theoretical part are applied. In the last part a testing of the created module is presented.

This thesis develops an alternative sensor fusion approach for object orientation using low-cost MEMS inertial sensors. The alternative approach focuses on the unique challenges of small UAVs. Such challenges include the vibrational induced noise onto the accelerometer and bias offset errors of the rate gyroscope. To overcome these challenges, a sensor fusion algorithm combines the measured data from the accelerometer and rate gyroscope to achieve a single output free from vibrational noise and bias offset errors. One of the most prevalent sensor fusion algorithms used for orientation estimation is the Extended Kalman filter (EKF). The EKF filter performs the fusion process by first creating the process model using the nonlinear equations of motion and then establishing a measurement model. With the process and measurement models established, the filter operates by propagating the mean and covariance of the states through time. The success of EKF relies on the ability to establish a representative process and measurement model of the system. In most applications, the EKF measurement model utilizes the accelerometer and GPS-derived accelerations to determine an estimate of the orientation. However, if the GPS-derived accelerations are not available then the measurement model becomes less reliable when subjected to harsh vibrational environments. This situation led to the alternative approach, which focuses on the correlation between the rate gyroscope and accelerometer-derived angle. The correlation between the two sensors then determines how much the algorithm will use one sensor over the other. The result is a measurement that does not suffer from the vibrational noise or from bias offset errors.

L'épaule est un complexe articulaire formé par le thorax, la clavicule, la scapula et l'humérus. Alors que les orientation et position de ces derniers la rendent difficile à étudier, la compréhension approfondie de l'interrelation de ces segments demeure cliniquement importante. Ainsi, un nouveau modèle du membre supérieur est développé et présenté. La cinématique articulaire de 15 sujets sains est collectée et reconstruite à l'aide du modèle. Celle-ci s'avère être généralement moins variable et plus facilement interprétable que le modèle de référence. Parallèlement, l'utilisation de simplifications, issues de la 2D, sur le calcul d'amplitude de mouvement en 3D est critiquée. Cependant, des cas d'exception où ces simplifications s'appliquent sont dégagés et prouvés. Ainsi, ils sont une éventuelle avenue d'amélioration supplémentaire des modèles sans compromission de leur validé. / The shoulder is an articulated complex composed of the thorax, clavicle, scapula and humerus. While the relative orientation and position of the segments makes an in-depth study of the shoulder difficult, understanding the interaction between the segments remains clinically important. Thus, a new model of the upper limb is proposed. Joint kinematics of 15 subjects were collected and reconstructed using the model, and were found to be less variable and easier to interpret when compared to the reference model. Meanwhile, simplifications involving the use of 2D analysis to calculate range of motion in 3D are criticized. Exceptions where these simplifications apply, were however, shown. Thus, such simplifications can be applied to models in certain situations without compromising the models validity.

L'épaule est un complexe articulaire formé par le thorax, la clavicule, la scapula et l'humérus. Alors que les orientation et position de ces derniers la rendent difficile à étudier, la compréhension approfondie de l'interrelation de ces segments demeure cliniquement importante. Ainsi, un nouveau modèle du membre supérieur est développé et présenté. La cinématique articulaire de 15 sujets sains est collectée et reconstruite à l'aide du modèle. Celle-ci s'avère être généralement moins variable et plus facilement interprétable que le modèle de référence. Parallèlement, l'utilisation de simplifications, issues de la 2D, sur le calcul d'amplitude de mouvement en 3D est critiquée. Cependant, des cas d'exception où ces simplifications s'appliquent sont dégagés et prouvés. Ainsi, ils sont une éventuelle avenue d'amélioration supplémentaire des modèles sans compromission de leur validé. / The shoulder is an articulated complex composed of the thorax, clavicle, scapula and humerus. While the relative orientation and position of the segments makes an in-depth study of the shoulder difficult, understanding the interaction between the segments remains clinically important. Thus, a new model of the upper limb is proposed. Joint kinematics of 15 subjects were collected and reconstructed using the model, and were found to be less variable and easier to interpret when compared to the reference model. Meanwhile, simplifications involving the use of 2D analysis to calculate range of motion in 3D are criticized. Exceptions where these simplifications apply, were however, shown. Thus, such simplifications can be applied to models in certain situations without compromising the models validity.

This diploma thesis deals with processing of measured data from inertial navigation system in order these could be used for stabilization. There is general information about aerial vehicles called copters with emphasis on four-rotor construction called quadrocopter at first. Then mathematical model of quadrocopter in state space form is derived, the particular implementation of university developed quadrocopter is described and the design of data processing algorithm is presented with measured results. Finally achieved results are discussed.