Academic literature on the topic 'Forward/inverse kinematics'

This thesis deals with the usefulness of the application of quaternions in representing robot kinematics. It begins by showing the relationship of quaternions to the more commonly-known complex numbers and how it can represent rotations in three-dimensions. Then, the dual quaternions are introduced to represent both the three-dimensional rotation and translation. It will then be used to derive the forward and inverse kinematics, particularly, for the Universal Robot UR3 which is a 6-DOF robotic arm. Lastly, an actual application of dual quaternions in robot programming will be demonstrated

The aim of the thesis is to propose and make a robot, which is made of identical modules. These modules are able to connect or disconnect themselves and thanks to this feature new structures of robot can be achieved. This problem is solved by the design proposal of a module, which is capable to rotate in two axis and has connection connectors for other modules. Communication is carried out by Wi-fi connection to the computer and angles required for reconfiguration are calculated by inverse kinematics in Matlab program. On these modules the reconfiguration test was succesfully demonstrated.

This master thesis is focused on Modular Self-Reconfigurable Robotic Systems. Their description is made at first and then possibilities of their use are listed. The next chapter concerns Molecubes modular system. The design of similar system where the construction of the individual modules is described follows. The transformations of coordinated systems in the individual modules are described and the calculation of forward kinematics and simulation of inverse kinematics is made at the end of the thesis.

Modeling and simulations are useful tools to help understand knee function and injuries. As there are more muscles in the human knee joint than equations of motion, optimization protocols are required to solve a problem. The purpose of this thesis was to improve the biofidelity of these simulations by adding in vivo constraints derived from experimental intra-cortical pin data and stability-inspired objective functions within an OpenSim-Matlab forward-inverse dynamics simulation framework on lower limb muscle activation predictions. Results of this project suggest that constraining the model knee joint’s ranges of motion with pin data had a significant impact on lower limb kinematics, especially in rotational degrees of freedom. This affected muscle activation predictions and knee joint loading when compared to unconstrained kinematics. Furthermore, changing the objective will change muscle activation predictions although minimization of muscle activation as an objective remains more accurate than the stability inspired functions, at least for gait. /// La modélisation et les simulations in-silico sont des outils importants pour approfondir notre compréhension de la fonction du genou et ses blessures. Puisqu’il y a plus de muscles autour du genou humain que d’équations de mouvement, des procédures d’optimisation sont requises pour résoudre le système. Le but de cette thèse était d’explorer l’effet de changer l’objectif de cette optimisation à des fonctions inspirées par la stabilité du genou par l’entremise d’un cadre de simulation de dynamique directe et inverse utilisant MatLab et OpenSim ainsi qu'un model musculo-squelétaire contraint cinématiquement par des données expérimentales dérivées de vis intra-corticales, sur les prédictions d’activation musculaire de la jambe. Les résultats de ce projet suggèrent que les contraintes de mouvement imposées sur le genou modélisé ont démontré des effets importants sur la cinématique de la jambe et conséquemment sur les prédictions d'activation musculaire et le chargement du genou. La fonction objective de l'optimisation change aussi les prédictions d’activations musculaires, bien que la fonction minimisant la consommation énergétique soit la plus juste, du moins pour la marche.

This thesis focuses on the problem of determining appropriate skeletal configurations for which a virtual animated character moves to desired positions as smoothly, rapidly, and as accurately as possible. During the last decades, several methods and techniques, sophisticated or heuristic, have been presented to produce smooth and natural solutions to the Inverse Kinematics (IK) problem. However, many of the currently available methods suffer from high computational cost and production of unrealistic poses. In this study, a novel heuristic method, called Forward And Backward Reaching Inverse Kinematics (FABRIK), is proposed, which returnsvisually natural poses in real-time, equally comparable with highly sophisticated approaches. It is capable of supporting constraints for most of the known joint types and it can be extended to solve problems with multiple end effectors, multiple targets and closed loops. FABRIK wascompared against the most popular IK approaches and evaluated in terms of its robustness and performance limitations. This thesis also includes a robust methodology for marker prediction under multiple marker occlusion for extended time periods, in order to drive real-time centre of rotation (CoR) estimations. Inferred information from neighbouring markers has been utilised, assuming that the inter-marker distances remain constant over time. This is the firsttime where the useful information about the missing markers positions which are partially visible to a single camera is deployed. Experiments demonstrate that the proposed methodology can effectively track the occluded markers with high accuracy, even if the occlusion persists for extended periods of time, recovering in real-time good estimates of the true joint positions. In addition, the predicted positions of the joints were further improved by employing FABRIK to relocate their positions and ensure a fixed bone length over time. Our methodology is tested against some of the most popular methods for marker prediction and the results confirm that our approach outperforms these methods in estimating both marker and CoR positions. Finally, an efficient model for real-time hand tracking and reconstruction that requires a minimumnumber of available markers, one on each finger, is presented. The proposed hand modelis highly constrained with joint rotational and orientational constraints, restricting the fingers and palm movements to an appropriate feasible set. FABRIK is then incorporated to estimate the remaining joint positions and to fit them to the hand model. Physiological constraints, such as inertia, abduction, flexion etc, are also incorporated to correct the final hand posture. A mesh deformation algorithm is then applied to visualise the movements of the underlying hand skeleton for comparison with the true hand poses. The mathematical framework used for describing and implementing the techniques discussed within this thesis is Conformal GeometricAlgebra (CGA).

Táto diplomová práca sa zaoberá matematickými aparátmi popisujúcimi doprednú a inverznú kinematiku robotického ramena. Pre popis polohy koncového efektoru, teda doprednej kinematiky, je potrebné zaviesť špeciálnu Euklidovskú grupu zobrazení. Táto grupa môže byť reprezentovaná pomocou matíc alebo pomocou duálnych kvaterniónov. Problém inverznej kinematiky, kedy je potrebné z určenej polohy koncového efektoru dopočítať kĺbové parametre robotického ramena, je v tejto práci riešený pomocou exponenciálnych zobrazení a Grobnerovej bázy. Všetky spomenuté popisy doprednej a inverznej kinematiky sú aplikované na robotické rameno s troma rotačnými kĺbami. Odvodené postupy sú následne implementované a vizualizované v prostredí programu Mathematica.

Este trabalho trata do estudo de robôs de arquitetura paralela, focando na modelagem e otimização dos mesmos. Não foi construído nenhum tipo de protótipo físico, contudo os modelos virtuais poderão, no futuro, habilitar tal façanha. Após uma busca por uma aplicação que se beneficie do uso de um robô de arquitetura paralela, fez-se uma pesquisa por arquiteturas viáveis já existentes ou relatadas na literatura. Escolheu-se a mais apta e prosseguiu-se com os estudos e modelagem cinemática e dinâmica, dando uma maior ênfase na cinemática e dinâmica inversa, esta última utilizando a formulação de Newton - Euler. Foi construído um simulador virtual em ambiente MATLAB 6.5, dotado de várias capacidades como interpolação linear e circular, avanço e uso de múltiplos eixos coordenados. Seu propósito principal é o de demonstrar a funcionalidade e eficácia dos métodos utilizados. Depois foi incorporado ao simulador um algoritmo de cálculo do volume de trabalho da máquina que utiliza alguns dados do usuário para calcular o volume, que pode ser aquele atrelado a uma postura em particular ou o volume de trabalho de orientação total. Algoritmos para medir o desempenho da máquina quanto à uniformidade e utilização da força dos atuadores foram construídos e também incorporados ao simulador, que consegue mostrar o elipsóide de forças ao longo de quaisquer movimentos executados pela plataforma móvel. Quanto à otimização, parte do ferramental previamente construído foi utilizado para que se pudesse chegar a um modelo de uma máquina que respeitasse restrições mínimas quanto ao tamanho e forma de seu volume de trabalho, mas ainda mantendo o melhor desempenho possível dentro deste volume.<br>This work is about the study of parallel architecture robots, focusing in modeling and optimization. No physical prototypes were built, although the virtual models can help those willing to do so. After searching for an application that could benefit from the use of a parallel robot, another search was made, this time for the right architecture type. After selecting the architecture, the next step was the kinematics and dynamics analysis. The dynamics model is developed using the Newton ? Euler method. A virtual simulator was also developed in MATLAB 6.5 environment. The simulator?s main purpose was to demonstrate that the methods applied were correct and efficient, so it has several features such as linear and circular interpolations, capacity to use multiple coordinate systems and others. After finishing the simulator, an algorithm to calculate the machine workspace was added. The algorithm receives as input some desired requirements regarding the manipulator pose and then calculates the workspace, taking into consideration imposed constraints. Lastly, algorithms capable to measure the manipulator?s performance regarding to its actuator and end-effector force relationship were also incorporated into the simulator that calculates the machine?s force ellipsoid during any movement, for each desired workspace point. For the optimization procedures, some previously developed tools were used, so that the resulting model was capable to respect some workspace constraints regarding size and shape, but also maintaining the best performance possible inside this volume.

This thesis proposes an architecture of animation engine flexible enough to support large scale of animation algorithms with unified approach to each one of them. One of the major goals of the engine is to support creation of very complex animation seqences with high degree of animation execution control. The main animation technique used in the engine is skeletal animation and some variants of this technique are already implemented within, but it was never meant to be skeletal animation only engine and is designed that way.

Orientador: Suely Cunha Amaro Mantovani<br>Resumo: No estudo dos manipuladores são utilizados os conceitos da cinemática direta e a inversa. No cálculo da cinemática direta tem-se a facilidade da notação de Denavit-Hartenberg, mas o desafio maior é a resolução da cinemática inversa, que se torna mais complexa conforme aumentam os graus de liberdade do manipulador, além de apresentar múltiplas soluções. As variáveis angulares obtidas pelas equações da cinemática inversa são utilizadas pelo controlador, para posicionar o órgão terminal do manipulador em um ponto específico de seu volume de trabalho. Na busca de alternativas para contornar estes problemas, neste trabalho utilizam-se os Modelos Adaptativos de Inferência Neuro-Fuzzy - ANFIS para a resolução da cinemática inversa, por meio de simulações, para obter o posicionamento de um manipulador robótico de 5 graus de liberdade, composto por sete servomotores controlados pela plataforma de desenvolvimento Intel® Galileo Gen 2, usado como caso de estudo. Nas simulações usamse ANFIS com uma arquitetura com três e quatro funções de pertinência de entrada, do tipo gaussiana. O desempenho da arquitetura da ANFIS implementada foi comparado com uma Rede Perceptron Multicamadas, demonstrando com os resultados favoráveis a ANFIS, a sua capacidade de aprender e resolver com baixo erro quadrático médio e com precisão, a cinemática inversa para o manipulador em estudo. Verifica-se também, que a performance das ANFIS melhora, quanto à precisão dos resultados, demonstrado pelo desvio médio d... (Resumo completo, clicar acesso eletrônico abaixo)<br>Abstract: In the study of manipulator’s, the concepts of direct and inverse kinematics are used. In the computation of forward kinematics, it has of the ease of Denavit-Hartenberg notation, but the biggest challenge is the resolution of the inverse kinematics, which becomes more complex as the manipulator's degrees of freedom increase, besides presenting multiple solutions. The angular variables obtained by the inverse kinematics equations are used by the controller to position the terminal organ of the manipulator at a specific point in its work volume. In the search for alternatives to overcome these problems, in this work, the Adaptive Neuro-Fuzzy Inference Models (ANFIS) are used to solve the inverse kinematics, by means of simulations, to obtain the positioning of a robot manipulator of 5 degrees of freedom, consisting of seven servomotors controlled by the Intel® Galileo Gen 2 development platform, used as a case's study . In the simulations ANFIS's architecture are used three and four Gaussian membership functions of input. The performance of the implemented ANFIS architecture was compared to a Multi-layered Perceptron Network, demonstrating with the favorable results the ANFIS, its ability to learn and solve with low mean square error and with precision, the inverse kinematics for the manipulator under study. It is also verified that the performance of the ANFIS improves, as regards the accuracy of the results in the training process, , demonstrated by the mean deviation of the... (Complete abstract click electronic access below)<br>Mestre