Publication: Algoritmos de geometría diferencial para la locomoción y navegación bípedas de robots humanoides: Aplicación al robot RH0
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2005-09
Defense date
2005-12-19
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Abstract
Los humanos crean entornos adecuados para ser habitados por ellos mismos, por lo que un robot humanoide es un instrumento muy bien adaptado para proporcionar muchos servicios a las personas. Sin embargo, todavía nos encontramos lejos de una producción comercial masiva de humanoides fiables y útiles para la sociedad. Una de las principales razones que justifican la situación actual es el formidable desafío computacional que presentan estos sistemas mecánicos, debido a la complejidad dada por el gran número de restricciones y grados de libertad. Cuando la complejidad es grande, la necesidad de formulaciones matemáticas elegantes se convierte en un asunto de extrema importancia, porque nos permite construir soluciones eficaces. Por ello, este trabajo aborda la investigación en robótica utilizando técnicas de Geometría Diferencial, basadas en la teoría matemática de Grupos y Álgebras de Lie y herramientas de Geometría Computacional para el análisis de interfaces en evolución. Estas formulaciones conducen a aplicaciones con soluciones cerradas y completas, numéricamente estables y con una clara interpretación geométrica. Esta tesis pionera en el campo de la investigación con robots, tiene como objetivo fundamental la resolución completa del problema de Locomoción y Navegación Bípeda de Robots Humanoides. Para ello, desarrolla nuevos modelos y algoritmos geométricos de propósito general, no presentados anteriormente en la literatura. Estas nuevas soluciones son potentes, flexibles y válidas para aplicaciones en tiempo real. El nuevo algoritmo “Un Paso Adelante” (UPA), resuelve la locomoción bípeda de un humanoide, basándose en el nuevo modelo “División Cinemática Sagital” (DCS), que da soluciones cerradas al problema cinemático inverso del robot. El nuevo algoritmo “Método Modificado de Marcha Rápida” (M3R) proporciona trayectorias libres de colisiones para resolver problemas de planificación, sea cual fuere la estructura del entorno de trabajo. Para la navegación del robot humanoide, introducimos el nuevo modelo “Trayectoria Corporal Global” (TCG). Se ha creado un nuevo Simulador de Realidad Virtual (RobManSim) para robots, que permite desarrollar las teorías presentadas. Los nuevos modelos y algoritmos introducidos en esta tesis, se han probado con éxito en experimentos reales con el humanoide RH0 de la Universidad Carlos III de Madrid. Sinceramente, creemos que los mejores diseños y aplicaciones son concebidos con elegancia de pensamiento. Esta es la idea que ha inspirado los trabajos de esta tesis, para acercar siquiera en algo, ese futuro de humanoides socialmente útiles, diseñados a la medida del hombre.
The humankind creates environments suited to be inhabited by them, therefore a humanoid robot is a tool very well adapted to provide a lot of services to people. Nevertheless, we are still far from a commercial production of reliable humanoids really useful to our society. One of the main reasons which justify the current situation is the formidable computational challenge presented by these mechanical systems, mainly because of the complexity given by the high number of restrictions and degrees of freedom. When the complexity is huge, the need for some elegant mathematical formulations becomes a paramount issue, because it allows us to build up efficient solutions. Therefore, this work explores the research on robotics using some Differential Geometry techniques based on the mathematical theory of Lie Groups and Algebras, and some Computational Geometry tools from the analysis of evolving interfaces. These formulations lead to applications with closed and complete solutions, which are numerically stable, and with a very clear geometrical interpretation. This pioneering thesis on the field of research with robots has a fundamental goal; that is to obtain the complete solution for the Humanoid Robot Bipedal Locomotion and Navigation problem. For doing so, it develops new geometric models and algorithms of general purpose, which have not been presented in the literature before. These new solutions are powerful, flexible and valid to real time applications. The new algorithm “One Step Goal” (OSG), solves the bipedal locomotion based upon the new humanoid model called “Sagittal Kinematics Division” (SKD), which provides closed solutions for the robot inverse kinematics problem. The new algorithm “Fast Marching Method Modified” (FM3) delivers collision-free trajectories to solve the path planning problems, whatever the structure of the working environment. For the humanoid robot navigation problem, the new model “Whole Body Trajectory” (WBT) is introduced. A new Virtual Reality Simulator (RobManSim) for humanoid robots has been created, in order to develop the herein presented theories. The new models and algorithms introduced by this thesis have been successfully tested through real experiments with the humanoid RH0 of the University Carlos III of Madrid. Sincerely, we believe that the best designs and applications are conceived with elegance o mind and this is the inspirational idea for the new developments of this thesis, in order to bring a little bit closer, a future of socially useful humanoids made up to the measure of the mankind.
The humankind creates environments suited to be inhabited by them, therefore a humanoid robot is a tool very well adapted to provide a lot of services to people. Nevertheless, we are still far from a commercial production of reliable humanoids really useful to our society. One of the main reasons which justify the current situation is the formidable computational challenge presented by these mechanical systems, mainly because of the complexity given by the high number of restrictions and degrees of freedom. When the complexity is huge, the need for some elegant mathematical formulations becomes a paramount issue, because it allows us to build up efficient solutions. Therefore, this work explores the research on robotics using some Differential Geometry techniques based on the mathematical theory of Lie Groups and Algebras, and some Computational Geometry tools from the analysis of evolving interfaces. These formulations lead to applications with closed and complete solutions, which are numerically stable, and with a very clear geometrical interpretation. This pioneering thesis on the field of research with robots has a fundamental goal; that is to obtain the complete solution for the Humanoid Robot Bipedal Locomotion and Navigation problem. For doing so, it develops new geometric models and algorithms of general purpose, which have not been presented in the literature before. These new solutions are powerful, flexible and valid to real time applications. The new algorithm “One Step Goal” (OSG), solves the bipedal locomotion based upon the new humanoid model called “Sagittal Kinematics Division” (SKD), which provides closed solutions for the robot inverse kinematics problem. The new algorithm “Fast Marching Method Modified” (FM3) delivers collision-free trajectories to solve the path planning problems, whatever the structure of the working environment. For the humanoid robot navigation problem, the new model “Whole Body Trajectory” (WBT) is introduced. A new Virtual Reality Simulator (RobManSim) for humanoid robots has been created, in order to develop the herein presented theories. The new models and algorithms introduced by this thesis have been successfully tested through real experiments with the humanoid RH0 of the University Carlos III of Madrid. Sincerely, we believe that the best designs and applications are conceived with elegance o mind and this is the inspirational idea for the new developments of this thesis, in order to bring a little bit closer, a future of socially useful humanoids made up to the measure of the mankind.
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Robótica, Geometría diferencial