Optimal Impulse Control of Systems with Control Constraints and Application to HIV Treatment

In this paper, conditions for optimal impulse control of an impulsive system with constraints on control are derived. These hold for a system whose states can be changed instantaneously at discrete times with impulses while a continuous control is being applied between those times. The conditions derived are applied to the problem of optimal HIV treatment. Simulation results are presented to show the treatment procedure. The results obtained show that the intervention method developed leads to good results

Biped locomotion control via hybrid position control and gravity compensation modes /

Past three decades witnessed a growing interest in biped walking robots because of their advantageous use in the human environment. However, their control is challenging because of their many degrees of freedom and non-linearities in their dynamics. Various trajectory generation and walking control approaches ranging from open loop walking to systems with many sensors and feedback loops have been reported in the literature. The tuning of the parameters of reference gait is a common complication encountered. Another important problem of the walking control is the contact transients at the instant of landing. The method presented in this thesis generated position references for the upper body. Optimization techniques are employed to obtain suitable leg joint torques for the supporting leg to track body reference trajectories. Locomotion is achieved by a swinging leg control scheme, which is based on position control on certain directions, and artificial gravity compensation on certain directions. Soft landing and low impedance problem of the legs can easily be handled with this scheme. Another advantage is that limited number of parameters is required for gait generation. 3D dynamics and ground interaction simulation techniques are employed for a 12-DOF biped robot to test the proposed method. The simulations indicate the applicability of the method in real implementations

Climbing and Walking Robots

Nowadays robotics is one of the most dynamic fields of scientific researches. The shift of robotics researches from manufacturing to services applications is clear. During the last decades interest in studying climbing and walking robots has been increased. This increasing interest has been in many areas that most important ones of them are: mechanics, electronics, medical engineering, cybernetics, controls, and computers. Today’s climbing and walking robots are a combination of manipulative, perceptive, communicative, and cognitive abilities and they are capable of performing many tasks in industrial and non- industrial environments. Surveillance, planetary exploration, emergence rescue operations, reconnaissance, petrochemical applications, construction, entertainment, personal services, intervention in severe environments, transportation, medical and etc are some applications from a very diverse application fields of climbing and walking robots. By great progress in this area of robotics it is anticipated that next generation climbing and walking robots will enhance lives and will change the way the human works, thinks and makes decisions. This book presents the state of the art achievments, recent developments, applications and future challenges of climbing and walking robots. These are presented in 24 chapters by authors throughtot the world The book serves as a reference especially for the researchers who are interested in mobile robots. It also is useful for industrial engineers and graduate students in advanced study

Algoritmos de geometría diferencial para la locomoción y navegación bípedas de robots humanoides: Aplicación al robot RH0

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