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Kinematic and Dynamic Analysis for Biped Robots Design

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Kinematic and Dynamic Analysis for Biped Robots Design CORE Metadata, citation and similar papers at core.ac.uk Provided by Universidad Carlos III de Madrid e-Archivo Tesis Doctoral Kinematic and Dynamic Analysis for Biped Robots Design David Mauricio Alba Lucero Director: Juan Carlos Garc´ıaPrada Universidad Carlos III de Madrid Escuela Polit´ecnica Superior Departamento de Ingenier´ıa Mec´anica Legan´es, 2012 Departamento Ingeniería Mecánica Escuela Politécnica Superior Universidad Carlos III de Madrid Título de la Tesis Kinematic and Dynamic Analysis for Biped Robots Design Autor David Mauricio Alba Lucero Titulación Ingeniero Mecánico Escuela Superior Politécnica del Litoral Director Juan Carlos García Prada Tesis Doctoral Kinematic and Dynamic Analysis for Biped Robots Design Autor: David Mauricio Alba Lucero Director: Juan Carlos García Prada Firma del tribunal calificador: Presidente: Vocal: Vocal: Vocal: Secretario: Legan´es, de de A mis padres Acknowledgments This thesis is the contribution of many people around me. I would like to extend my sincerely gratitude to Professor Juan Carlos Garc´ıa Prada to offer his patience and knowl- edge to finish this work. My colleges from whom I have gathered important experience like Dr. Cristina Castejon, Dr. Higinio Rubio and Dr. Jesus Meneses. They have helped me to overcome many difficulties during my work. Also I would like to thank all the people who began this adventure at the IAI-CSIC specially Professor Manuel Armada who provide me the first contact with robotics and Dr. Roberto Ponticelli who gave me important advice at the beginning of my studies. Also, I would like to thank Professor Sebastian Dormido who helped me to get into the MAQLAB team and Dr. Alfonso Urquia for all Modelica advices. To my colleagues Alvaro, Javier, Patri, Nacho, Efren and Mar´ıa Jesus, they have been around to support me in important matters outside academic matters, but I must say, still very important. The human quality they have offered has been a provision to stand the long path covered to reach the completion of this work. I would like to show all my thankfulness to my family. My parents who have always been very supportive and selfless about all my decisions, they provide me a wiser point of view of trivial and very important matters that helped to continue my way. My brother and sister that no matter the distance are always with me. Veronica, who suffered with me the ups and downs of this thesis. Finally, Jesus and his family who embrace me as another kinfolk. Resumen En esta tesis un nuevo m´etodo para encontrar sistemas din´amicamente equivalentes es propuesto. El objetivo es el de crear una herramienta para el an´alisis de robots b´ıpedos. La herramienta consiste en modelos simplificados obtenidos del principio de equivalencia din´amica, que dice que si dos sistemas poseen la misma masa, el mismo centro de masa y el mismo momento de inercia entonces son din´amicamente equivalentes. Este concepto no es nuevo y es com´unmente utilizado en el dise~node m´aquinas alternativas, o para encontrar el sweet spot de objetos esbeltos tales como bates o espadas. Con la aplicaci´ondel principio de equivalencia din´amica se encuentra el centro de percusi´on.La aportaci´onen esta tesis es la aplicaci´onde este concepto al an´alisis de robots b´ıpedos, y la extensi´ondel centro de percusi´ona cadenas cinem´aticas. La herramienta fundamental para la obtenci´onde resultados de investigaci´onen esta tesis hace uso del lenguaje de simulaci´onModelica®. Las simulaciones son altamente detalladas gracias a la librer´ıa est´andar Multibody incluida en las especificaciones del mismo. Como conse- cuencia de los trabajos desarrollados se crearon nuevas clases para extender la capacidad de la librer´ıa y aplicarla a m´aquinas caminantes. El desarrollo de esta tesis est´acentrado en el desarrollo de dos modelos. El primero es un p´endulo invertido equivalente, con la caracter´ıstica que posee las mismas propiedades din´amicas del robot que modela. Dichas propiedades son la masas total, el centro de masa y el momento de inercia. Este modelo es luego utilizado para generar el caminar de un b´ıpedo simple. El b´ıpedo es simulado con un volante de inercia como cuerpo, y pies de contacto puntual. Posee rodillas y est´atotalmente actuado. Los eslabones del robot poseen propiedades de s´olido r´ıgido y ninguna simplificaci´onha sido considerada. El segundo modelo tiene el objetivo de imitar la topolog´ıa del b´ıpedo que representa, por lo tanto tiene un grado mayor de complejidad que el anterior. Este modelo es construido al dividir al robot en tres grupos: Las dos piernas, y otro grupo compuesto por la cabeza, los brazos y el torso (Denominado HAT por sus siglas en ingl´es). Este modelo es denominado modelo de cuatro masas puntuales. Este modelo es posteriormente validado utilizandolo para desacoplar la din´amica del sistema, la ´unica informaci´onutilizada para llevar a cabo esta tarea es proporcionada por dicho modelo. Abstract In this thesis a method to find dynamically equivalent systems is proposed. The objective is to provide a tool to analyze biped robots by simplifying their dynamics to simpler models. The equivalent models are obtained with the concept of dynamic equivalence that states that if two systems share the same total mass, the same center of mass, and the same moment of inertia then they are considered to be dynamically equivalent. This concept is not new and it is used in the design of alternative machines, or to find the sweet spot of long object like swords or bats. The result of the application of the dynamic equivalence principle is the point known as the center of percussion. The novelty in this thesis is to apply this concept to the analysis of biped robots, and the extension of the center of percussion to kinematic chains. The work in this thesis developed with the help of the simulation language Modelica®. The simulations are very detailed by implementing elaborated rigid body dynamics provided by the multibody standard library included in the language specifications. New classes were created in order to be able to simulate walking machines. Those classes introduce contact objects at ground foot interactions and mechanical stops for knee joints. The development of this thesis is centered around the proposal of two models. The first model is an equivalent inverted pendulum with the characteristic that it has the same dynamic properties, i.e., total mass, center of mass and moment of inertia, of the biped that models. This model is later used to synthesize gait in a simple, but realistic biped. The biped is simulated with a flywheel body, and point feet. It has knees and it is fully actuated. Also all the links have complete rigid body properties and no simplifications were done. The second model has the objective to resemble the topology of the biped it represents, therefore it is slightly more complex than the equivalent inverted pendulum. This model is constructed by grouping the components of the robot in three groups: Two legs and the HAT group (HAT stands for head, arms and trunk). This model is denominated four point masses model. The model is later validated by decoupling the dynamics of the system only with the information provided by the four point masses model. Contents 1 Motivation and objectives 1 1.1 Motivation . 1 1.2 Objectives . 2 2 State of the art 5 2.1 Basic inverted pendulum based models . 5 2.1.1 Inverted pendulum model . 6 2.1.2 Linear inverted pendulum model . 7 2.1.3 Reaction mass and reaction wheel pendulums . 9 2.1.4 Parametric pendulum . 12 2.2 Ground reference points for biped robots . 15 2.2.1 Zero moment point and center of pressure . 15 2.2.2 Centroidal moment pivot . 17 2.2.3 Capture points . 18 2.3 Other models . 21 2.3.1 Rimless wheel . 21 2.3.2 Complete models . 24 2.3.3 Reduced models . 28 3 Theoretical Framework and Methods 31 3.1 Dynamic equivalence . 32 3.1.1 Center of percussion . 32 3.1.2 What is missing? . 35 3.1.3 Center of percussion of a system of particles . 37 3.2 Object oriented modeling . 42 ii Contents 3.2.1 DAEs and computational causality . 43 3.2.2 Modelica . 44 3.2.3 Ground-foot interactions . 45 3.2.4 Joint simulation . 47 4 Center of percussion and gait design of biped robots 49 4.1 Finding the equivalent inverted pendulum of a biped robot . 49 4.2 Description of the model . 52 4.3 Gait generation . 54 4.3.1 Gait parameters . 55 4.3.2 Swinging leg control . 55 4.3.3 Stance leg control . 57 4.3.4 Putting it all together . 59 4.4 Simulation results . 60 4.5 Conclusions of the chapter . 64 4.5.1 Some words about stability . 65 4.5.2 Mass distribution of the biped . 65 4.6 Improvements of the technique . 66 4.6.1 Adding a torso and feet . 66 4.6.2 Energy optimization . 66 5 Four point masses equivalent model of a biped robot 69 5.1 Modeling a biped with four point masses . 69 5.1.1 Selection of a suitable reference . 70 5.1.2 Calculating the equivalent model . 71 5.2 Some words about impedance control . 75 5.3 Fast swinging of one leg . 76 5.3.1 Selection of the parameters . 76 5.3.2 \Kicking" experiments . 78 5.3.3 Results of the \kicking" experiments . 80 5.4 Oscillation experiments . 85 5.4.1 Parameters used in the simulations .
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