This research investigates the possibility of controlling a simple biped having two degrees of freedom only. The biped robot walked on large feet. Having large feet enabled the robot to stand on one leg stably. At any time, the robotà ­s center of gravity remained above the area covered by one of the feet. Two servos actuated the two degrees of freedom tilting the robot to the side or moving the legs forward and backward. The biped moved by alternately tilting and striding. Turns were produced by dragging the feet along the ground. As the feet dragged, the friction generated under the feet created a turning moment that rotated the robot. Thus, the robot was able to step and turn on a flat surface. A control algorithm was developed to attempt trajectory tracking with the biped. Trajectories along a surface can be defined in terms of linear and angular velocities. In this research, it was assumed that a high level controller had transformed a desired trajectory into discrete steps of linear and angular velocities. Motion tests showed how various settings of the servos affected the step length and turning angle of the robot. To produce the desired velocities, a program was created to select the servo commands and set the speed parameters. This program applied knowledge of the expected step length and turning angle and performed feedforward control of the velocities. This investigation identified a trajectory tracking scheme that could be used in an observer feedback scenario to achieve accurate control. / Master of Science

Teaching simulated biped robots to walk is a popular problem in machine learning. However, until this thesis, evolving a biped controller has not been attempted through an indirect encoding, i.e. a compressed representation of the solution, despite the fact that natural bipeds such as humans evolved through such an indirect encoding (i.e. DNA). Thus the promise for indirect encoding is to evolve gaits that rival those seen in nature. In this thesis, an indirect encoding called HyperNEAT evolves a controller for a biped robot in a computer simulation. To most effectively explore the deceptive behavior space of biped walkers, novelty search is applied as a fitness metric. The result is that although the indirect encoding can evolve a stable bipedal gait, the overall neural architecture is brittle to small mutations. This result suggests that some capabilities might be necessary to include beyond indirect encoding, such as lifetime adaptation. Thus this thesis provides fresh insight into the requisite ingredients for the eventual achievement of fluid bipedal walking through artificial evolution.

This research studies the electrical power reduction and control analysis of various motion tasks of a humanoid robot. These motions include standing up and sitting down. Each motion’s tasks have their stable and unstable phases throughout the complete motion cycle. Unstable phases can be caused by gravity forces and improper handling of the upper body of the humanoid robot leaning too forward or backward. Even though most of the dynamic motions seem to be accomplished very simply by humans; standing up and sitting down could create challenges for humanoid robots. Some of the critical challenges researches face are: dynamic nature of motions, humanoid robot joint coordination, whole body balance, stability of the model, limited energy source, energy saving techniques and modeling. Dynamic motions of humanoid robots can be modeled and analyzed to reduce electrical power use. In order to accomplish such energy savings, a researcher needs to study the kinematics, dynamics of a humanoid, and motion tasks with given constraints. The robot in this research is modeled as a planar humanoid robot. All motion tasks of a humanoid robot are characterized in terms of motion variables. These motion variables include joint angular positions, joint angular velocity, joint angular acceleration, humanoid robot center of mass (CoM) position, velocity and acceleration change and center of pressure (CoP) position change. All mathematical models are completed so that electrical power analysis of each task produce comparable results. Humanoid robot joint cost functions related to energy consumption are used to define joint input electrical power used, joint mechanical power used, joint mechanical power dispersion and joint power loss due to torque required. In this research, a 4-link 3-joint humanoid is modeled for standing up and sitting down tasks. For each task, kinematics and dynamics models are created, motion constraints are found, energy and power usage analysis for whole robot and for individual joint motors are accomplished. By finding the best energy usage per motion variable, humanoid robot used less input electrical power to accomplish the motion task.

Este trabalho apresenta o desenvolvimento de um modelo simplificado dos membros inferiores de um robô bípede, composto basicamente por uma cintura, dois fêmures, duas tíbias e dois pés. A estrutura mecânica do modelo em questão, possui seis graus de liberdade e tem as dimensões aproximadas de um ser humano de estrutura mediana. Seu sistema de controle e de geração de trajetórias é desenvolvido utilizando funcionalidades disponíveis no Robot Operating System (ROS), porém ao contrário da maioria dos controladores existentes no ROS, este projeto propõe implementar um pacote contendo um controlador multivariável (multi-input, multi-output (MIMO)), utilizando a técnica de controle por torque calculado. Para a geração de trajetórias das pernas do robô, implementam-se três tipos diferentes de geração, a interpolação linear, cubica e de quinto grau. Para os testes de validação do sistema de controle e de geração de trajetórias utiliza-se o simulador Gazebo. / This work presents the development of a simplified model of a biped robot’s lower limbs, composed basically by the waist, two femurs, two tibia and two feet. The model’s mechanical structure has six degree of freedom and its dimensions are comparable to a human being’s body. Its control and trajectory generation systems are developed making use of some features available in the Robot Operation System (ROS) tool. However, contrary to most of the controllers offered by ROS, this project suggests the implementation of a new package, including a MIMO (multi-input multi-output) controller, making use of the calculated torque technique. As for the trajectory generation system, three different methodologies are applied of the interpolation: linear, cubic and polynomial quintic. To validate both control and trajectory generation systems, the Gazebo simulator is used.

Este trabalho apresenta o desenvolvimento de um modelo simplificado dos membros inferiores de um robô bípede, composto basicamente por uma cintura, dois fêmures, duas tíbias e dois pés. A estrutura mecânica do modelo em questão, possui seis graus de liberdade e tem as dimensões aproximadas de um ser humano de estrutura mediana. Seu sistema de controle e de geração de trajetórias é desenvolvido utilizando funcionalidades disponíveis no Robot Operating System (ROS), porém ao contrário da maioria dos controladores existentes no ROS, este projeto propõe implementar um pacote contendo um controlador multivariável (multi-input, multi-output (MIMO)), utilizando a técnica de controle por torque calculado. Para a geração de trajetórias das pernas do robô, implementam-se três tipos diferentes de geração, a interpolação linear, cubica e de quinto grau. Para os testes de validação do sistema de controle e de geração de trajetórias utiliza-se o simulador Gazebo. / This work presents the development of a simplified model of a biped robot’s lower limbs, composed basically by the waist, two femurs, two tibia and two feet. The model’s mechanical structure has six degree of freedom and its dimensions are comparable to a human being’s body. Its control and trajectory generation systems are developed making use of some features available in the Robot Operation System (ROS) tool. However, contrary to most of the controllers offered by ROS, this project suggests the implementation of a new package, including a MIMO (multi-input multi-output) controller, making use of the calculated torque technique. As for the trajectory generation system, three different methodologies are applied of the interpolation: linear, cubic and polynomial quintic. To validate both control and trajectory generation systems, the Gazebo simulator is used.

Este trabalho apresenta o desenvolvimento de um modelo simplificado dos membros inferiores de um robô bípede, composto basicamente por uma cintura, dois fêmures, duas tíbias e dois pés. A estrutura mecânica do modelo em questão, possui seis graus de liberdade e tem as dimensões aproximadas de um ser humano de estrutura mediana. Seu sistema de controle e de geração de trajetórias é desenvolvido utilizando funcionalidades disponíveis no Robot Operating System (ROS), porém ao contrário da maioria dos controladores existentes no ROS, este projeto propõe implementar um pacote contendo um controlador multivariável (multi-input, multi-output (MIMO)), utilizando a técnica de controle por torque calculado. Para a geração de trajetórias das pernas do robô, implementam-se três tipos diferentes de geração, a interpolação linear, cubica e de quinto grau. Para os testes de validação do sistema de controle e de geração de trajetórias utiliza-se o simulador Gazebo. / This work presents the development of a simplified model of a biped robot’s lower limbs, composed basically by the waist, two femurs, two tibia and two feet. The model’s mechanical structure has six degree of freedom and its dimensions are comparable to a human being’s body. Its control and trajectory generation systems are developed making use of some features available in the Robot Operation System (ROS) tool. However, contrary to most of the controllers offered by ROS, this project suggests the implementation of a new package, including a MIMO (multi-input multi-output) controller, making use of the calculated torque technique. As for the trajectory generation system, three different methodologies are applied of the interpolation: linear, cubic and polynomial quintic. To validate both control and trajectory generation systems, the Gazebo simulator is used.

Current state-of-the-art walking controllers for humanoid robots use simple models, such as Linear Inverted Pendulum Mode (LIPM), to approximate Center of Mass(CoM) dynamics of a robot. These models are then used to generate CoM trajectories that keep the robot balanced while walking. Such controllers need prior information of foot placements, which is generated by a walking pattern generator. While the robot is walking, any change in the goal position leads to aborting the existing foot placement plan and re-planning footsteps, followed by CoM trajectory generation. This thesis proposes a tightly coupled walking pattern generator and a reactive balancing controller to plan and execute one step at a time. Walking is an emergent behavior from such a controller which is achieved by applying a virtual force in the direction of the goal. This virtual force, along with external forces acting on the robot, is used to compute desired CoM acceleration and the footstep parameters for only the next step. Step location is selected based on the capture point, which is a point on the ground at which the robot should step to stay balanced. Because each footstep location is derived as needed based on the capture point, it is not necessary to compute a complete set of footsteps. Experiments show that this approach allows for simpler inputs, results in faster operation, and is inherently immune to external perturbing and other reaction forces from the environment. Experiments are performed on Boston Dynamic's Atlas robot and NASA's Valkyrie R5 robot in simulation, and on Atlas hardware.

Current state-of-the-art walking controllers for humanoid robots use simple models, such as Linear Inverted Pendulum Mode (LIPM), to approximate Center of Mass(CoM) dynamics of a robot. These models are then used to generate CoM trajectories that keep the robot balanced while walking. Such controllers need prior information of foot placements, which is generated by a walking pattern generator. While the robot is walking, any change in the goal position leads to aborting the existing foot placement plan and re-planning footsteps, followed by CoM trajectory generation. This thesis proposes a tightly coupled walking pattern generator and a reactive balancing controller to plan and execute one step at a time. Walking is an emergent behavior from such a controller which is achieved by applying a virtual force in the direction of the goal. This virtual force, along with external forces acting on the robot, is used to compute desired CoM acceleration and the footstep parameters for only the next step. Step location is selected based on the capture point, which is a point on the ground at which the robot should step to stay balanced. Because each footstep location is derived as needed based on the capture point, it is not necessary to compute a complete set of footsteps. Experiments show that this approach allows for simpler inputs, results in faster operation, and is inherently immune to external perturbing and other reaction forces from the environment. Experiments are performed on Boston Dynamic's Atlas robot and NASA's Valkyrie R5 robot in simulation, and on Atlas hardware.

Mimicking human motion with a humanoid robot can prove to be useful for studying gaits, designing better prostheses, or assisting the elderly or disabled. Directly mimicking and implementing a motion of a human on a humanoid robot may not be successful because of the different dynamic characteristics between them, which may cause the robot to fall down due to instability. Using the Zero Moment Point as the stability criteria, this work proposes an Analytical Motion Filter (AMF), which stabilizes a reference motion that can come from human motion capture data, gait synthesis using kinematics, or animation software, while satisfying common constraints. In order to determine how the AMF stabilized a motion, the different kinds of instabilities were identified and classified when examining the reference motions. The different cases of instability gave more insight as to why a particular motion was unstable: the motion was too fast, too slow, or inherently unstable. In order to stabilize the gait two primary methods were utilized: time and spatial scaling. Spatial scaling scaled the COM trajectory down towards a known stable trajectory. Time scaling worked similarly by changing the speed of the motion, but was limited in effectiveness based on the types of instabilities in the motion and the coupling of the spatial directions. Other constraints applied to the AMF and combinations of the different methods produced interesting results that gave more insight into the stability of the gait. The AMF was tested using both simulations and physical experiments using the DARwIn miniature humanoid robot developed by RoMeLa at Virginia Tech as the test platform. The simulations proved successful and provided more insight to understanding instabilities that can occur for different gait generation methods. The physical experiments worked well for non-walking motions, but because of insufficient controllability in the joint actuators of the humanoid robot used for the experiment, the high loads during walking motions prevented them from proper testing. The algorithms used in this work could also be expanded to legged robots or entirely different platforms that depend on stability and can use the ZMP as a stability criterion. One of the primary contributions of this work was showing that an entire reference motion could be stabilized using a single set of closed form solutions and equations. Previous work by others considered optimization functions and numeric schemes to stabilize all or a portion of a gait. Instead, the Analytical Motion Filter gives a direct relationship between the input reference motion and the resulting filtered output motion. / Ph. D.

Os dispositivos robóticos bípedes tem um grande potencial de aplicações tanto comerciais como para pesquisa. Dentre as presentes lacunas existentes que limitam a sua aplicabilidade prática tem um destaque especial a incapacidade de realizar uma marcha estável, robusta, versátil e eficiente no ponto de vista energético. No presente estado da arte, existem três principais estratégias de abordagem para o problema e algumas de suas implementações obtiveram sucesso em satisfazer pelo menos um dos requisitos listados, porém nunca todos eles de forma simultânea. Dentro deste cenário, este trabalho se propôs desenvolver um novo critério de estabilidade para marcha bípede que possibilite marchas versáteis, robustas e eficientes. Inicialmente foi realizada uma avaliação de diversos simuladores de código aberto e o Simbody foi definido como o mais apropriado para ser utilizado no desenvolvimento das simulações dinâmicas realizadas nesta Tese. Uma toolbox de MATLAB para auxiliar nos cálculos cinemáticos e dinâmicos foi desenvolvida em conjunto com um módulo de Inter Process Communication para realizar a comunicação entre o MATLAB e o simulador. Foi realizado um estudo da marcha bípede, implementando e avaliando as estratégias do Zero Moment Point e do Limit CycleWalking. Este estudo resultou numa proposta de controlador não linear comutado para robôs em Ciclo Limite. Na procura de um novo critério de estabilidade foi abordado o estudo da marcha humana. Um procedimento para identificar os mecanismos que controlam a estabilidade da marcha humana é analisar a mesma sob perturbações, como tropeços, ou na ultrapassagem de obstáculos. Na literatura existiam bastantes referências sobre este tema, porém, faltou uma comparação da marcha humana sob diferentes condições de visão com a marcha de robôs que utilizam o ZMP. Foi descoberto que os seres humanos privados de visão têm uma estratégia de ultrapassagem de obstáculos semelhante a um robô com ZMP. A partir do conhecimento adquirido deste estudo é proposto e formulado um novo critério de estabilidade, o Step Viability, inspirado na marcha humana e no conceito de N-Step Capturability. O Step Viability baseia-se na definição de restrições que garantem a viabilidade de realizar passos futuros que garantam a convergência para um ponto fixo em tempo finito. O critério foi implementado utilizando-se uma otimização de trajetória multi-fase. Múltiplos testes foram realizados utilizando-se o modelo Compass Gait com diferentes parâmetros (distribuição de massa, torque máximo disponível), com diferentes inclinações e com vários padrões de marcha desejados (periódico, aumento uniforme e até aleatório não periódico). Adicionalmente o critério foi testado em um modelo de 5 segmentos, sintetizando uma marcha com variação tanto linear quanto aleatória. O critério foi bem-sucedido na geração de uma marcha estável em todos os testes e os resultados foram consistentes. A marcha pode ser sintetizada completamente desacoplada do critério de estabilidade, e o modelo renunciou automaticamente do padrão desenhado em favor da estabilidade. / Bipedal robots present a great potential for both commercial and research applications. However, there are some drawbacks that limit their applicability in the real world. The most prominent is the inability to perform a stable, robust, versatile and efficient gait. There are three main state of the art strategies to approach this problem. However, none of them has been successful in satisfying all the listed requirements simultaneously. In this context, this work conducted a study of bipedal gait, both in humans and robots, in order to implement and evaluate existing stability strategies. As a first step, an evaluation of several open source simulators was performed and Simbody was chosen as the most adequate for the dynamic simulations carried out in this Thesis. A MATLAB toolbox to help in the kinematic and dynamic calculations was developed in conjunction with a module of an Inter Process Communication to perform the communication between MATLAB and the simulator. A bipedal gait study was carried out, implementing and evaluating Zero Moment Point and Limit Cycle Walking strategies. This study resulted in a proposed nonlinear switched controller for Limit Cycle robots. In the search for a new stability criterion, human gait was analyzed. A procedure to identify the mechanisms controlling human gait stability is to analyze gait under disturbances such as stumbling or overcoming obstacles. In the literature, there were many references on this subject, however, there was a lack of comparison of the human gait under different vision conditions with the gait of robots that use the ZMP. It was found that vision-deprived humans have an obstacle crossing strategy similar to robots with ZMP. From the knowledge acquired from this study, it is proposed a novel stability criterion, the Step Viability, inspired on human gait and the N-Step Capturability concept. The Step Viability is based on the definition of constraints that ensure the viability of performing future steps that guarantee convergence to a fixed point in finite time. The criterion was implemented using a multi-phase trajectory optimization. Multiple tests were performed using the Compass Gait model with different parameters (mass distribution, maximum available torque), with different slopes and with several desired gait patterns (periodic, uniform increase and even random non-periodic). Additionally, the criterion was tested in a 5-links model, synthesizing a gait with both linear and random velocity variation. The criterion was successful on generating a stable gait in all the tests and the results presented consistent data. The gait could be designed completely uncoupled from the stability criterion, yet the model automatically renounced to follow the desired pattern in favor of maintaining stability.