Globally stable control of a dynamic bipedal walker using adaptive frequency oscillators

We present a control method for a simple limit-cycle bipedal walker that uses adaptive frequency oscillators (AFOs) to generate stable gaits. Existence of stable limit cycles is demonstrated with an inverted-pendulum model. This model predicts a proportional relationship between hip torque amplitude and stride frequency. The closed-loop walking control incorporates adaptive Fourier analysis to generate a uniform oscillator phase. Gait solutions (fixed points) are predicted via linearization of the walker model, and employed as initial conditions to generate exact solutions via simulation. Global stability is determined via a recursive algorithm that generates the approximate basin of attraction of a fixed point. We also present an initial study on the implementation of AFO-based control on a bipedal walker with realistic mass distribution and articulated knee joint

Stable locomotion control of bipedal walking robots : synchronization with neural oscillators and switching control

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (leaves 105-110).Two novel approaches to stable legged locomotion control (neural-oscillator based control and switching control) are studied for achieving bipedal locomotion stability. Postural stability is realized by structural dynamics shaping, and gait stability is achieved by synchronization with neural oscillators and switching control. A biologically inspired control with neural oscillators (central pattern generator, abbreviated as CPG) is used for global stable locomotion of bipeds based on a mutually inhibited neural oscillator model (Matsuoka, 1985). A systematic design approach is studied for the entrainment between the dynamics of neural oscillators and the natural dynamics of the plant (bipedal skeletal dynamics) in the neural oscillator driven rhythmic control. This design can guarantee global dynamic entrainment, bipedal gait stability and system robustness, which are explored and analyzed using nonlinear system theories. The second control approach, called nonlinear switching control, is proposed to achieve stable locomotion control for a bipedal walking robot. This approach applies nonlinear switching control theory in the locomotion control system so as to ensure bipedal gait stability in the stable limit cycle sense. The switching surface is determined by means of the orbital contraction tuning technique. Both the structural dynamics stability and gait stability are analyzed. The convergence of the walking gait is proved based on nonlinear system theory. Two common features for the above control approaches are that a global state machine based switching module and a closed-loop gait stabilization mechanism are used in both control systems. In neural oscillator driven locomotion control, the sensory feedback signals are switched according to the states of global state machine. However, in the switching control, the global state machine is used to select the appropriate control sub-systems in addition to a contraction tuning mechanism. In both approaches, an explicit closed-loop gait control mechanism is implemented to guarantee the bipedal gait stability. Simulations of 2-D and 3-D bipedal walking robots demonstrate the effectiveness of the above locomotion control approaches. Different simulated experiments are given in the system analysis and evaluations. It has been shown that the above two bipedal locomotion control approaches can be further applied in the real-time control of bipedal walking robotic systems with proper locomotion stability and robustness.by Jianjuen J. Hu.Ph.D

Evolutionary robotics and neuroscience

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Rich and Robust Bio-Inspired Locomotion Control for Humanoid Robots

Bipedal locomotion is a challenging task in the sense that it requires to maintain dynamic balance while steering the gait in potentially complex environments. Yet, humans usually manage to move without any apparent difficulty, even on rough terrains. This requires a complex control scheme which is far from being understood. In this thesis, we take inspiration from the impressive human walking capabilities to design neuromuscular controllers for humanoid robots. More precisely, we control the robot motors to reproduce the action of virtual muscles commanded by stimulations (i.e. neural signals), similarly to what is done during human locomotion. Because the human neural circuitry commanding these muscles is not completely known, we make hypotheses about this control scheme to simplify it and progressively refine the corresponding rules. This thesis thus aims at developing new walking algorithms for humanoid robots in order to obtain fast, human-like and energetically efficient gaits. In particular, gait robustness and richness are two key aspects of this work. In other words, the gaits developed in the thesis can be steered by an external operator, while being resistant to external perturbations. This is mainly tested during blind walking experiments on COMAN, a 95 cm tall humanoid robot. Yet, the proposed controllers can be adapted to other humanoid robots. In the beginning of this thesis, we adapt and port an existing reflex-based neuromuscular model to the real COMAN platform. When tested in a 2D simulation environment, this model was capable of reproducing stable human-like locomotion. By porting it to real hardware, we show that these neuromuscular controllers are viable solutions to develop new controllers for robotics locomotion. Starting from this reflex-based model, we progressively iterate and transform the stimulation rules to add new features. In particular, gait modulation is obtained with the inclusion of a central pattern generator (CPG), a neural circuit capable of producing rhythmic patterns of neural activity without receiving rhythmic inputs. Using this CPG, the 2D walker controllers are incremented to generate gaits across a range of forward speeds close to the normal human one. By using a similar control method, we also obtain 2D running gaits whose speed can be controlled by a human operator. The walking controllers are later extended to 3D scenarios (i.e. no motion constraint) with the capability to adapt both the forward speed and the heading direction (including steering curvature). In parallel, we also develop a method to automatically learn stimulation networks for a given task and we study how flexible feet affect the gait in terms of robustness and energy efficiency. In sum, we develop neuromuscular controllers generating human-like gaits with steering capabilities. These controllers recruit three main components: (i) virtual muscles generating torque references at the joint level, (ii) neural signals commanding these muscles with reflexes and CPG signals, and (iii) higher level commands controlling speed and heading. Interestingly, these developments target humanoid robots locomotion but can also be used to better understand human locomotion. In particular, the recruitment of a CPG during human locomotion is still a matter open to debate. This question can thus benefit from the experiments performed in this thesis

Learning control of bipedal dynamic walking robots with neural networks

Thesis (Elec.E.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 90-94).Stability and robustness are two important performance requirements for a dynamic walking robot. Learning and adaptation can improve stability and robustness. This thesis explores such an adaptation capability through the use of neural networks. Three neural network models (BP, CMAC and RBF networks) are studied. The RBF network is chosen as best, despite its weakness at covering high dimensional input spaces. To overcome this problem, a self-organizing scheme of data clustering is explored. This system is applied successfully in a biped walking robot system with a supervised learning mode. Generalized Virtual Model Control (GVMC) is also proposed in this thesis, which is inspired by a bio-mechanical model of locomotion, and is an extension of ordinary Virtual Model Control. Instead of adding virtual impedance components to the biped skeletal system in virtual Cartesian space, GVMC uses adaptation to approximately reconstruct the dynamics of the biped. The effectiveness of these approaches is proved both theoretically and experimentally (in simulation).by Jianjuen Hu.Elec.E

An admittance shaping controller for exoskeleton assistance of the lower extremities

We present a method for lower-limb exoskeleton control that defines assistance as a desired dynamic response for the human leg. Wearing the exoskeleton can be seen as replacing the leg's natural admittance with the equivalent admittance of the coupled system. The control goal is to make the leg obey an admittance model defined by target values of natural frequency, peak magnitude and zero-frequency response. No estimation of muscle torques or motion intent is necessary. Instead, the controller scales up the coupled system's sensitivity transfer function by means of a compensator employing positive feedback. This approach increases the leg's mobility and makes the exoskeleton an active device capable of performing net positive work on the limb. Although positive feedback is usually considered destabilizing, here performance and robust stability are successfully achieved through a constrained optimization that maximizes the system's gain margins while ensuring the desired location of its dominant poles

Humanoid Robots

For many years, the human being has been trying, in all ways, to recreate the complex mechanisms that form the human body. Such task is extremely complicated and the results are not totally satisfactory. However, with increasing technological advances based on theoretical and experimental researches, man gets, in a way, to copy or to imitate some systems of the human body. These researches not only intended to create humanoid robots, great part of them constituting autonomous systems, but also, in some way, to offer a higher knowledge of the systems that form the human body, objectifying possible applications in the technology of rehabilitation of human beings, gathering in a whole studies related not only to Robotics, but also to Biomechanics, Biomimmetics, Cybernetics, among other areas. This book presents a series of researches inspired by this ideal, carried through by various researchers worldwide, looking for to analyze and to discuss diverse subjects related to humanoid robots. The presented contributions explore aspects about robotic hands, learning, language, vision and locomotion

Goal-Based Control and Planning in Biped Locomotion Using Computational Intelligence Methods

Este trabajo explora la aplicación de campos neuronales, a tareas de control dinámico en el domino de caminata bípeda. En una primera aproximación, se propone una arquitectura de control que usa campos neuronales en 1D. Esta arquitectura de control es evaluada en el problema de estabilidad para el péndulo invertido de carro y barra, usado como modelo simplificado de caminata bípeda. El controlador por campos neuronales, parametrizado tanto manualmente como usando un algoritmo evolutivo (EA), se compara con una arquitectura de control basada en redes neuronales recurrentes (RNN), también parametrizada por por un EA. El controlador por campos neuronales parametrizado por EA se desempeña mejor que el parametrizado manualmente, y es capaz de recuperarse rápidamente de las condiciones iniciales más problemáticas. Luego, se desarrolla una arquitectura extendida de control y planificación usando campos neurales en 2D, y se aplica al problema caminata bípeda simple (SBW). Para ello se usa un conjunto de valores _óptimos para el parámetro de control, encontrado previamente usando algoritmos evolutivos. El controlador óptimo por campos neuronales obtenido se compara con el controlador lineal propuesto por Wisse et al., y a un controlador _optimo tabular que usa los mismos parámetros óptimos. Si bien los controladores propuestos para el problema SBW implementan una estrategia activa de control, se aproximan de manera más cercana a la caminata dinámica pasiva (PDW) que trabajos previos, disminuyendo la acción de control acumulada. / Abstract. This work explores the application of neural fields to dynamical control tasks in the domain of biped walking. In a first approximation, a controller architecture that uses 1D neural fields is proposed. This controller architecture is evaluated using the stability problem for the cart-and-pole inverted pendulum, as a simplified biped walking model. The neural field controller is compared, parameterized both manually and using an evolutionary algorithm (EA), to a controller architecture based on a recurrent neural neuron (RNN), also parametrized by an EA. The non-evolved neural field controller performs better than the RNN controller. Also, the evolved neural field controller performs better than the non-evolved one and is able to recover fast from worst-case initial conditions. Then, an extended control and planning architecture using 2D neural fields is developed and applied to the SBW problem. A set of optimal parameter values, previously found using an EA, is used as parameters for neural field controller. The optimal neural field controller is compared to the linear controller proposed by Wisse et al., and to a table-lookup controller using the same optimal parameters. While being an active control strategy, the controllers proposed here for the SBW problem approach more closely Passive Dynamic Walking (PDW) than previous works, by diminishing the cumulative control action.Maestrí

Locomotion through morphology, evolution and learning for legged and limbless robots

Mención Internacional en el título de doctorRobot locomotion is concerned with providing autonomous locomotion capabilities to mobile robots. Most current day robots feature some form of locomotion for navigating in their environment. Modalities of robot locomotion includes: (i) aerial locomotion, (ii) terrestrial locomotion, and (iii) aquatic locomotion (on or under water). Three main forms of terrestrial locomotion are, legged locomotion, limbless locomotion and wheel-based locomotion. A Modular Robot (MR), on the other hand, is a robotic system composed of several independent unit modules, where, each module is a robot by itself. The objective in this thesis is to develop legged locomotion in a humanoid robot, as well as, limbless locomotion in modular robotic configurations. Taking inspiration from biology, robot locomotion from the perspective of robot’s morphology, through evolution, and through learning are investigated in this thesis. Locomotion is one of the key distinguishing characteristics of a zoological organism. Almost all animal species, and even some plant species, produce some form of locomotion. In the past few years, robots have been “moving out” of the factory floor and research labs, and are becoming increasingly common in everyday life. So, providing stable and agile locomotion capabilities for robots to navigate a wide range of environments becomes pivotal. Developing locomotion in robots through biologically inspired methods, also facilitates furthering our understanding on how biological processes may function. Connected modules in a configuration, exert force on each other as a result of interaction between each other and their environment. This phenomenon is studied and quantified, and then used as implicit communication between robot modules for producing locomotion coordination in MRs. Through this, a strong link between robot morphology and the gait that emerge in it is established. A variety of locomotion controller, some periodic-function based and some morphology based, are developed for MR locomotion and bipedal gait generation. A hybrid Evolutionary Algorithm (EA) is implemented for evolving gaits, both in simulation as well as in the real-world on a physical modular robotic configuration. Limbless gaits in MRs are also learnt by learning optimal control policies, through Reinforcement Learning (RL).En robótica, la locomoción trata de proporcionar capacidades de locomoción autónoma a robots móviles. La mayoría de los robots actuales tiene alguna forma de locomoción para navegar en su entorno. Los modos de locomoción robótica se pueden repartir entre: (i) locomoción aérea, (ii) locomoción terrestre, y (iii) locomoción acuática (sobre o bajo el agua). Las tres formas básicas de locomoción terrestre son la locomoción mediante piernas, la locomoción sin miembros, y la locomoción basada en ruedas. Un Robot Modular, por otra parte, es un sistema robótico compuesto por varios módulos independientes, donde cada módulo es un robot en sí mismo. El objetivo de esta tesis es el desarrollo de la locomoción mediante piernas para un robot humanoide, así como el de la locomoción sin miembros para varias configuraciones de robots modulares. Inspirándose en la biología, también se investiga en esta tesis el desarrollo de la locomoción del robot según su morfología, gracias a técnicas de evolución y de aprendizaje. La locomoción es una de las características distintivas de un organismo zoológico. Casi todas las especies animales, e incluso algunas especies de plantas, poseen algún tipo de locomoción. En los últimos años, los robots han “migrado” desde las fábricas y los laboratorios de investigación, y se están integrando cada vez más en nuestra vida diaria. Por estas razones, es crucial proporcionar capacidades de locomoción estables y ágiles a los robots para que puedan navegar por todo tipo de entornos. El uso de métodos de inspiración biológica para alcanzar esta meta también nos ayuda a entender mejor cómo pueden funcionar los procesos biológicos equivalentes. En una configuración de módulos conectados, puesto que cada uno interacciona con su entorno, los módulos ejercen fuerza los unos sobre los otros. Este fenómeno se ha estudiado y cuantificado, y luego se ha usado como comunicación implícita entre los módulos para producir la coordinación en la locomoción de este robot. De esta manera, se establece un fuerte vínculo entre la morfología de un robot y el modo de andar que este desarrolla. Se han desarrollado varios controladores de locomoción para robots modulares y robots bípedos, algunos basados en funciones periódicas, otros en la morfología del robot. Un algoritmo evolutivo híbrido se ha implementado para la evolución de locomociones, tanto en simulación como en el mundo real en una configuración física de robot modular. También se pueden generar locomociones sin miembros para robots modulares, determinando las políticas de control óptimo gracias a técnicas de aprendizaje por refuerzo. Se presenta en primer lugar en esta tesis el estado del arte de la robótica modular, enfocándose en la locomoción de robots modulares, los controladores, la locomoción bípeda y la computación morfológica. A continuación se describen cinco configuraciones diferentes de robot modular que se utilizan en esta tesis, seguido de cuatro controladores de locomoción. Estos controladores son el controlador heterogéneo, el controlador basado en funciones periódicas, el controlador homogéneo y el controlador basado en la morfología del robot. Se desarrolla como parte de este trabajo un controlador de locomoción lineal, periódico, basado en features, para la locomoción bípeda de robots humanoides. Los parámetros de control se ajustan primero a mano para reproducir un modelo cart-table, y el controlador se evalúa en un robot humanoide simulado. A continuación, gracias a un algoritmo evolutivo, la optimización de los parámetros de control permite desarrollar una locomoción sin modelo predeterminado. Se desarrolla como parte de esta tesis un enfoque sobre algoritmos de Embodied Evolución, en otras palabras el uso de robots modulares físicos en la fase de evolución. La implementación material, la configuración experimental, y el Algoritmo Evolutivo implementado para Embodied Evolución, se explican detalladamente. El trabajo también incluye una visión general de las técnicas de aprendizaje por refuerzo y de los Procesos de Decisión de Markov. A continuación se presenta un algoritmo popular de aprendizaje por refuerzo, llamado Q-Learning, y su adaptación para aprender locomociones de robots modulares. Se proporcionan una implementación del algoritmo de aprendizaje y la evaluación experimental de la locomoción generada.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Antonio Barrientos Cruz.- Secretario: Luis Santiago Garrido Bullón.- Vocal: Giuseppe Carbon

Applied optimal control for dynamically stable legged locomotion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 79-84).Online learning and controller adaptation will be an essential component for legged robots in the next few years as they begin to leave the laboratory setting and join our world. I present the first example of a learning system which is able to quickly and reliably acquire a robust feedback control policy for 3D dynamic bipedal walking from a blank slate using only trials implemented on the physical robot. The robot begins walking within a minute and learning converges in approximately 20 minutes. The learning works quickly enough that the robot is able to continually adapt to the terrain as it walks. This success can be attributed in part to the mechanics of our robot, which is capable of stable walking down a small ramp even when the computer is turned off. In this thesis, I analyze the dynamics of passive dynamic walking, starting with reduced planar models and working up to experiments on our real robot. I describe, in detail, the actor-critic reinforcement learning algorithm that is implemented on the return map dynamics of the biped. Finally, I address issues of scaling and controller augmentation using tools from optimal control theory and a simulation of a planar one-leg hopping robot. These learning results provide a starting point for the production of robust and energy efficient walking and running robots that work well initially, and continue to improve with experience.by Russell L. Tedrake.Ph.D