Feedback Control of an Exoskeleton for Paraplegics: Toward Robustly Stable Hands-free Dynamic Walking

This manuscript presents control of a high-DOF fully actuated lower-limb exoskeleton for paraplegic individuals. The key novelty is the ability for the user to walk without the use of crutches or other external means of stabilization. We harness the power of modern optimization techniques and supervised machine learning to develop a smooth feedback control policy that provides robust velocity regulation and perturbation rejection. Preliminary evaluation of the stability and robustness of the proposed approach is demonstrated through the Gazebo simulation environment. In addition, preliminary experimental results with (complete) paraplegic individuals are included for the previous version of the controller.Comment: Submitted to IEEE Control System Magazine. This version addresses reviewers' concerns about the robustness of the algorithm and the motivation for using such exoskeleton

Probabilistic Models of Motor Production

N. Bernstein defined the ability of the central neural system (CNS) to control many degrees of freedom of a physical body with all its redundancy and flexibility as the main problem in motor control. He pointed at that man-made mechanisms usually have one, sometimes two degrees of freedom (DOF); when the number of DOF increases further, it becomes prohibitively hard to control them. The brain, however, seems to perform such control effortlessly. He suggested the way the brain might deal with it: when a motor skill is being acquired, the brain artificially limits the degrees of freedoms, leaving only one or two. As the skill level increases, the brain gradually "frees" the previously fixed DOF, applying control when needed and in directions which have to be corrected, eventually arriving to the control scheme where all the DOF are "free". This approach of reducing the dimensionality of motor control remains relevant even today. One the possibles solutions of the Bernstetin's problem is the hypothesis of motor primitives (MPs) - small building blocks that constitute complex movements and facilitite motor learnirng and task completion. Just like in the visual system, having a homogenious hierarchical architecture built of similar computational elements may be beneficial. Studying such a complicated object as brain, it is important to define at which level of details one works and which questions one aims to answer. David Marr suggested three levels of analysis: 1. computational, analysing which problem the system solves; 2. algorithmic, questioning which representation the system uses and which computations it performs; 3. implementational, finding how such computations are performed by neurons in the brain. In this thesis we stay at the first two levels, seeking for the basic representation of motor output. In this work we present a new model of motor primitives that comprises multiple interacting latent dynamical systems, and give it a full Bayesian treatment. Modelling within the Bayesian framework, in my opinion, must become the new standard in hypothesis testing in neuroscience. Only the Bayesian framework gives us guarantees when dealing with the inevitable plethora of hidden variables and uncertainty. The special type of coupling of dynamical systems we proposed, based on the Product of Experts, has many natural interpretations in the Bayesian framework. If the dynamical systems run in parallel, it yields Bayesian cue integration. If they are organized hierarchically due to serial coupling, we get hierarchical priors over the dynamics. If one of the dynamical systems represents sensory state, we arrive to the sensory-motor primitives. The compact representation that follows from the variational treatment allows learning of a motor primitives library. Learned separately, combined motion can be represented as a matrix of coupling values. We performed a set of experiments to compare different models of motor primitives. In a series of 2-alternative forced choice (2AFC) experiments participants were discriminating natural and synthesised movements, thus running a graphics Turing test. When available, Bayesian model score predicted the naturalness of the perceived movements. For simple movements, like walking, Bayesian model comparison and psychophysics tests indicate that one dynamical system is sufficient to describe the data. For more complex movements, like walking and waving, motion can be better represented as a set of coupled dynamical systems. We also experimentally confirmed that Bayesian treatment of model learning on motion data is superior to the simple point estimate of latent parameters. Experiments with non-periodic movements show that they do not benefit from more complex latent dynamics, despite having high kinematic complexity. By having a fully Bayesian models, we could quantitatively disentangle the influence of motion dynamics and pose on the perception of naturalness. We confirmed that rich and correct dynamics is more important than the kinematic representation. There are numerous further directions of research. In the models we devised, for multiple parts, even though the latent dynamics was factorized on a set of interacting systems, the kinematic parts were completely independent. Thus, interaction between the kinematic parts could be mediated only by the latent dynamics interactions. A more flexible model would allow a dense interaction on the kinematic level too. Another important problem relates to the representation of time in Markov chains. Discrete time Markov chains form an approximation to continuous dynamics. As time step is assumed to be fixed, we face with the problem of time step selection. Time is also not a explicit parameter in Markov chains. This also prohibits explicit optimization of time as parameter and reasoning (inference) about it. For example, in optimal control boundary conditions are usually set at exact time points, which is not an ecological scenario, where time is usually a parameter of optimization. Making time an explicit parameter in dynamics may alleviate this

Design and Evaluation of Pediatric Gait Rehabilitation Robots

Gait therapy methodologies were studied and analyzed for their potential for pediatric patients. Using data from heel, metatarsal, and toe trajectories, a nominal gait trajectory was determined using Fourier transforms for each foot point. These average trajectories were used as a basis of evaluating each gait therapy mechanism. An existing gait therapy device (called ICARE) previously designed by researchers, including engineers at the University of Nebraska-Lincoln, was redesigned to accommodate pediatric patients. Unlike many existing designs, the pediatric ICARE did not over- or under-constrain the patient’s leg, allowing for repeated, comfortable, easily-adjusted gait motions. This design was assessed under clinical testing and deemed to be acceptable. A gait rehabilitation device was designed to interface with both pediatric and adult patients and more closely replicate the gait-like metatarsal trajectory compared to an elliptical machine. To accomplish this task, the nominal gait path was adjusted to accommodate for rotation about the toe, which generated a new trajectory that was tangent to itself at the midpoint of the stride. Using knowledge of the bio-mechanics of the foot, the gait path was analyzed for its applicability to the general population. Several trajectory-replication methods were evaluated, and the crank-slider mechanism was chosen for its superior performance and ability to mimic the gait path adequately. Adjustments were made to the gait path to further optimize its realization through the crank-slider mechanism. Two prototypes were constructed according to the slider-crank mechanism to replicate the gait path identified. The first prototype, while more accurately tracing the gait path, showed difficulty in power transmission and excessive cam forces. This prototype was ultimately rejected. The second prototype was significantly more robust. However, it lacked several key aspects of the original design that were important to matching the design goals. Ultimately, the second prototype was recommended for further work in gait-replication research. Advisor: Carl A. Nelso

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient

Optimization-based Framework for Stability and Robustness of Bipedal Walking Robots

As robots become more sophisticated and move out of the laboratory, they need to be able to reliably traverse difficult and rugged environments. Legged robots -- as inspired by nature -- are most suitable for navigating through terrain too rough or irregular for wheels. However, control design and stability analysis is inherently difficult since their dynamics are highly nonlinear, hybrid (mixing continuous dynamics with discrete impact events), and the target motion is a limit cycle (or more complex trajectory), rather than an equilibrium. For such walkers, stability and robustness analysis of even stable walking on flat ground is difficult. This thesis proposes new theoretical methods to analyse the stability and robustness of periodic walking motions. The methods are implemented as a series of pointwise linear matrix inequalities (LMI), enabling the use of convex optimization tools such as sum-of-squares programming in verifying the stability and robustness of the walker. To ensure computational tractability of the resulting optimization program, construction of a novel reduced coordinate system is proposed and implemented. To validate theoretic and algorithmic developments in this thesis, a custom-built “Compass gait” walking robot is used to demonstrate the efficacy of the proposed methods. The hardware setup, system identification and walking controller are discussed. Using the proposed analysis tools, the stability property of the hardware walker was successfully verified, which corroborated with the computational results

Hierarchical and Safe Motion Control for Cooperative Locomotion of Robotic Guide Dogs and Humans: A Hybrid Systems Approach

This paper presents a hierarchical control strategy based on hybrid systems theory, nonlinear control, and safety-critical systems to enable cooperative locomotion of robotic guide dogs and visually impaired people. We address high-dimensional and complex hybrid dynamical models that represent collaborative locomotion. At the high level of the control scheme, local and nonlinear baseline controllers, based on the virtual constraints approach, are designed to induce exponentially stable dynamic gaits. The baseline controller for the leash is assumed to be a nonlinear controller that keeps the human in a safe distance from the dog while following it. At the lower level, a real-time quadratic programming (QP) is solved for modifying the baseline controllers of the robot as well as the leash to avoid obstacles. In particular, the QP framework is set up based on control barrier functions (CBFs) to compute optimal control inputs that guarantee safety while being close to the baseline controllers. The stability of the complex periodic gaits is investigated through the Poincare return map. To demonstrate the power of the analytical foundation, the control algorithms are transferred into an extensive numerical simulation of a complex model that represents cooperative locomotion of a quadrupedal robot, referred to as Vision 60, and a human model. The complex model has 16 continuous-time domains with 60 state variables and 20 control inputs

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

Analytical Workspace, Kinematics, and Foot Force Based Stability of Hexapod Walking Robots

Many environments are inaccessible or hazardous for humans. Remaining debris after earthquake and fire, ship hulls, bridge installations, and oil rigs are some examples. For these environments, major effort is being placed into replacing humans with robots for manipulation purposes such as search and rescue, inspection, repair, and maintenance. Mobility, manipulability, and stability are the basic needs for a robot to traverse, maneuver, and manipulate in such irregular and highly obstructed terrain. Hexapod walking robots are as a salient solution because of their extra degrees of mobility, compared to mobile wheeled robots. However, it is essential for any multi-legged walking robot to maintain its stability over the terrain or under external stimuli. For manipulation purposes, the robot must also have a sufficient workspace to satisfy the required manipulability. Therefore, analysis of both workspace and stability becomes very important. An accurate and concise inverse kinematic solution for multi-legged robots is developed and validated. The closed-form solution of lateral and spatial reachable workspace of axially symmetric hexapod walking robots are derived and validated through simulation which aid in the design and optimization of the robot parameters and workspace. To control the stability of the robot, a novel stability margin based on the normal contact forces of the robot is developed and then modified to account for the geometrical and physical attributes of the robot. The margin and its modified version are validated by comparison with a widely known stability criterion through simulated and physical experiments. A control scheme is developed to integrate the workspace and stability of multi-legged walking robots resulting in a bio-inspired reactive control strategy which is validated experimentally