Asymmetric swing-leg motions for speed-up of biped walking

This study presents a novel swing-leg control strategy for speed-up of biped robot walking. The trajectory of tip of the swing-leg is asymmetric at the center line of the torso in the sagittal plane for this process. A methodology is proposed that enables robots to achieve the synchronized asymmetric swing-leg motions with the stance-leg angle to accelerate their walking speed. The effectiveness of the proposed method was simulated using numerical methods

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

3LP: a linear 3D-walking model including torso and swing dynamics

In this paper, we present a new model of biped locomotion which is composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to double support, this model has different actuation possibilities in the swing hip and stance ankle which could be widely used to produce different walking gaits. Without the need for numerical time-integration, closed-form solutions help finding periodic gaits which could be simply scaled in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such property is coming from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract high level template space. The proposed model produces human-like torque and ground reaction force profiles and thus, compared to point-mass models, it is more promising for precise control of humanoid robots. Despite being linear and lacking many other features of human walking like CoM excursion, knee flexion and ground clearance, we show that the proposed model can predict one of the main optimality trends in human walking, i.e. nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis still remain for future works.Comment: Journal paper under revie

Stability analysis and control for bipedal locomotion using energy methods

In this thesis, we investigate the stability of limit cycles of passive dynamic walking. The formation process of the limit cycles is approached from the view of energy interaction. We introduce for the first time the notion of the energy portrait analysis originated from the phase portrait. The energy plane is spanned by the total energy of the system and its derivative, and different energy trajectories represent the energy portrait in the plane. One of the advantages of this method is that the stability of the limit cycles can be easily shown in a 2D plane regardless of the dimension of the system. The energy portrait of passive dynamic walking reveals that the limit cycles are formed by the interaction between energy loss and energy gain during each cycle, and they are equal at equilibria in the energy plane. In addition, the energy portrait is exploited to examine the existence of semi-passive limit cycles generated using the energy supply only at the take-off phase. It is shown that the energy interaction at the ground contact compensates for the energy supply, which makes the total energy invariant yielding limit cycles. This result means that new limit cycles can be generated according to the energy supply without changing the ground slope, and level ground walking, whose energy gain at the contact phase is always zero, can be achieved without actuation during the swing phase. We design multiple switching controllers by virtue of this property to increase the basin of attraction. Multiple limit cycles are linearized using the Poincare map method, and the feedback gains are computed taking into account the robustness and actuator saturation. Once a trajectory diverges from a basin of attraction, we switch the current controller to one that includes the trajectory in its basin of attraction. Numerical simulations confirm that a set of limit cycles can be used to increase the basin of attraction further by switching the controllers one after another. To enhance our knowledge of the limit cycles, we performed sophisticated simulations and found all stable and unstable limit cycles from the various ground slopes not only for the symmetric legs but also for the unequal legs that cause gait asymmetries. As a result, we present a novel classification of the passive limit cycles showing six distinct groups that are consecutive and cyclical

Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Energetics of an Inertia Coupled and Simple Rimless Wheel

It has been shown by others that it is theoretically possible for a walking robot to achieve a perfectly efficient gait. The simplest model capable of highly efficient walking motions is the Inertial Coupled Rimless (ICR) Wheel. To examine the dynamics of the ICR wheel, two related studies were done. To determine the lowest energy cost for the ICR wheel we examined one mechanism of energy loss, non-elastic deformation of the elastic elements. Quasi-static experimental tension tests determined that the minimal energy loss for our system was 8:4x10�4 Joules per cycle. A more realistic, high frequency test, showed that the energy loss increased by a factor of 9.16. The ICR wheel walks down a ramp which is assumed to be very at. But no surface in reality can be perfectly at. For a more realistic study, rough terrain is introduced to the ramp. To better understand the dynamics of the motion of the ICR wheel, a simple rimless (SR) wheel is examined on a ramp with roughness. The roughness of the ground is randomly generated but bounded in magnitude. The minimum angle of inclination required for a rimless wheel to walk down both smooth and rough ramps is determined. For the rimless wheel we examined with 5 legs, the minimum slope required for a rough surface is 12.4% higher than that required for a smooth surface, and for 10 legs, the minimum slope for a rough surface is 40.83% higher than the smooth surface. This work has formed the foundation for the design of an energy efficient walking robot and has given insight into its behavior over rough terrain

Locomoção de humanoides robusta e versátil baseada em controlo analítico e física residual

Humanoid robots are made to resemble humans but their locomotion abilities are far from ours in terms of agility and versatility. When humans walk on complex terrains or face external disturbances, they combine a set of strategies, unconsciously and efficiently, to regain stability. This thesis tackles the problem of developing a robust omnidirectional walking framework, which is able to generate versatile and agile locomotion on complex terrains. We designed and developed model-based and model-free walk engines and formulated the controllers using different approaches including classical and optimal control schemes and validated their performance through simulations and experiments. These frameworks have hierarchical structures that are composed of several layers. These layers are composed of several modules that are connected together to fade the complexity and increase the flexibility of the proposed frameworks. Additionally, they can be easily and quickly deployed on different platforms. Besides, we believe that using machine learning on top of analytical approaches is a key to open doors for humanoid robots to step out of laboratories. We proposed a tight coupling between analytical control and deep reinforcement learning. We augmented our analytical controller with reinforcement learning modules to learn how to regulate the walk engine parameters (planners and controllers) adaptively and generate residuals to adjust the robot’s target joint positions (residual physics). The effectiveness of the proposed frameworks was demonstrated and evaluated across a set of challenging simulation scenarios. The robot was able to generalize what it learned in one scenario, by displaying human-like locomotion skills in unforeseen circumstances, even in the presence of noise and external pushes.Os robôs humanoides são feitos para se parecerem com humanos, mas suas habilidades de locomoção estão longe das nossas em termos de agilidade e versatilidade. Quando os humanos caminham em terrenos complexos ou enfrentam distúrbios externos combinam diferentes estratégias, de forma inconsciente e eficiente, para recuperar a estabilidade. Esta tese aborda o problema de desenvolver um sistema robusto para andar de forma omnidirecional, capaz de gerar uma locomoção para robôs humanoides versátil e ágil em terrenos complexos. Projetámos e desenvolvemos motores de locomoção sem modelos e baseados em modelos. Formulámos os controladores usando diferentes abordagens, incluindo esquemas de controlo clássicos e ideais, e validámos o seu desempenho por meio de simulações e experiências reais. Estes frameworks têm estruturas hierárquicas compostas por várias camadas. Essas camadas são compostas por vários módulos que são conectados entre si para diminuir a complexidade e aumentar a flexibilidade dos frameworks propostos. Adicionalmente, o sistema pode ser implementado em diferentes plataformas de forma fácil. Acreditamos que o uso de aprendizagem automática sobre abordagens analíticas é a chave para abrir as portas para robôs humanoides saírem dos laboratórios. Propusemos um forte acoplamento entre controlo analítico e aprendizagem profunda por reforço. Expandimos o nosso controlador analítico com módulos de aprendizagem por reforço para aprender como regular os parâmetros do motor de caminhada (planeadores e controladores) de forma adaptativa e gerar resíduos para ajustar as posições das juntas alvo do robô (física residual). A eficácia das estruturas propostas foi demonstrada e avaliada em um conjunto de cenários de simulação desafiadores. O robô foi capaz de generalizar o que aprendeu em um cenário, exibindo habilidades de locomoção humanas em circunstâncias imprevistas, mesmo na presença de ruído e impulsos externos.Programa Doutoral em Informátic

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