Biomechanical models and stability analysis of bipedal running = Biomechanische Modelle und Stabilitätsanalyse des zweibeinigen Rennens

Humans and birds both walk and run bipedally on compliant legs. However, differences in leg architecture may result in species-specific leg control strategies as indicated by the observed gait patterns. In this work, control strategies for stable running are derived based on a conceptual model and compared with experimental data on running humans and pheasants (Phasianus colchicus). From a model perspective, running with compliant legs can be represented by the planar spring mass model. However, to compare experimental data to simulated spring mass running, an effective leg stiffness has to be defined. In chapter 2, different methods of estimating a leg stiffness during running are compared to running patterns predicted by the spring mass model, and a new method only relying on temporal parameters is proposed and used in the further course of this work. It has been shown that spring mass running is self-stabilizing for sufficiently high running speeds. However, to provide stability over a broader range of running, control strategies can be applied and swing leg control is one elegant approach to stabilize the running pattern, while maintaining the system energy conservative. Here, linear adaptations of the swing leg parameters, leg angle, leg length and leg stiffness, are assumed. Experimentally observed kinematic control parameters (leg rotation and leg length change) of running humans (chapter 3 and 4) and pheasants (chapter 4) are compared, and interpreted within the context of this model, with specific focus on stability and robustness characteristics

A Dynamics and Stability Framework for Avian Jumping Take-off

Jumping take-off in birds is an explosive behaviour with the goal of providing a rapid transition from ground to airborne locomotion. An effective jump is predicated on the need to maintain dynamic stability through the acceleration phase. The present study concerns understanding how birds retain control of body attitude and trajectory during take-off. Cursory observation suggests that stability is achieved with relatively little cost. However, analysis of the problem shows that the stability margins during jumping are actually very small and that stability considerations play a significant role in selection of appropriate jumping kinematics. We use theoretical models to understand stability in prehensile take-off (from a perch) and also in non-prehensile take-off (from the ground). The primary instability is tipping, defined as rotation of the centre of gravity about the ground contact point. Tipping occurs when the centre of pressure falls outside the functional foot. A contribution of the paper is the development of graphical tipping stability margins for both centre of gravity location and acceleration angle. We show that the nose-up angular acceleration extends stability bounds forward and is hence helpful in achieving shallow take-offs. The stability margins are used to interrogate simulated take-offs of real birds using published experimental kinematic data from a guinea fowl (ground take-off) and a diamond dove (perch take-off). For the guinea fowl the initial part of the jump is stable, however simulations exhibit a stuttering instability not observed experimentally that is probably due to absence of compliance in the idealised joints. The diamond dove model confirms that the foot provides an active torque reaction during take-off, extending the range of stable jump angles by around 45{\deg}.Comment: 21 pages, 11 figures; supplementary material: https://figshare.com/s/86b12868d64828db0d5d; DOI: 10.6084/m9.figshare.721056

Multi-segmented Adaptive Feet for Versatile Legged Locomotion in Natural Terrain

Most legged robots are built with leg structures from serially mounted links and actuators and are controlled through complex controllers and sensor feedback. In comparison, animals developed multi-segment legs, mechanical coupling between joints, and multi-segmented feet. They run agile over all terrains, arguably with simpler locomotion control. Here we focus on developing foot mechanisms that resist slipping and sinking also in natural terrain. We present first results of multi-segment feet mounted to a bird-inspired robot leg with multi-joint mechanical tendon coupling. Our one- and two-segment, mechanically adaptive feet show increased viable horizontal forces on multiple soft and hard substrates before starting to slip. We also observe that segmented feet reduce sinking on soft substrates compared to ball-feet and cylinder-feet. We report how multi-segmented feet provide a large range of viable centre of pressure points well suited for bipedal robots, but also for quadruped robots on slopes and natural terrain. Our results also offer a functional understanding of segmented feet in animals like ratite birds

Optimal elastic coupling in form of one mechanical spring to improve energy efficiency of walking bipedal robots

This paper presents a method to optimize the energy efficiency of walking bipedal robots by more than 80% in a speed range from 0.3 to 2.3 m/s using elastic couplings – mechanical springs with movement speed independent parameters. The considered planar robot consists of a trunk, two two-segmented legs, two actuators in the hip joints, two actuators in the knee joints and an elastic coupling between the shanks. It is modeled as underactuated system to make use of its natural dynamics and feedback controlled via input-output linearization. A numerical optimization of the joint angle trajectories as well as the elastic couplings is performed to minimize the average energy expenditure over the whole speed range. The elastic couplings increase the swing leg motion’s natural frequency thus making smaller steps more efficient which reduce the impact loss at the touchdown of the swing leg. The process of energy turnover is investigated in detail for the robot with and without elastic coupling between the shanks. Furthermore, the influences of the elastic couplings’ topology and of joint friction are analyzed. It is shown that the optimization of the robot’s motion and elastic coupling towards energy efficiency leads to a slightly slower convergence rate of the controller, yet no loss of stability but a lower sensitivity with respect to disturbances. The optimal elastic coupling discovered via numerical optimization is a linear torsion spring with transmissions between the shanks. A design proposal for this elastic coupling – which does not affect the robot’s trunk and parallel shank motion and can be used to enhance an existing robot – is given for planar as well as spatial robots

Simulating a Flexible Robotic System based on Musculoskeletal Modeling

Humanoid robotics offers a unique research tool for understanding the human brain and body. The synthesis of human motion is a complex procedure that involves accurate reconstruction of movement sequences, modeling of musculoskeletal kinematics, dynamics and actuation, and characterization of reliable performance criteria. Many of these processes have much in common with the problems found in robotics research, with the recent advent of complex humanoid systems. This work presents the design and development of a new-generation bipedal robot. Its modeling and simulation has been realized by using an open-source software to create and analyze dynamic simulation of movement: OpenSim. Starting from a study by Fuben He, our model aims to be used as an innovative approach to the study of a such type of robot in which there are series elastic actuators represented by active and passive spring components in series with motors. It has provided of monoarticular and biarticular joint in a very similar manner to human musculoskeletal model. This thesis is only the starting point of a wide range of other possible future works: from the control structure completion and whole-body control application, to imitation learning and reinforcement learning for human locomotion, from motion test on at ground to motion test on rough ground, and obviously the transition from simulation to practice with a real elastic bipedal robot biologically-inspired that can move like a human bein

Advancing Musculoskeletal Robot Design for Dynamic and Energy-Efficient Bipedal Locomotion

Achieving bipedal robot locomotion performance that approaches human performance is a challenging research topic in the field of humanoid robotics, requiring interdisciplinary expertise from various disciplines, including neuroscience and biomechanics. Despite the remarkable results demonstrated by current humanoid robots---they can walk, stand, turn, climb stairs, carry a load, push a cart---the versatility, stability, and energy efficiency of humans have not yet been achieved. However, with robots entering our lives, whether in the workplace, in clinics, or in normal household environments, such improvements are increasingly important. The current state of research in bipedal robot locomotion reveals that several groups have continuously demonstrated enhanced locomotion performance of the developed robots. But each of these groups has taken a unilateral approach and placed the focus on only one aspect, in order to achieve enhanced movement abilities;---for instance, the motion control and postural stability or the mechanical design. The neural and mechanical systems in human and animal locomotion, however, are strongly coupled and should therefore not be treated separately. Human-inspired musculoskeletal design of bipedal robots offers great potential for enhanced dynamic and energy-efficient locomotion but also imposes major challenges for motion planning and control. In this thesis, we first present a detailed review of the problems related to achieving enhanced dynamic and energy-efficient bipedal locomotion, from various important perspectives, and examine the essential properties of the human locomotory apparatus. Subsequently, existing insights and approaches from biomechanics, to understand the neuromechanical motion apparatus, and from robotics, to develop more human-like robots that can move in our environment, are discussed in detail. These thorough investigations of the interrelated essential design decisions are used to develop a novel design for a musculoskeletal bipedal robot, BioBiped1, such that, in the long term, it is capable of realizing dynamic hopping, running, and walking motions. The BioBiped1 robot features a highly compliant tendon-driven actuation system that mimics key functionalities of the human lower limb system. In experiments, BioBiped1's locomotor function for the envisioned gaits is validated globally. It is shown that the robot is able to rebound passively, store and release energy, and actively push off from the ground. The proof of concept of BioBiped1's locomotor function, however, marks only the starting point for our investigations, since this novel design concept opens up a number of questions regarding the required design complexity for the envisioned motions and the appropriate motion generation and control concept. For this purpose, a simulator specifically designed for the requirements of musculoskeletally actuated robotic systems, including sufficiently realistic ground reaction forces, is developed. It relies on object-oriented design and is based on a numerical solver, without model switching, to enable the analysis of impact peak forces and the simulation of flight phases. The developed library also contains the models of the actuated and passive mono- and biarticular elastic tendons and a penalty-based compliant contact model with nonlinear damping, to incorporate the collision, friction, and stiction forces occurring during ground contact. Using these components, the full multibody system (MBS) dynamics model is developed. To ensure a sufficiently similar behavior of the simulated and the real musculoskeletal robot, various measurements and parameter identifications for sub-models are performed. Finally, it is shown that the simulation model behaves similarly to the real robot platform. The intelligent combination of actuated and passive mono- and biarticular tendons, imitating important human muscle groups, offers tremendous potential for improved locomotion performance but also requires a sophisticated concept for motion control of the robot. Therefore, a further contribution of this thesis is the development of a centralized, nonlinear model-based method for motion generation and control that utilizes the derived detailed dynamics models of the implemented actuators. The concept is used to realize both computer-generated hopping and human jogging motions. Additionally, the problem of appropriate motor-gear unit selection prior to the robot's construction is tackled, using this method. The thesis concludes with a number of simulation studies in which several leg actuation designs are examined for their optimality with regard to systematically selected performance criteria. Furthermore, earlier paradoxical biomechanical findings about biarticular muscles in running are presented and, for the first time, investigated by detailed simulation of the motion dynamics. Exploring the Lombard paradox, a novel reduced and energy-efficient locomotion model without knee extensor has been simulated successfully. The models and methods developed within this thesis, as well as the insights gained, are already being employed to develop future prototypes. In particular, the optimal dimensioning and setting of the actuators, including all mono- and biarticular muscle-tendon units, are based on the derived design guidelines and are extensively validated by means of the simulation models and the motion control method. These developments are expected to significantly enhance progress in the field of bipedal robot design and, in the long term, to drive improvements in rehabilitation for humans through an understanding of the neuromechanics underlying human walking and the application of this knowledge to the design of prosthetics

Nomenclature

ABSTRACT — Bouncing, balancing and swinging the leg forward can be considered as three basic control tasks for bipedal locomotion. Defining the trunk by an unstable inverted pendulum, balancing as being translated to trunk stabilization is the main focus of this paper. The control strategy is to generate a hip torque to have upright trunk to achieve robust hopping and running. It relies on the Virtual Pendulum (VP) concept which is recently proposed for trunk stabilization, based on human/animal locomotion analysis. Based on this concept, a control approach, named Virtual Pendulum Posture control (VPPC) is presented, in which the trunk is stabilized by redirecting the ground reaction force to a virtual support point. The required torques patterns generated by the controller, could partially be exerted by elastic structures like hip springs. Hybrid Zero Dynamics (HZD) control approach is also applied as an exact method of keeping the trunk upright. Stability of the motion which is investigated by Poincare ´ map analysis could be achieved by hip springs, VPPC and HZD. The results show that hip springs, revealing muscle properties, could facilitate trunk stabilization. Compliance in hip produces acceptable performance and robustness compared with VPPC and HZD, while it is a passive structure

Influence of “J”-Curve Spring Stiffness on Running Speeds of Segmented Legs during High-Speed Locomotion

Both the linear leg spring model and the two-segment leg model with constant spring stiffness have been broadly used as template models to investigate bouncing gaits for legged robots with compliant legs. In addition to these two models, the other stiffness leg spring models developed using inspiration from biological characteristic have the potential to improve high-speed running capacity of spring-legged robots. In this paper, we investigate the effects of “J”-curve spring stiffness inspired by biological materials on running speeds of segmented legs during high-speed locomotion. Mathematical formulation of the relationship between the virtual leg force and the virtual leg compression is established. When the SLIP model and the two-segment leg model with constant spring stiffness and with “J”-curve spring stiffness have the same dimensionless reference stiffness, the two-segment leg model with “J”-curve spring stiffness reveals that (1) both the largest tolerated range of running speeds and the tolerated maximum running speed are found and (2) at fast running speed from 25 to 40/92 m s−1 both the tolerated range of landing angle and the stability region are the largest. It is suggested that the two-segment leg model with “J”-curve spring stiffness is more advantageous for high-speed running compared with the SLIP model and with constant spring stiffness

3D Modelling and design of a bioloid compliant quadruped leg

Dissertação de mestrado integrado em Engenharia BiomédicaIn the growing fields of rehabilitation robotics, prosthetics, and walking robots, the modeling of a real robot is a complex and passionate challenge. On the crossing point of mechanics, physics and computer-science, the development of a complete model involves multiple tasks ranging from the 3D modeling of the different body parts, the measure of the different physic properties, the understanding of the requirements for an accurate simulation, to the development of a robotic controller. In order to minimize large forces due to shocks, to safely interact with the user or the environment, and knowing the ability of passive elastic elements to store and release energy, compliant mechanisms are increasingly being applied in robots applications. This work aims to the elaboration of an accurate efficient three-dimensional model of the legs of the quadruped Bioloid robot and the development of a world showing the effect on WebotsTM simulation software developed by Cyberbotics Ltd. The goal was to design a segmented pantographic leg with compliant joints, in order to actively retract the collision and the impact of the quadruped legs with the ground during locomotion. Geometrical and mechanical limits have to be evaluated and considered for the modeling setup. Finally a controller based on the use of Central Pattern Generators was improved in order to adapt to the novel model and simple tests were performed in the WebotsTM, rendering a 3D model simulation for the different values of spring-damping coefficients at the legs knee joint. Through the a MATLAB® algorithm, the characterization of the joint angles during simulation was possible to be assessed.A modelação de um robot real é um desafio complexo e fascinante na crescente área da Robótica, que engloba desde robots de reabilitação, próteses a uma diversidade de outros dispositivos locomotores. No cruzamento da mecânica com a física e as ciências computacionais, o desenvolvimento de um modelo completo envolve várias tarefas que vão desde a modelação 3D das diferentes partes do corpo, a medição das propriedades físicos inerentes, a compreensão dos requisitos para uma simulação precisa bem como a aplicação de um controlador robótico. A fim de minimizar grandes forças devido a choques, interagir com segurança com o utilizador ou o ambiente e conhecendo a capacidade de armazenagem de energia por parte de elementos elásticos passivos, um sistema de amortecimento-mola demonstra ser uma aplicação de crescente interesse na Robótica. Este trabalho visa a elaboração de um modelo tridimensional eficiente e preciso das pernas do robô quadrúpede Bioloid a ser reproduzido num mundo no software WebotsTM desenvolvido pela Cyberbotics Ltd. O objectivo foi desenhar uma perna pantográfica segmentada tridimensional a ser aplicada em paralelo com um sistema de amortecimento-mola de forma a retrair activamente a colisão e o impacto das patas do quadrúpede com o solo durante a locomoção. Deste modo para uma configuração do modelo bem sucedida são tidos em conta limites geométricos e mecânicos. Por ultimo, o controlador com base no uso de ‘Central Pattern Generators’ foi melhorado a fim de se adaptar ao novo modelo e por conseguinte foram realizados testes simples usando o simulador WebotsTM. Nesta parte experimental é realizada a simulação do modelo permitindo avaliar o comportamento do modelo 3D para diferentes valores de coeficientes de mola e de amortecimento aplicados a nível do joelho da perna. Através de um algoritmo MATLAB® é possível caracterizar e analisar o comportamento doa ângulos das juntas durante a simulação