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

Design Optimization, Analysis, and Control of Walking Robots

Passive dynamic walking refers to the dynamical behavior of mechanical devices that are able to naturally walk down a shallow slope in a stable manner, without using actuation or sensing of any kind. Such devices can attain motions that are remarkably human-like by purely exploiting their natural dynamics. This suggests that passive dynamic walking machines can be used to model and study human locomotion; however, there are two major limitations: they can be difficult to design, and they cannot walk on level ground or uphill without some kind of actuation. This thesis presents a mechanism design optimization framework that allows the designer to find the best design parameters based on the chosen performance metric(s). The optimization is formulated as a convex problem, where its solutions are globally optimal and can be obtained efficiently. To enable locomotion on level ground and uphill, this thesis studies a robot based on a passive walker: the rimless wheel with an actuated torso. We design and validate two control policies for the robot through the use of scalable methodology based on tools from mathematical analysis, optimization theory, linear algebra, differential equations, and control theory

Opinions and Outlooks on Morphological Computation

Morphological Computation is based on the observation that biological systems seem to carry out relevant computations with their morphology (physical body) in order to successfully interact with their environments. This can be observed in a whole range of systems and at many different scales. It has been studied in animals – e.g., while running, the functionality of coping with impact and slight unevenness in the ground is "delivered" by the shape of the legs and the damped elasticity of the muscle-tendon system – and plants, but it has also been observed at the cellular and even at the molecular level – as seen, for example, in spontaneous self-assembly. The concept of morphological computation has served as an inspirational resource to build bio-inspired robots, design novel approaches for support systems in health care, implement computation with natural systems, but also in art and architecture. As a consequence, the field is highly interdisciplinary, which is also nicely reflected in the wide range of authors that are featured in this e-book. We have contributions from robotics, mechanical engineering, health, architecture, biology, philosophy, and others

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

Mechanics and energetics of running at steady and non-steady speed (sprint and shuttles): the effects of muscle-tendon behaviour

When humans move, they could do it in steady or non-steady conditions. In the former case the speed of locomotion is constant (or with minimal oscillations) and occurs in a definite direction (e.g. walking or running along a linear path), whereas in the latter case the body accelerates, decelerates or moves in different directions. In both cases, the minimum work required to sustain locomotion is given by the product of the resistance offered by the environment and the distance covered. Finally, the efficiency of the locomotor apparatus may be expressed as the ratio between the work necessary to maintain motion and the chemical energy transformed by the muscles. However, whereas the energetics and mechanics of running at constant speed are well known, only few studies have investigated so far non-steady running conditions (e.g. accelerated or decelerated running as well as running with changes of direction). The role of muscles and tendons in determining the mechanical and physiological responses during human locomotion is another topic that needs to be further investigated, both in steady and unsteady conditions. As an example, when humans run at constant speed muscles and tendons stretch and recoil; into this succession of stretch-shortening cycles, tendons could play an important role as energy savers allowing this form of locomotion to be particularly efficient. Locomotion (apparent) efficiency during constant speed running can be, indeed, as high as 0.70 at high running speeds whereas in un-steady conditions (e.g. shuttle runs) the efficiency is much lower, approaching the values of muscle efficiency (0.25) when fast accelerations and decelerations are required; locomotion (apparent) efficiency is thus enhanced when tendon elastic recoil is maximized. Investigating the role of muscle and tendon behaviour during steady and non-steady state running could, therefore, provide important information about the underpinning mechanisms that determine the mechanical and energetic demands of human locomotion. For these reasons, this thesis focuses on two main topics (running at non-steady speeds and running at constant speed), each with its own specific aims

A Biologically Inspired Jumping and Rolling Robot

Mobile robots for rough terrain are of interest to researchers as their range of possible uses is large, including exploration activities for inhospitable areas on Earth and on other planets and bodies in the solar system, searching in disaster sites for survivors, and performing surveillance for military applications. Nature generally achieves land movement by walking using legs, but additional modes such as climbing, jumping and rolling are all produced from legs as well. Robotics tends not to use this integrated approach and adds additional mechanisms to achieve additional movements. The spherical device described within this thesis, called Jollbot, integrated a rolling motion for faster movement over smoother terrain, with a jumping movement for rougher environments. Jollbot was developed over three prototypes. The first achieved pause-and-leap style jumps by slowly storing strain energy within the metal elements of a spherical structure using an internal mechanism to deform the sphere. A jump was produced when this stored energy was rapidly released. The second prototype achieved greater jump heights using a similar structure, and added direction control to each jump by moving its centre of gravity around the polar axis of the sphere. The final prototype successfully combined rolling (at a speed of 0.7 m/s, up 4° slopes, and over 44 mm obstacles) and jumping (0.5 m cleared height), both with direction control, using a 0.6 m spherical spring steel structure. Rolling was achieved by moving the centre of gravity outside of the sphere’s contact area with the ground. Jumping was achieved by deflecting the sphere in a similar method to the first and second prototypes, but through a larger percentage deflection. An evaluation of existing rough terrain robots is made possible through the development of a five-step scoring system that produces a single numerical performance score. The system is used to evaluate the performance of Jollbot.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Human locomotion: centre of mass and symmetry

In ambito di ricerca (clinica e sportiva), la necessit\ue0 di sviluppare un approccio \u2018multilaterale\u2019 (qualitativo e quantitativo) che caratterizzi matematicamente la traiettoria tri-dimensionale di una variabile fisica assolutamente importante ma spesso dimenticata, quale il centro di massa corporeo (CMC) (ovvero, il punto immaginario assimilabile al corpo umano in cui si suppone che tutte le masse corporee stiano concentrate), diviene oggi sempre pi\uf9 impellente e quanto mai urgente. Pertanto l\u2019obiettivo di questo dottorato, perseguito tramite un differente utilizzo delle classiche metodologie biomeccaniche, \ue8 rappresentare le grandezze cinematiche che descrivono il movimento dei segmenti corporei e del suddetto CMC nel tempo e nello spazio. Per conseguire questo traguardo si sono pensati e realizzati due diversi progetti. Con il primo progetto si sono previsti: a) lo sviluppo di un metodo matematico quantitativo (Serie di Fourier) per descrivere e rappresentare graficamente la traiettoria tri-dimensionale del CMC durante la locomozione su treadmill (la cosiddetta Impronta Digitale Locomotoria, specifica per soggetto/popolazione); b) la caratterizzazione della simmetria nella traiettoria del CMC (il cosiddetto Indice di Simmetria); infine, c) la costituzione di un database di valori normali (coefficienti di equazioni) in un insieme piuttosto esteso di condizioni, al variare di sesso (maschi versus femmine), et\ue0 (dai 6 ai 65 anni), tipologia di locomozione (marcia versus corsa), velocit\ue0 e pendenza (piano, salita e discesa). Questo database iniziale rappresenta il parametro principale di riferimento per la locomozione sana. Attraverso questo studio \ue8 stato ampiamente dimostrato che la locomozione umana risulta genericamente asimmetrica. Nello specifico: 1) tra maschi e femmine non si sono riscontrate differenze significative; 2) indipendentemente da et\ue0 e pendenza, le velocit\ue0 pi\uf9 basse, meno naturali e comuni, sono caratterizzate da pattern di Impronte Digitali Locomotorie pi\uf9 variabili. Viceversa, un aumento di velocit\ue0 \ue8 accoppiato con un progressivo e continuo innalzamento del CMC; 3) l\u2019asimmetria destra e sinistra del passo \ue8 molto probabilmente correlata sia con l\u2019anatomia (lunghezza della gamba) che con la predominanza dell\u2019arto; in linea con l\u2019ipotesi iniziale, 4) mediamente, la corsa \ue8 pi\uf9 asimmetrica della marcia; infine, 5) i bambini e gli anziani presentano maggiori asimmetrie (marcia e corsa): questo \ue8 dovuto alla progressiva maturazione del ciclo del cammino (nei bambini) ed alle caratteristiche muscolari e scheletriche dell\u2019apparato locomotore (negli anziani). Pertanto, attraverso una caratterizzazione matematica della traiettoria tri-dimensionale del CMC, si \ue8 potuto: a) quantificare il suo spostamento nel tempo e nello spazio; b) individuare l\u2019Impronta Digitale Locomotoria specifica di sesso, et\ue0, tipologia di locomozione, velocit\ue0 e pendenza. Questo importante traguardo permetter\ue0, in un immediato futuro, la comparazione con la situazione di normalit\ue0 di condizioni di locomozione compromessa o impedita (ad esempio, bambini con paralisi cerebrale infantile, obesi e amputati). Infine, la stima della principali variabili biomeccaniche \ue8 risultata fondamentale sia nel descrivere la meccanica di marcia e corsa che nel caratterizzarne la corrispondente impronta locomotoria. Le nostre misure di tali variabili (semplici e complesse), ottenute con metodo discreto (ciclo per ciclo), con l\u2019impiego di una funzione matematica continua (Serie di Fourier) e con l\u2019applicazione di un\u2019equazione predittiva (misura indiretta), soddisfano completamente ed addirittura ampliano la letteratura gi\ue0 esistente. Nel secondo progetto, partendo da uno studio sulla performance dei cavalli, si \ue8 cercato di verificare se esiste una correlazione tra simmetrie corporee (statiche e dinamiche) ed economia nella corsa anche in corridori umani variamente allenati (classificati in tre gruppi sulla base del loro miglior tempo nella maratona). Inoltre: a) si sono sviluppati metodi di analisi bi- e tri-dimensionale delle Risonanze Magnetiche per Immagini (regione pelvica ed arti inferiori), impiegate come riferimento per le simmetrie statiche; b) attraverso sia l\u2019Impronta Digitale Locomotoria che l\u2019Indice di Simmetria si sono caratterizzate le simmetrie dinamiche; infine c) l\u2019economia della corsa \ue8 stata espressa attraverso il suo reciproco, ovvero il costo metabolico. L\u2019analisi sia bi- che tri-dimensionale delle immagini ha evidenziato differenze davvero esigue in base al livello di allenamento. Positivamente ed indipendentemente dai corridori, si \ue8 dimostrato che ad una maggiore simmetria nella regione del ginocchio corrisponde una maggiore simmetria nella regione della caviglia. Inoltre l\u2019analisi delle simmetrie dinamiche ha permesso di osservare che: 1) il CMC si solleva leggermente in funzione della velocit\ue0; 2) le asimmetrie destre e sinistre del passo sono principalmente marcate lungo la direzione di movimento e, contemporaneamente, ridotte lungo la direzione verticale. Esse sono strettamente dipendenti dall\u2019anatomia e dall\u2019arto dominante; 3) diversamente da quanto ci si aspettava, sono state comunque evidenziate solamente poche differenze tra i corridori. Negativamente, l\u2019economia della corsa non mostra differenze significative tra i gruppi testati. Perci\uf2, diversamente dall\u2019ipotesi iniziale, non \ue8 stata evidenziata l\u2019esistenza di alcuna relazione tra le simmetrie corporee e l\u2019economia della corsa, quanto piuttosto solo la presenza di una discreta variabilit\ue0 in simmetria statica e dinamica. Infine, l\u2019analisi di bioenergetica (treadmill versus pista) e biomeccanica (variabili semplici/complesse e variabilit\ue0 spazio/temporale del CMC) della corsa ha evidenziato la presenza solamente di poche differenze dovute al livello di allenamento dei soggetti studiati.In both research laboratory and sport/clinical settings, it becomes very important to develop a \u2018multilateral approach\u2019 (qualitative and quantitative) to fully describe the individual behaviour of the centre of mass of the human body (BCOM) (i.e. the imaginary specific point at which the body behaves as if its masses were concentrated) over time and space. Consequently, the aim of this doctorate is to describe kinematic variables of the BCOM in varying locomotion conditions. This purpose, focusing on the BCOM as the investigation object fulfilling such a need, has been achieved through a different use of classic biomechanical procedures. In effect, two different studies were carried out. The first project sought: a) to develop a mathematical method (Fourier Series) which could describe and graphically represent each individual (subject or population) gait signature (i.e. Digital Locomotory Signature, a global index of the BCOM dynamics) during locomotion on a treadmill; b) to assess the symmetry (i.e. Symmetry Index) in each movement direction, along the BCOM trajectory, between the two stride phases; finally, c) to build up an initial comprehensive database of \u2018healthy values\u2019 (equation coefficients) in a set of different conditions considering gender (males versus females), age (from 6 to 65 years), gait (walking versus running), speed and gradient (level, uphill and downhill). Although only slight gender differences were found, human \u2018healthy\u2019 gait is rather asymmetrical. To be precise: 1) the lowest speeds have the most peculiar signature independently of age and gradient: indeed, these speeds are not so completely natural and common. However, if speed increases, the BCOM raises in such a way that its corresponding 3D contour becomes more regular; 2) right and left sides of the stride are quite asymmetrical (i.e. in the forward direction). Globally, this asymmetry is probably related both to anatomy (i.e. leg length) and which hand you use (i.e. right-handedness); 3) on average, the symmetry pattern is slightly lower in running gaits; and as expected, 4) young children and elderly adults are the most asymmetrical subjects, independently of testing conditions: while, during the early stages of life, this global asymmetry could be ascribed to the process of gait development, old age asymmetries are probably due to structural wearing down of the musculoskeletal system. Importantly, the mathematical methodology used here, by analysing even subtle changes in the 3D BCOM trajectory: a) characterizes its displacements over both time and space; b) quantitatively describes the individual gait signature; and c) represents the basis for the evaluation of gait anomaly/pathology (e.g. children with cerebral palsy, obese people and amputees). Finally, knowing the main biomechanical variables becomes fundamental both to fully describe the mechanics of walking and running and to extract and characterize the individual gait signature. In effect, our measurements (discrete method versus continuous mathematical function, and direct versus indirect measurement) of both simple and complex variables wholly confirm, complete and amplify previous literature data. Similarly to what previously demonstrated in horse performances, the second project tried: a) to verify both static anatomical and kinematic functional symmetries as important and relevant indicators of running economy (i.e. the reciprocal of metabolic cost) in humans featuring different running levels (i.e. occasional, skilled and top runners categorized primarily upon their best marathon time); b) to develop imaging based bi- and three-dimensional methods to analyse static symmetries recorded by Magnetic Resonance Imaging (lower limbs and pelvic area); c) to describe the kinematic symmetries defining both the Digital Locomotory Signature and the Symmetry Index; finally, d) to investigate running economy as a performance determinant. In effect, both the 2D/3D analysis of static symmetries highlight very few differences among runners; however, a strong relationship between ankle and knee areas has been underlined in all runners. Furthermore, independently of training ability: as expected, 1) the BCOM raises and lifts slightly as a function of running speed; 2) right and left steps are mostly asymmetrical in the forward direction and symmetrical in the vertical direction (i.e. combined action of gravity and ground reaction force); 3) differently to what was expected, slight differences have been found among runners. On the whole, the asymmetry is probably related both to anatomy and handedness. Other than that, no running economy differences were found. In conclusion, while a relationship between symmetries and running economy has not been found, significant results have however been underlined in each trial (static and dynamic symmetries). Finally, the deep investigation of both bioenergetics (treadmill versus over-ground) and biomechanics (simple/complex variables and spatial/temporal variability of the BCOM) of running has highlights only little (significant) differences among groups

Modeling and analysis of passive viscoelastic-legged rimless wheel that generates measurable period of double-limb support

Limit cycle walking including passive-dynamic walkers is generally modeled as a nonlinear hybrid dynamical system with state jumps. The inelastic collision model is usually derived on the assumption that the rear leg leaves the ground immediately after landing of the fore leg. This model is, however, inappropriate in the case of compliant-legged walkers. This paper then reconsiders the traditional collision model and discusses the conditions for transition to double-limb support (DLS) motion which is not instantaneous through investigations of passive dynamic walking of a viscoelastic-legged rimless wheel. First, we experimentally confirm that measurable period of DLS motion emerges after landing of the fore leg, and develop the corresponding mathematical model. Second, we numerically analyze the fundamental properties of the generated passive-dynamic gaits. Furthermore, we discuss the conditions for transition to DLS motion and specify the computational procedures