This thesis explores the development of time-varying virtual constraint controllers that allow stable and agile gaits for full-order hybrid dynamical models of quadrupedal locomotion. Unlike time-invariant nonlinear controllers, time-varying controllers do not rely on sensor data for gait phasing and can initiate locomotion from zero velocity. Motivated by these properties, we investigate the stability guarantees that can be provided by the time-varying approach. More specifically, we systematically establish necessary and sufficient conditions that guarantee exponential stability of periodic orbits for time-varying hybrid dynamical systems utilizing the Poincar� return map. Leveraging the results of the presented proof, we develop time-varying virtual constraint controllers to stabilize bounding, trotting, and walking gaits of a 14 degree of freedom quadrupedal robot, Minitaur. A framework for selecting the parameters of virtual constraint controllers to achieve exponential stability is shown, and the feasibility of the analytical results is numerically validated in full-order model simulations of Minitaur. / Master of Science / This thesis extends a class of controllers designed to address the full dynamics of stable locomotion in quadrupedal robots. As of yet, there is no widely-accepted standard methodology for controlling the complex maneuvers of quadrupedal locomotion, as most strategies rely on simplified models to ease computational constraints. "Virtual constraint'' controllers - also known as Hybrid Zero Dynamics controllers - are a class of controllers designed to address the full dynamics of legged locomotion by coordinating the links of a legged robot model to follow a periodic trajectory representing the desired gait pattern. However, the formalized "time-invariant'' model of virtual constraint controllers relies on sensor data to track progress on the desired gait trajectory. This dependence on sensor data makes the resulting controllers unable to start from a state of zero velocity and sensitive to disturbances generated by high velocity impacts. The proposed "time-varying'' virtual constraints controllers utilize the elapsed time to track gait progress and do not have the previously mentioned limitations. Motivated by these benefits, we develop a formalized methodology for designing time-varying virtual constraint controllers for quadrupedal robots. This includes extending time-invariant means of mathematically validating the stability of the gait controllers to time-varying systems. With strategies of designing and validating time-varying virtual constraint controllers formalized, the methodology is implemented on numerical simulations of bounding, trotting, and walking gaits for the quadrupedal robot Minitaur which validates the stability and feasibility of the developed controllers.

Existing state-of-the-art legged robots often require complex mechanisms with multi-level controllers and computationally expensive algorithms. Part of this is owed to the multiple degrees of freedom (DOFs) these intricate mechanisms possess and the other is a result of the complex nature of dynamic legged locomotion. The underlying dynamics of this class of non-linear systems must be addressed in order to develop systems that perform natural human/animal-like locomotion. However, there are no stringent rules for the number of DOFs in a system; this is merely a matter of the locomotion requirements of the system. In general, most systems designed for dynamic locomotion consist of multiple actuators per leg to address the balance and locomotion tasks simultaneously. In contrast, this research hypothesizes the decoupling of locomotion and balance by omitting the DOFs whose primary purpose is dynamic disturbance rejection to enable a far simplified mechanical design for the legged system. This thesis presents a novel single DOF mechanism that is topologically arranged to execute a trajectory conducive to dynamic locomotive gaits. To simplify the problem of dynamic balancing, the mechanism is designed to be utilized in a quadrupedal platform in the future. The preliminary design, based upon heuristic link lengths, is presented and subjected to kinematic analysis to evaluate the resulting trajectory. To improve the result and to analyze the effect of key link lengths, sensitivity analysis is then performed. Further, a reference trajectory is established and a parametric optimization over the design space is performed to drive the system to an optimal configuration. The evolved design is identified as the Bio-Inspired One-DOF Leg for Trotting (BOLT). The dynamics of this closed kinematic chain mechanism is then simplified, resulting in a minimal order state space representation. A prototype of the robotic leg was integrated and mounted on a treadmill rig to perform various experiments. Finally, open loop running is implemented on the integrated prototype demonstrating the locomotive performance of BOLT. / MS / Existing state-of-the-art legged robots often require complex mechanisms with multi-level controllers and computationally expensive algorithms. Part of this is owed to the multiple degrees of freedom (DOFs) these intricate mechanisms possess and the other is a result of the complex nature of dynamic legged locomotion. The underlying dynamics of this class of non-linear systems must be addressed in order to develop systems that perform natural human/animal-like locomotion. However, the number of active DOF is merely a designers choice. To simplify the problem at both levels: design and controls of dynamic locomotion, we developed a novel mechanism that incorporates the benefits of higher DOF legs while accommodating the simplicity of single DOF leg. The preliminary design of the mechanism was designed with parameters (lengths of the femur,tibia) that were directly derived from a domestic dog. Synthesis of the mechanism suggested that the design was not suitable for an intended running-trot gait observed in biological counterparts. However, to gain a deeper understanding of the mechanism, it was necessary to perform a sensitivity analysis, as a result we arrived at a mechanism whose performance was better than the initial but still not satisfactory.With the insight gained through the analysis and an ideal gait design exercise, then an optimization on the design space was performed with carefully tuned bounds. The final result is a novel mechanism identified as Biologically inspired One DOF Leg for Trotting (BOLT) that is topologically arranged to execute a running-trot gait. Finally, the design choice presented with a challenge that has not been actively addressed. The dynamics of the mechanism can not be modeled using traditional methods due to presence of constraints that characterize the closed loops of the mechanism. We present an adaption of the Singularly perturbed dynamic model for systems that are hybrid in nature. The resulting dynamics are simplified, resulting in a minimal order state space representation, which is more amenable to model based control development in future. A prototype of the robotic leg was integrated and mounted on a treadmill rig to perform various experiments.Finally, open loop running is implemented on the integrated prototype demonstrating the locomotive performance of BOLT.

No / This study investigated the importance of binocular vision to foot placement accuracy when stepping onto a floor-based target during gait initiation. Starting from stationary, participants placed alternate feet onto targets sequentially positioned along a straight travel path with the added constraint that the initial target (target 1) could move in the medio-lateral (M-L) direction. Repeated trials when target 1 remained stationary or moved laterally at the instant of lead-limb toe-off (TO) or 200 ms after TO (early swing) were undertaken under binocular and monocular viewing. Catch trials when target 1 shifted medially were also undertaken. Foot-reach kinematics, foot trajectory corrections and foot placement accuracy for the step onto target 1 were determined via 3D motion analyses. Peak foot-reach velocity and initial foot-reach duration were unaffected by vision condition but terminal foot-reach duration was prolonged under monocular conditions (p = 0.002). Foot trajectory alteration onsets were unaffected by vision condition, but onsets occurred sooner when the target shifted in early swing compared to at TO (p = 0.033). M-L foot placement accuracy decreased (p = 0.025) and variability increased (p = 0.05) under monocular conditions, particularly when stepping onto the moving target. There was no difference between vision conditions in A-P foot placement accuracy. Results indicate that monocular vision provides sufficient information to determine stepping distance and correctly transport the foot towards the target but binocular vision is required to attain a precise M-L foot placement; particularly so when stepping onto a moving target. These findings are in agreement with those found in the reaching and grasping literature, indicating that binocular vision is important for end-point precision. / The Health Foundation, UK. Grant (3991/3322)

Notre motivation est de comprendre la locomotion humaine pour un meilleur contrôle des systèmes virtuels (robots et mannequins). La locomotion humaine a été étudiée depuis longtemps dans des domaines différents. Nous considérons la locomotion comme le déplacement d’un repère attaché au corps humain (direction et orientation) au lieu de la trajectoire articulaire du corps complet. Notre approche est basée sur le fondement calculatoire de la locomotion humaine. Le but est de trouver un modèle qui explique la forme de la locomotion humaine dans l’espace. Pour ce faire, nous étudions tout d’abord le comportement des trajectoires au sol pendant la locomotion intentionnelle. Quand un humain marche, il met un pied devant l’autre et par conséquence, l’orientation du corps suit la direction tangente de la trajectoire. C’est ce qu’on appelle l’hypothèse de comportement nonholonome. Cependant, dans le cas d’un pas de côté, l’orientation du corps n’est plus semblable à la direction de trajectoire, et l’hypothèse n’est plus valable. Le comportement de la locomotion devient holonome. Le but de la thèse est de distinguer ces deux comportements et de les exploiter en neuroscience, robotique et animation graphique. La première partie de la thèse présente une étude qui permet de déterminer des configurations de comportement holonome par un protocole expérimental et par une fonction qui segmente les comportements nonholonomes et holonomes d’une trajectoire. Dans la deuxième partie, nous établissons un modèle unifiant comportements nonholonomes et holonomes. Ce modèle combine trois vitesses générant la locomotion humaine : tangentielle, angulaire et latérale. Par une approche de commande optimale inverse nous proposons une fonction multi-objectifs qui optimise des trajectoires calculées pour les rendre proches des trajectoires humaines naturelles. La dernière partie est l’application qui utilise les deux comportements pour synthétiser des locomotions humaines dans un environnement d’animation graphique. Chaque locomotion est caractérisée par trois vitesses et est donc considérée comme un point dans l’espace de commande 3D (de trois vitesses). Nous avons collecté une librairie qui contient des locomotions de vitesses différentes – des points dans l’espace 3D. Ces points sont structurés en un nuage de tétraèdres. Quand une vitesse désirée est donnée, elle est projetée dans l’espace 3D et on trouve le tétraèdre qui la contient. La nouvelle animation est interpolée par quatre locomotions correspondant aux quatre sommets du tétraèdre. On expose plusieurs scénarios d’animations sur un personnage virtuel. / Our motivation is to understand human locomotion to better control locomotion of virtual systems (robots and mannequins). Human locomotion has been studied so far in different disciplines. We consider locomotion as the level of a body frame (in direction and orientation) instead of the complexity of many kinematic joints systems as other approaches. Our approach concentrates on the computational foundation of human locomotion. The ultimate goal is to find a model that explains the shape of human locomotion in space. To do that, we first base on the behavior of trajectories on the ground during intentional locomotion. When human walk, they put one foot in front of the other and consequently, the direction of motion is deduced by the body orientation. That’s what we called the nonholonomic behavior hypothesis. However, in the case of a sideward step, the body orientation is not coupled to the tangential direction of the trajectory, and the hypothesis is no longer validated. The behavior of locomotion becomes holonomic. The aim of this thesis is to distinguish these two behaviors and to exploit them in neuroscience, robotics and computer animation. The first part of the thesis is to determine the configurations of the holonomic behavior by an experimental protocol and an original analytical tool segmenting the nonholonomic and holonomic behaviors of any trajectory. In the second part, we present a model unifying nonholonomic and holonomic behaviors. This model combines three velocities generating human locomotion: forward, angular and lateral. The experimental data in the first part are used in an inverse optimal control approach to find a multi-objective function which produces calculated trajectories as those of natural human locomotion. The last part is the application that uses the two behaviors to synthesize human locomotion in computer animation. Each locomotion is characterized by three velocities and is therefore considered as a point in 3D control space (of three speeds). We collected a library that contains locomotions at different velocities - points in 3D space. These points are structured in a tetrahedra cloud. When a desired speed is given, it is projected into the 3D space and we find the corresponding tetrahedron that contains it. The new animation is interpolated by four locomotions corresponding to four vertices of the selected tetrahedron. We exhibit several animation scenarios on a virtual character.

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

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Effective movement is central to survival and it is essential for all animals to react in response to changes around them. In many animals the rhythmic signals that drive locomotion are generated intrinsically by small networks of neurons in the nervous system which can be switched on and off. In this thesis I use a very simple animal, in which the behaviours and neuronal networks have been well characterised experimentally, to explore the salient features of such networks. Two days after hatching, tadpoles of the frog Xenopus laevis respond to a brief touch to the head by starting to swim. The swimming rhythm is driven by a small population of electrically coupled brainstem neurons (called dINs) on each side of the tadpole. These neurons also receive synaptic input following head skin stimulation. I build biophysical computational models of these neurons based on experimental data in order to address questions about the effects of electrical coupling, synaptic feedback excitation and initiation pathways. My aim is better understanding of how swimming activity is initiated and sustained in the tadpole. I find that the electrical coupling between the dINs causes their firing properties to be modulated. This allows two experimental observations to be reconciled: that a dIN only fires a single action potential in response to step current injections but the population fires like pacemakers during swimming. I build on this hypothesis and show that long-lasting, excitatory feedback within the population of dINs allows rhythmic pacemaker activity to be sustained in one side of the nervous system. This activity can be switched on and off at short latency in response to biologically realistic synaptic input. I further investigate models of synaptic input from a defined swim initiation pathway and show that electrical coupling causes a population of dINs to be recruited to fire either as a group or not at all. This allows the animal to convert continuously varying sensory stimuli into a discrete decision. Finally I find that it is difficult to reliably start swimming-like activity in the tadpole model using simple, short-latency, symmetrical initiation pathways but that by using more complex, asymmetrical, neuronal-pathways to each side of the body, consistent with experimental observations, the initiation of swimming is more robust. Throughout this work, I make testable predictions about the population of brainstem neurons and also describe where more experimental data is needed. In order to manage the parameters and simulations, I present prototype libraries to build and manage these biophysical model networks.

This thesis addresses modeling and simulation of the human lower extremities in order to track walking motion and estimate walking distance. The lower extremities are modeled as an articulated object, which consists of rigid bars connected to each other by joints. This model is tested by using both synthetic and real data. The synthetic data is created based on the main principles of biomechanics. The real data is obtained from the MARG sensors and is processed by the Factored Quaternion algorithm. Next, it is implemented in a simulation program written in Matlab. The program utilizes a mathematical model that represents the human gait-cycle and is based on the theory of forward kinematics as well as on the theory of manipulator kinematics. The simulation program is able to track the motion of the limbs that represent the lower extremities and estimate the traveled distance. Extensive laboratory tests verified the validity of the configuration.