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.

A discussion of the theory and methodology for creating believable quadrupedal locomotion for computer animation applications. The study focuses on a variety of issues related to producing realistic animal gait animations and includes a case study for rigging and animating the various gaits of a horse. Visualization of unnatural gaits for the horse will also be discussed and animated. The process of rigging involves setting up the character control system in a high-end 3d computer animation program such as Maya which is used extensively by the computer graphics industry.

Achieving a believable gait pattern for a virtual quadrupedal character requires a significant time investment from an animator. This thesis presents a prototype system for creating a foundational layer of natural-looking animation to serve as a starting point for an animator. Starting with video of an actual horse walking, joints are animated over the footage to create a rotoscoped animation. This animation represents the animal’s natural motion. Joint angle values for the legs are sampled per frame of the animation and conditioned for Fourier analysis. The Fast Fourier Transform provides frequency information that is used to create mathematical descriptions of each joint’s movement. A model representing the horse’s overall gait pattern is created once each of the leg joints has been analyzed and defined. Lastly, a new rig for a virtual quadruped is created and its leg joints are animated using the gait pattern model derived through the analysis.

This thesis aims to address the real-time planning and nonlinear control of quadrupedal locomotion such that the resulting gaits are robust to various kinds of disturbances. Specifically, this work addresses two scenarios. Namely, a quasi-static formulation in which an inertial appendage (i.e., a tail) is used to assist the quadruped in negating external push disturbances, and an agile formulation which is derived in a manner such that an appendage could easily be added in future work to examine the affect of tails on agile and high-speed motions. Initially, this work presents a unified method in which bio-inspired articulated serpentine robotic tails may be integrated with walking robots, specifically quadrupeds, in order to produce stable and highly robust locomotion. The design and analysis of a holonomically constrained 2 degree of freedom (DOF) tail is shown and its accompanying nonlinear dynamic model is presented. The model created is used to develop a hierarchical control scheme which consists of a high-level path planner and a full-order nonlinear low-level controller. The high-level controller is based on model predictive control (MPC) and acts on a linear inverted pendulum (LIP) model which has been extended to include the forces produced by the tail by augmenting the LIP model with linearized tail dynamics. The MPC is used to generate center of mass (COM) and tail trajectories and is subject to the net ground reaction forces of the system, tail shape, and torque saturation of the tail in order to ensure overall feasibility of locomotion. At the lower level, a full-order nonlinear controller is implemented to track the generated trajectories using quadratic program (QP) based input-output (I-O) feedback linearization which acts on virtual constraints. The analytical results of the proposed approach are verified numerically through simulations using a full-order nonlinear model for the quadrupedal robot, Vision60, augmented with a tail, totaling at 20 DOF. The simulations include a variety of disturbances to show the robustness of the presented hierarchical control scheme. The aforementioned control scheme is then extended in the latter portion of this thesis to achieve more dynamic, agile, and robust locomotion. In particular, we examine the use of a single rigid body model as the template model for the real-time high-level MPC, which is linearized using variational based linearization (VBL) and is solved at 200 Hz as opposed to an event-based manner. The previously defined virtual constraints controller is also extended so as to include a control Lyapunov function (CLF) which contributes to both numerical stability of the QP and aids in stability of the output dynamics. This new hierarchical scheme is validated on the A1 robot, with a total of 18 DOF, through extensive simulations to display agility and robustness to ground height variations and external disturbances. The low-level controller is then further validated through a series of experiments displaying the ability for this algorithm to be readily transferred to hardware platforms. / Master of Science / This thesis aims to address the real-time planning and nonlinear control of four legged walking robots such that the resulting gaits are robust to various kinds of disturbances. Initially, this work presents a method in which a robotic tail can be integrated with legged robots to produce very stable walking patterns. A model is subsequently created to develop a multi-layer control scheme which consists of a high-level path planner, based on a reduced-order model and model predictive control techniques, that determines the trajectory for the quadruped and tail, followed by a low-level controller that considers the full-order dynamics of the robot and tail for robust tracking of the planned trajectory. The reduced-order model considered here enforces quasi-static motions which are slow but generally stable. This formulation is validated numerically through extensive full-order simulations of the Vision60 robot. This work then proceeds to develop an agile formulation using a similar multi-layer structure, but uses a reduced-order model which is more amenable to dynamic walking patterns. The low-level controller is also augmented slightly to provide additional robustness and theoretical guarantees. The latter control algorithm is extensively numerically validated in simulation using the A1 robot to show the large increase in robustness compared to the quasi-static formulation. Finally, this work presents experimental validation of the low-level controller formulated in the latter half of this work.

Title: Phylogenetical consequenses of human locomotion realizated during the schoulder girdle Objectives: Description of phylogenetic context of human locomotion realized through the shoulder girdle Methods: Study and analysis of the available literature Analytic-synthetic comparison of the current knowledge of evolution Study of available sources of phylogeny of locomotion in terrestrial vertebrates Results: It was found similarity in the basic control of human bipedal locomotion to control of quadrupedal locomotion of other animals and similarity in the specific form of human locomotion to locomotion of non-human primates Keywords: Bipedal locomotion, quadrupedal locomotion, control of locomotion, interlimb coordination

Orientador: Carlos Alberto dos Reis Filho / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-10T09:10:45Z (GMT). No. of bitstreams: 1 Nadalin_EvertonZaccaria_M.pdf: 2191420 bytes, checksum: 38decb6d182261bd5e5fc2df03ad1b9a (MD5) Previous issue date: 2007 / Resumo: Este trabalho está relacionado com o problema da pesagem de um bovino criado em campo aberto, não confinado, destinado ao corte. O conhecimento da evolução contínua do peso do animal é de grande importância neste ramo de negócios e uma solução tecnicamente satisfatória, de custo aceitável e de tecnologia proprietária, certamente representa uma significativa contribuição ao Brasil. Uma solução idealizada, que é a meta maior do projeto em que este trabalho se enquadra, prevê o uso de um dispositivo instalado nas patas do animal, contendo um sensor de pressão ou de impacto e uma unidade eletrônica local que condiciona, digitaliza e armazena os sinais do sensor. Além disto, a unidade eletrônica transmite estes dados através de uma rede de comunicação de dados sem fio e de baixo consumo de energia para centrais de coleta e processamento estrategicamente situadas na área em que o gado se desenvolve. Tal sistema viabiliza, deste modo, acumular no tempo as informações de cada pisada de cada animal. O sinal produzido por um sensor em conseqüência do impacto de cada pisada é influenciado por diversos parâmetros, dentre os quais o peso do animal. Sendo assim, é impossível estabelecer uma relação direta e exclusiva entre o sinal do sensor e o peso. Entretanto, os valores acumulados destes sinais descrevem uma função de múltiplas variáveis que pode ser tratada juntamente com algumas informações complementares sobre o ambiente, buscando-se o isolamento da variável peso. Para isto, uma abordagem adequada prevê o desenvolvimento ou adoção de um modelo do mecanismo de movimentação do animal e o tratamento numérico dos dados acumulados aplicando filtragens e buscas de correlações. Trata-se, portanto, de uma solução de natureza multidisciplinar, que exige uma aliança de conhecimentos complementares para a sua realização. Coube ao presente trabalho, desenvolvido no âmbito da engenharia eletrônica, a implementação de uma etapa preliminar e necessária que consiste de um sistema de caracterização de pisadas constituído de um conjunto de sensores piezoelétricos, uma interface que permite a transferência dos dados destes sensores a um computador e um ambiente de software através do qual foram testados algoritmos para a verificação de correlação entre os sinais associados às pisadas e o peso do agente. São frutos deste trabalho um sistema de coleta automática dos sinais de pisadas, que permitiu a captura de sinais com sensores instalados tanto numa plataforma fixa como num sapato tênis, e um estudo comparativo dos resultados obtidos de tratamentos numéricos distintos aplicados aos dados experimentais / Abstract: This work deals with the problem of weighting non-confined cattle raised in open field for meat production. The knowledge of the continuous weight change of the animal is of great importance in this business field. Therefore, a technically satisfactory solution, with acceptable price and customized technology, certainly represents a significant contribution to Brazil. The idealized solution, which is the major goal to be pursued by the project in which this work takes part, considers the use of a device placed into the animal¿s hooves. It would contain a pressure or impact sensor and a local electronic unit, which conditions, digitizes and stores the signals received from the sensor. The electronic unit also transmits this data through a low-energy wireless communication network to reception and processing stations placed strategically around the area where the cattle raises. Such a system enables accumulating data about the steps of each animal throughout time. Several parameters, including the animal¿s weight, influence the signal produced by a sensor as a consequence to the impact of a step. Therefore, it is impossible to establish a direct and exclusive relation between the signal given by the sensor and the weight. Nevertheless, the accumulated data of these signals describe a multiple variable function that can be treated together with some complementary information about the environment, seeking the isolation of the weight variable. An adequate approach predicts the development or use of a model of the animal¿s locomotion mechanism and the numeric treatment of the accumulated data by applying filtering and seeking correlations. The multidisciplinary nature of this solution demands an alliance of complementary knowledge for its accomplishment. This work, developed in the scope of electrical engineering, implemented a necessary and preliminary stage that consists of: a step characterization system, made of a set of piezoelectric sensors, an interface that allows transferring data from the sensors to a computer and a software environment, in which algorithms were tested to verify the correlation between the signals associated to the steps and the agent¿s weight. The main result of this work are a system that performs automatic collecting of steps, which allowed the capture of the signals with sensors installed both on a fixed platform and inside tennis shoes, and the comparative study of the results of different numerical treatments applied to the experimental data / Mestrado / Eletrônica, Microeletrônica e Optoeletrônica / Mestre em Engenharia Elétrica

Quadrupedal robots play a vital role in various applications, from search and rescue operations to exploration in challenging terrains. However, locomotion tasks involving unknown payload transportation on rough terrains pose significant challenges, requiring adaptive control strategies to ensure stability and performance. This dissertation contributes to the advancement of adaptive motion planning and control solutions that enable quadrupedal robots to traverse unknown rough environments while tasked with transporting unknown payloads. In the first project, a novel hierarchical planning and control framework for robust payload transportation by quadrupedal robots is developed. This framework integrates an adaptive model predictive control (AMPC) algorithm with a gradient-descent-based adaptive updating law applied to reduced-order locomotion (i.e., template) models. At the high level of the control hierarchy, an indirect adaptive law estimates unknown parameters of the reduced-order locomotion model under varying payloads, ensuring stability during trajectory planning. The optimal trajectories generated by the AMPC are then passed to a low-level and full-order nonlinear whole-body controller (WBC) for tracking. Extensive numerical investigations and hardware experiments on the A1 quadru[pedal robot validate the framework's capabilities, showcasing significant improvements in payload transportation on both flat and rough terrains compared to conventional MPC strategies. Specifically, the robot demonstrates proficiency in transporting unmodeled, unknown static payloads up to 109% of its own mass in experiments on flat terrains and 91% on rough experimental terrains. Moreover, the robot successfully manages dynamic payloads with 73% of its mass on rough terrains. Adaptive controllers must also address external disturbances inherent in real-world environments. Therefore, the second project introduces a hierarchical planning and control scheme with an adaptive L1 nonlinear model predictive control (ANMPC) at the high level, which integrates nonlinear MPC (NMPC) with an L1 adaptive controller. The prescribed optimal state and control input profiles generated by the ANMPC are then fed to the low-level nonlinear WBC. This approach aims to stabilize locomotion gaits in the presence of parametric uncertainties and external disturbances. The proposed controller is analyzed to accommodate uncertainties and external disturbances. Comprehensive numerical simulations and experimental validations on the A1 quadrupedal robot demonstrate its effectiveness on rough terrains. Numerical results suggest that ANMPC significantly improves the stability of the gaits in the presence of uncertainties and external disturbances compared to NMPC and AMPC. The robot can carry payloads up to 109% of its own mass on its trunk on flat and rough terrains. Simulation results show that the robot achieves a maximum payload capacity of 26.3 (kg), which is equivalent to 211% of its own mass on rough terrains with uncertainties and disturbances. / Doctor of Philosophy / In the rapidly advancing domain of robotics, there is a growing demand for intelligent robotic systems capable of adeptly addressing novel and unforeseen scenarios, such as uneven paths or external forces applied to the robots, like kicks and hits. This necessitates robots with the capability to handle diverse tasks with precision, particularly in the domains of object transportation and navigation through unknown terrains in applications such as search and rescue operations or cargo handling. This dissertation introduces innovative motion planning and control frameworks designed to imbue robots with adaptive capabilities, enabling them to adapt to real-world unanticipated scenarios and uncertainties during their movement, particularly when carrying unknown payloads. In the first project, a new framework is developed to enhance payload transportation by quadrupedal robots. This framework integrates an adaptive model predictive control (AMPC) algorithm with a gradient-descent-based adaptive updating law. Through extensive experiments and simulations, the framework shows remarkable improvements in payload transportation on both flat and rough terrains. The robot successfully transports payloads exceeding its own mass by up to 109% on flat terrains and 91% on rough terrains. Recognizing the need to address uncertainties in real-world environments, the second project introduces a hierarchical planning and control scheme with adaptive L1 nonlinear model predictive control (ANMPC). This approach stabilizes legged locomotion in the presence of uncertainties and disturbances. Results demonstrate that ANMPC significantly improves gait stability compared to existing methods. The robot achieves a payload capacity of up to 109% of its own mass on both experimental flat and rough terrains and reaches a maximum of 26.3 kg (around 212% of its own mass) on rough terrain simulations with uncertainties and disturbances.

Tittle: Description quadrupedal locomotion diagonal pattern in specific sport activity (rope climbing, walking, pull-up) Aim of work: The aim is to find a description kvadrupedal locomotion diagonal pattern with rope climbing and its motion pattern compared with the motion pattern of walking and pull-up. Methods: This work is descriptively-association study with quantitative and qualitative analysis. The dates were measured by surface electromyography and 2-D video-analysis. Results: Alternating activation of upper extremities (rope climbing without the lower extremities), we proved that the movement supporting lower extremities is quadruped locomotion diagonal pattern. Symmetric work of upper extremities (pull-up) is not in response at lower extremities quadruped locomotion diagonal pattern. Key words: Electromyography (EMG), quadruped, diagonal pattern, rope climbing, pull-up, walking

Tittle: Description quadrupedal locomotion diagonal pattern in specific sport activity (rope climbing, walking, pull-up) Aim of work: The aim is to find a description kvadrupedal locomotion diagonal pattern with rope climbing and its motion pattern compared with the motion pattern of walking and pull-up. Methods: This work is descriptively-association study with quantitative and qualitative analysis. The dates were measured by surface electromyography and 2-D video-analysis. Results: Alternating activation of upper extremities (rope climbing without the lower extremities), we proved that the movement supporting lower extremities is quadruped locomotion diagonal pattern. Symmetric work of upper extremities (pull-up) is not in response at lower extremities quadruped locomotion diagonal pattern. Key words: Electromyography (EMG), quadruped, diagonal pattern, rope climbing, pull-up, walking

This report is a bachelor thesis in Mechatronics at KTH. The purpose of the thesis is to design a statically stable walking robot capable of forward movement. A quadrupedal robot is designed, as well as a PID control system. To easily control the legs with sufficient accuracy servo motors are used. The control system is used to generate an effective gait pattern that gives rise to the desired functionality. To achieve this the center of mass needs to be approximated, which is done through force sensitive resistors in its feet. The control systems and mathematical models used are tested with the help of a simulation in Simulink. A prototype is also built in order to test the models in practice. The results show that the robot is capable of upholding balance in the simulations, even with shifts in parameters such as the weight and the location of the center of mass. The prototype performed significantly worse, which is mainly accredited to the lack of quality among the force sensors. In future projects the use of different methods to approximate the location of the center of mass is recommended. If the use of sensors is preferred, strain gauges could be a viable alternative to the force sensitive resistors used. More expensive force sensitive resistors of a higher quality could also be an option. / Denna rapport är ett kandidatexamensarbete i Mekatronik på KTH. Syftet med rapporten är att designa en gående robot som erhåller statiskt stabilitet vid gång framåt. En fyrbent robot samt ett PID regler system designades. För att styra benen med bra noggranhet används servomotorer. Reglersystemet används för att generera en stabil bana för fötterna att följa. Detta kräver en uppskattning av robotens masscentrum som möjliggös m.h.a. tryckkänsliga motstånd i fötterna. Reglersystemet samt framtagna matematiska modeller testas med hjälp av simulering i Simulink. Sedan byggs en prototyp av roboten för att testa modellerna i verkligheten. Resultat visar att roboten kan balansera och presterar bra i simulationen, även då parametrar så som vikt och masscentrumets läge ändras. I verkligheten fungerade roboten betydligt sämre, vilket tycks vara orsakat av opålitliga kraftsensorer i fötterna. I framtida projekt föreslås användning av olika metoder för att uppskatta positionen av robotens masscentrum. Om användningen av sensorer är föredragen kan tryckkänsliga motstånd ersättas med töjningsgivare för att mäta normalkrafterna, alternativt kan tryckkänsliga motstånd av högre kvalitet användas.