This report will cover the work involved in building a quadruped robot which should to a certain extent resemeble a four-legged mammal. The introduction will present information related to what has inspired the project, purpose/aim, specifications, limitations and research questions. Most important in the introduction are probably the purpose/aim and research questions. Mainly, the goal was to have the robot be able to self-balance and later also be able to walk to some degree if possible. The first research question concerns how well a PID controller would affect the stability of the robot and the second question is about answering if referencing a fourlegged mammal is a good idea when building a quadruped robot. Theory and methods were combined and written as one chapter. This way relevant information could be provided in the appropriate places as the method for creating the robot was described. The chapter dives into the primary parts of the robot which are the choice of components, construction, inverse kinematics and last but not least the code including the implementation of a PID. The results show that PID regulation improves stability and performance, but PI regulation actually performed the best. Furthermore, the question regarding referencing a four-legged mammal remains inconclusive even though the model was sufficient for the task.

O presente trabalho visa à modelagem e ao controle ótimo de um robô quadrúpede autônomo. Devido a variações na topologia e nos graus de liberdade do robô ao longo do seu movimento, duas abordagens diferentes de modelagem foram consideradas: na primeira, foi considerado o robô com pelo menos duas pernas suportando seu corpo ou plataforma e, na segunda, considerou-se o modelo de uma perna no ar. Em ambos os casos, apresentou-se a solução dos problemas cinemáticos de posição direta e inversa por meio da parametrização de Denavit-Hartenberg. Analisaram-se também os problemas cinemáticos de velocidade e suas singularidades através da Matriz Jacobiana, e ainda obtiveram-se os modelos dinâmicos do sistema utilizando-se o Principio do Trabalho Virtual e o método iterativo de Newton-Euler para a plataforma e as pernas, respectivamente. A partir destes modelos dinâmicos, desenvolveu-se um algoritmo de otimização das perdas de energia elétrica dos motores das juntas. Neste sentido, utilizou-se a estratégia do controle independente por junta. Estratégia esta que, junto com a discretização no tempo do modelo do sistema, permitiu transformar o problema inicial de otimização para cada junta em outro de Programação Quadrática bem mais simples de ser resolvido. Depois de resolver estes problemas, para levar em conta as interações entre as dinâmicas das várias juntas, procedeu-se à busca de um ponto fixo ou mínimo global que caracterizasse a energia total gasta no movimento do sistema. Finalmente, realizada a demonstração e a análise de convergência do algoritmo, este foi testado no controle da andadura (gait) do robô Kamambaré. Como resultado do teste, observou-se o bom desempenho da formulação e a viabilidade de sua implementação em sistemas reais. / The present work aims the modeling and optimal control of an autonomous quadruped robot. Due to variations in the topology and the degree of freedom of the robot during its motion, two different modeling approaches were considered: firstly, the robot was considered with at least two legs supporting its body or platform and, second one, was considered the model of a leg in the air. In both cases, was presented the solution of the direct and inverse kinematic problem of position through the Denavit-Hartenberg parameterization. Were analyzed also, the kinematic problem of speed and the singularities through the Jacobian matrix, and was also obtained the dynamic model of the system using the Principle of Virtual Work or the dAlembert method and the iterative Newton-Euler method for the platform and legs, respectively. From these two dynamic model, were developed an algorithm for optimizing the power losses of the motors that driven the joints. In this sense, was used the strategy of independent control for each joint. Such a strategy, along with the discretization in time of the system model, has helped to change the initial optimization problem for each joint in a Quadratic Programming Problem, more simpler to solve. After solving these problems, and to take into account the interactions between the dynamics of various joints, was proceeded to search for a fixed point or a global minimum that would characterize the total energy spent in moving for the system. Finally, held the demonstration and analysis of convergence of the algorithm was tested in the control of gait of the Kamambaré robot. As a result of the test, we observed the good performance of the formulation and the feasibility of its implementation in real systems.

This thesis addresses the problem of generating smooth and efficiently executable locomotion trajectories for legged robots under contact constraints. In addition, we want the trajectories to have the property that small changes in the foot position generate small changes in the joint target path. The first part of this thesis explores methods to select poses for a legged robot that maximises the workspace reachability while maintaining stability and contact constraints. It also explores methods to select configurations based on a reduced-dimensional search of the configuration space. The second part analyses time scaling strategy which tries to minimize the execution time while obeying the velocity and acceleration constraints. These two parts effectively result in smooth feasible trajectories for legged robots. Experiments on the RoboSimian robot demonstrate the effectiveness and scalability of the strategies described for walking and climbing on a rock climbing wall.

The ability to control balance and stability are essential to prevent falls during locomotion. Maintenance of stable locomotion is challenging especially when complicated by amputation and prosthesis use. Humans employ several motor strategies to maintain stability during walking on complex terrain: decreasing walking speed, adjusting stride length and stance width, lowering the center of mass, and prolonging the double support time. The mechanisms of selecting these motor strategies by the primary motor cortex are unknown and cannot be studied directly in humans. There is also little information about dynamic stability of prosthetic gait with bone-anchored prostheses, which are thought to provide sensory feedback to the amputee through osseoperception. Therefore, the Specific Aims of my research were to (1) evaluate dynamic stability and the activity of the primary motor cortex during walking with different constraints on the base of support and (2) develop an animal model to evaluate mechanics and stability of prosthetic gait with a bone-anchored prosthesis. To address these aims, I developed a feline model that allows for investigating (1) the role of the primary motor cortex in regulation of dynamic stability of intact locomotion, (2) skin and bone integration with a percutaneous porous titanium implant facilitating prosthetic attachment, and (3) dynamic stability of walking on a bone-anchored prosthesis. The results of Specific Aim 1 demonstrated that the area and shape of the base of support influence the margins of dynamic stability during quadrupedal walking. For example, I found that the animal is dynamically unstable in the sagittal plane and frontal plane (although to a lesser degree) during a double-support by a forelimb and the contralateral hindlimb. Elevated neuronal activity from the right forelimb representation in the primary motor cortex during these phases suggests that the motor cortex may contribute to selection of paw placement location and thus to regulation of stability. The results of Specific Aim 2 on the development of skin-integrated bone-anchored prostheses demonstrated the following. Skin ingrowth into 3 types of porous titanium pylons (pore sizes 40-100 μm and 100-160 μm and nano-tubular surface treatment) implanted under skin of rats was seen 3 and 6 weeks after implantation, and skin filled at least 30% of available implant space. The duration of implantation, but not implant pore size (in the studied range) or surface treatment statistically influenced skin ingrowth; pore size and time of implantation affected the implant extrusion length (p<0.05). The implant type with the slowest extrusion rate (pore size 40-100 μm) was used in a feline model of prosthetic gait with skin-integrated bone-anchored prosthesis. The developed implantation methods, rehabilitation procedures and feline prostheses allowed 2 animals to utilize skin- and bone-integrated prostheses for dynamically stable locomotion. Prosthetic gait analysis demonstrated that the animals loaded the prosthetic limb, but increased reliance on intact limbs for weight support and propulsion. The obtained results and developed animal model improve the understanding of locomotor stability control and integration of skin with percutaneous implants.

O presente trabalho visa à modelagem e ao controle ótimo de um robô quadrúpede autônomo. Devido a variações na topologia e nos graus de liberdade do robô ao longo do seu movimento, duas abordagens diferentes de modelagem foram consideradas: na primeira, foi considerado o robô com pelo menos duas pernas suportando seu corpo ou plataforma e, na segunda, considerou-se o modelo de uma perna no ar. Em ambos os casos, apresentou-se a solução dos problemas cinemáticos de posição direta e inversa por meio da parametrização de Denavit-Hartenberg. Analisaram-se também os problemas cinemáticos de velocidade e suas singularidades através da Matriz Jacobiana, e ainda obtiveram-se os modelos dinâmicos do sistema utilizando-se o Principio do Trabalho Virtual e o método iterativo de Newton-Euler para a plataforma e as pernas, respectivamente. A partir destes modelos dinâmicos, desenvolveu-se um algoritmo de otimização das perdas de energia elétrica dos motores das juntas. Neste sentido, utilizou-se a estratégia do controle independente por junta. Estratégia esta que, junto com a discretização no tempo do modelo do sistema, permitiu transformar o problema inicial de otimização para cada junta em outro de Programação Quadrática bem mais simples de ser resolvido. Depois de resolver estes problemas, para levar em conta as interações entre as dinâmicas das várias juntas, procedeu-se à busca de um ponto fixo ou mínimo global que caracterizasse a energia total gasta no movimento do sistema. Finalmente, realizada a demonstração e a análise de convergência do algoritmo, este foi testado no controle da andadura (gait) do robô Kamambaré. Como resultado do teste, observou-se o bom desempenho da formulação e a viabilidade de sua implementação em sistemas reais. / The present work aims the modeling and optimal control of an autonomous quadruped robot. Due to variations in the topology and the degree of freedom of the robot during its motion, two different modeling approaches were considered: firstly, the robot was considered with at least two legs supporting its body or platform and, second one, was considered the model of a leg in the air. In both cases, was presented the solution of the direct and inverse kinematic problem of position through the Denavit-Hartenberg parameterization. Were analyzed also, the kinematic problem of speed and the singularities through the Jacobian matrix, and was also obtained the dynamic model of the system using the Principle of Virtual Work or the dAlembert method and the iterative Newton-Euler method for the platform and legs, respectively. From these two dynamic model, were developed an algorithm for optimizing the power losses of the motors that driven the joints. In this sense, was used the strategy of independent control for each joint. Such a strategy, along with the discretization in time of the system model, has helped to change the initial optimization problem for each joint in a Quadratic Programming Problem, more simpler to solve. After solving these problems, and to take into account the interactions between the dynamics of various joints, was proceeded to search for a fixed point or a global minimum that would characterize the total energy spent in moving for the system. Finally, held the demonstration and analysis of convergence of the algorithm was tested in the control of gait of the Kamambaré robot. As a result of the test, we observed the good performance of the formulation and the feasibility of its implementation in real systems.

This bachelor project in mechatronics aimed to design and build a versatile robot that can both roll and walk using four legs. Control of the robot’s movement was to be achieved by a joystick, with the ability to alter direction in both rolling and walking mode. However, due to time constraints, the rolling algoritm was not implemented. Nevertheless, the final prototype achieved the ability to transform between a ball and a quadruped robot and move in four directions. The accuracy and precision of the walking sequences were evaluated and demonstrated moderate precision and a suboptimal level of accuracy. / Detta kandidatprojekt i mekatronik syftade till att designa och bygga en mångsidig robot som både kan rulla och gå med fyra ben. Kontroll av robotens rörelse ska uppnås med joystick, med möjligheten att ändra riktning i både rillande och gångläge. Men på grund av tidsbrist implementerades inte rullalgorithmen. Ändå uppnådde den slutliga prototypen förmågan att tranformera mellan en boll och en fyrbent robot och röra sig i fyra riktningar. Noggrannheten och precisionen i gångsekvenserna utvärderades och visade måttlig precision och en suboptimal nivå av noggrannhet.

No / We introduce a new "marker-based" model for use in capturing equine movement. This model is informed by a sound biomechanical study of the animal and can be deployed in the pursuit of many undertakings. Unlike many other approaches, our method provides a high level of automation and hides the intricate biomechanical knowledge required to produce realistic results. Due to this approach, it is possible to acquire solved data with minimal manual intervention even in real-time conditions. The approach introduced can be replicated for the production of many other animals. The model is first informed by the veterinary world through studies of the subject's anatomy. Second, further medical studies aimed at understanding and addressing surface processes, inform model creation. The latter studies address items such as skin sliding. If not otherwise corrected these processes may hinder marker based capture. The resultant model has been tested in feasibility studies for practicality and subject acceptance during production. Data is provided for scrutiny along with the subject digitally captured through a variety of methods. The digital subject in mesh form as well as the motion capture model aid in comparison and show the level of accurateness achieved. The video reference and digital renders provide an insight into the level of realism achieved.

Legged robots have the potential to be a valuable technology that provides agile and adaptive locomotion over complex terrain. To realize legged locomotion's full abilities a control design must consider the nonlinear piecewise dynamics of the systems. This paper aims to develop a controller for the planar bounding of a quadrupedal robot. The bounding of the quadruped robot is characterized by a simplified hybrid model that consists of two subsystems for stance and flight phases and the switching laws between the two states. An additional model, the Multibody model, with fewer simplifications, is used concurrently to best approximate real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: stance-phase and swing-phase control. The stance phase implements reaction force control utilizing a body state feedback controller and a gait stabilizer, while the swing phase deploys position control in conjunction with a trajectory planning algorithm to ensure proper footfall. Numerical simulations are carried out for the system with/without control. The control strategy is further validated by simulations of the Simscape multibody model. The overall simulated controller results are promising and demonstrate stable bounding for four system cycles.

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There are a lot of quadruped robots in the world, but few are omnidirectional. Therefore this thesis describes the production and design process of such a robot. Examining earlier quadruped robots determined that a central microcontroller is required to control it, and servo motors are used to power the robots joints. Reaserch also determined the base of the mathematical methods used. Additionally, there are multiple types of sprawling gaits, ranging from statically stable to dynamically stable. In this project astatically stable gait is used. The thesis illustrates the mathematical models used to define the omnidirectional movement, and describes the code used to implement it. The result is a robot that can move omnidirectionally, both normally and upside down. The results show that there is a deviation depending upon the direction, but it is small. The main advantage of omnidirectionallity is the ability to change movement direction without stopping or turning. It also enables directional adjustment without requiring any steps. / Det här projektet gick ut på att skapa en krypande fyrbent robot som kan gå i alla riktningar utan att rotera runt sitt eget centrum. Det finns idag redan ett stort antal olika fyrbenta robotar, men få kan gå i alla riktningar. Därav så beskriver den här rapporten framtagningen och designprocessen för en sådan robot. Undersökning av fyrbenta robotar visade att en mikrokontroller är nödvändigför att kontrollera roboten och servomotorer bör användas för att driva lederna. Förstudeierna gav även basen för de matematiska modellerna som används for rörelserna, samt vetskapen om ett flertal olika typer av gångstilar, allt från statiskt stabil till dynamiskt stabil. I det här projektet beskrivs de matematiska modellerna som används för att definiera rörelsen i alla riktningar och hur dessa appliceras i programmeringen av roboten. Resultatet blev en robot som kan gå i alla riktningar utan att rotera runt sitt centrum, både normalt och uppochner. Detta ger möjligheten att byta rörelse riktning utan att behöva stanna eller vända sig, samt möjliggör även riktnings korrektioner utan att kräva extra steg.