In order for a mobile robot to complete its task it must be able to plan and follow a trajectory. Depending on the environment, it may also be necessary to follow a given velocity profile. This is known as temporal planning. Temporal planning can be used to minimize time of motion and to avoid moving obstacles. For example, assuming the mobile robot is an intelligent wheelchair, it must follow a prescribed path (sidewalk, hospital corridor) while following a strict speed limit (slowing down for pedestrians, cars). Computing a realistic velocity profile for a mobile robot is a challenging task due to a large number of kinematic and dynamic constraints that are involved. Unlike prior works which performed temporal planning in a 2-dimensional environment, this thesis presents a new temporal planning algorithm in a 3-dimensional environment. This algorithm is implemented on a wheeled mobile robot that is to be used in a healthcare setting. The path planning stage is accomplished by using cubic spline functions. A rudimentary trajectory is created by assigning an arbitrary time to each segment of the path. This trajectory is made feasible by applying a number of constraints and using a linear scaling technique. When a velocity profile is provided, a non-linear time scaling technique is used to fit the robots center linear velocity to the specified velocity. A method for avoiding moving obstacles is also implemented. Both simulation and experimental results for the wheeled mobile robot are presented. These results show good agreement with each other. For both simulation and experimentation, six different examples of paths in the Engineering Building of the University of Saskatchewan, were used. Experiments were performed using the PowerBot mobile robot in the robotics lab at the University of Saskatchewan.

In order for a mobile robot to complete its task it must be able to plan and follow a trajectory. Depending on the environment, it may also be necessary to follow a given velocity profile. This is known as temporal planning. Temporal planning can be used to minimize time of motion and to avoid moving obstacles. For example, assuming the mobile robot is an intelligent wheelchair, it must follow a prescribed path (sidewalk, hospital corridor) while following a strict speed limit (slowing down for pedestrians, cars). Computing a realistic velocity profile for a mobile robot is a challenging task due to a large number of kinematic and dynamic constraints that are involved. Unlike prior works which performed temporal planning in a 2-dimensional environment, this thesis presents a new temporal planning algorithm in a 3-dimensional environment. This algorithm is implemented on a wheeled mobile robot that is to be used in a healthcare setting. The path planning stage is accomplished by using cubic spline functions. A rudimentary trajectory is created by assigning an arbitrary time to each segment of the path. This trajectory is made feasible by applying a number of constraints and using a linear scaling technique. When a velocity profile is provided, a non-linear time scaling technique is used to fit the robots center linear velocity to the specified velocity. A method for avoiding moving obstacles is also implemented. Both simulation and experimental results for the wheeled mobile robot are presented. These results show good agreement with each other. For both simulation and experimentation, six different examples of paths in the Engineering Building of the University of Saskatchewan, were used. Experiments were performed using the PowerBot mobile robot in the robotics lab at the University of Saskatchewan.

Les robots mobiles à roues orientables gagnent de la mobilité en employant des roues conventionnelles entièrement orientables, comportant deux joints actifs, un pour la direction et un autre pour la conduite. En dépit d'avoir seulement un degré de mobilité (DOM) (défini ici comme degrés de liberté instantanément autorisés DOF), correspondant à la rotation autour du centre de rotation instantané (ICR), ces robots peuvent effectuer des trajectoires planaires complexes de $ 2D $. Ils sont moins chers et ont une capacité de charge plus élevée que les roues non conventionnelles (par exemple, Sweedish ou Omni-directional) et, en tant que telles, préférées aux applications industrielles. Cependant, ce type de structure de robot mobile présente des problèmes de contrôle textit {basic} difficiles de la coordination de la direction pour éviter les combats d'actionneur, en évitant les singularités cinématiques (ICR à l'axe de la direction) et les singularités de représentation (du modèle mathématique). En plus de résoudre les problèmes de contrôle textit {basic}, cette thèse attire également l'attention et présente des solutions aux problèmes de textit {niveau d'application}. Plus précisément, nous traitons deux problèmes: la première est la nécessité de reconfigurer "de manière discontinue" les articulations de direction, une fois que la discontinuité dans la trajectoire du robot se produit. Une telle situation - la discontinuité dans le mouvement du robot - est plus susceptible de se produire de nos jours, dans le domaine émergent de la collaboration homme-robot. Les robots mobiles qui fonctionnent à proximité des travailleurs humains en mouvement rapide rencontrent généralement une discontinuité dans la trajectoire calculée en ligne. Le second apparaît dans les applications nécessitant que l'angle de l'angle soit maintenu, certains objets ou fonctionnalités restent dans le champ de vision (p. Ex., Pour les tâches basées sur la vision) ou les changements de traduction. Ensuite, le point ICR est nécessaire pour déplacer de longues distances d'un extrême de l'espace de travail à l'autre, généralement en passant par le centre géométrique du robot, où la vitesse du robot est limitée. Dans ces scénarios d'application, les contrôleurs basés sur l'ICR à l'état de l'art conduiront à des comportements / résultats insatisfaisants. Dans cette thèse, nous résolvons les problèmes de niveau d'application susmentionnés; à savoir la discontinuité dans les commandes de vitesse du robot et une planification meilleure / efficace pour le contrôle du mouvement du point ICR tout en respectant les limites maximales de performance des articulations de direction et en évitant les singularités cinématiques et représentatives. Nos résultats ont été validés expérimentalement sur une base mobile industrielle. / Steerable wheeled mobile robots gain mobility by employing fully steerable conventional wheels, having two active joints, one for steering, and another for driving. Despite having only one degree of mobility (DOM) (defined here as the instantaneously accessible degrees of freedom DOF), corresponding to the rotation about the instantaneous center of rotation (ICR), such robots can perform complex $2D$ planar trajectories. They are cheaper and have higher load carrying capacity than non-conventional wheels (e.g., Sweedish or Omni-directional), and as such preferred for industrial applications. However, this type of mobile robot structure presents challenging textit{basic} control issues of steering coordination to avoid actuator fighting, avoiding kinematic (ICR at the steering joint axis) and representation (from the mathematical model) singularities. In addition to solving the textit{basic} control problems, this thesis also focuses attention and presents solutions to textit{application level} problems. Specifically we deal with two problems: the first is the necessity to "discontinuously" reconfigure the steer joints, once discontinuity in the robot trajectory occurs. Such situation - discontinuity in robot motion - is more likely to happen nowadays, in the emerging field of human-robot collaboration. Mobile robots working in the vicinity of fast moving human workers, will usually encounter discontinuity in the online computed trajectory. The second appears in applications requiring that some heading angle is to be maintained, some object or feature stays in the field of view (e.g., for vision-based tasks), or the translation verse changes. Then, the ICR point is required to move long distances from one extreme of the workspace to the other, usually passing by the robot geometric center, where the feasible robot velocity is limited. In these application scenarios, the state-of-art ICR based controllers will lead to unsatisfactory behavior/results. In this thesis, we solve the aforementioned application level problems; namely discontinuity in robot velocity commands, and better/efficient planning for ICR point motion control while respecting the maximum steer joint performance limits, and avoiding kinematic and representational singularities. Our findings has been validated experimentally on an industrial mobile base.

Assistive mobile robots, such as intelligent wheelchairs, that can navigate autonomously in response to high level commands from a user can greatly benefit people with cognitive and physical disabilities by increasing their mobility. In this work, we address the problem of safe, comfortable, and customizable motion planning of such assistive mobile robots. We recognize that for an assistive robot to be acceptable to human users, its motion should be safe and comfortable. Further, different users should be able to customize the motion according to their comfort. We formalize the notion of motion comfort as a discomfort measure that can be minimized to compute comfortable trajectories, and identify several properties that a trajectory must have for the motion to be comfortable. We develop a motion planning framework for planning safe, comfortable, and customizable trajectories in small-scale space. This framework removes the limitations of existing methods for planning motion of a wheeled mobile robot moving on a plane, none of which can compute trajectories with all the properties necessary for comfort. We formulate a discomfort cost functional as a weighted sum of total travel time, time integral of squared tangential jerk, and time integral of squared normal jerk. We then define the problem of safe and comfortable motion planning as that of minimizing this discomfort such that the trajectories satisfy boundary conditions on configuration and its higher derivatives, avoid obstacles, and satisfy constraints on curvature, speed, and acceleration. This description is transformed into a precise mathematical problem statement using a general nonlinear constrained optimization approach. The main idea is to formulate a well-posed infinite-dimensional optimization problem and use a conforming finite-element discretization to transform it into a finite-dimensional problem for a numerical solution. We also outline a method by which a user may customize the motion and present some guidelines for conducting human user studies to validate or refine the discomfort measure presented in this work. Results show that our framework is capable of reliably planning trajectories that have all the properties necessary for comfort. We believe that our work is an important first step in developing autonomous assistive robots that are acceptable to human users. / text

In this thesis work, a mobile robot is designed to be used in search and rescue operations to help the human rescue workers. The difficult physical conditions in the ruins obstruct the movement. Therefore, it is aimed to design a search and rescue robot which can move easily on rough terrain and climb over the obstacles. The designed robot is made up of three modules. A connecting unit is designed that is situated between each module. This connecting unit which is composed of two universal and one revolute joint gives 5 DOF relative motions to the modules. On the other hand, the wheel&rsquo / s continuous contact with the ground is important while moving on rough terrain. In order to increase the adaptation of the robot to the rough terrain the rear axle is connected to the body with a revolute joint. Besides, skid steering system is used in the design of the robot to attain a compact and light solution which requires few parts. In the study, kinematic equations and dynamic equations of the robot are obtained to be used by the control program. The dynamic equations are obtained by using the Newton &ndash / Euler formulation. The forces, which are transmitted by the connecting unit to the modules, and the reaction forces formed between the wheels and the ground are derived by using these equations. &ldquo / Follow-the-Leader approach&rdquo / is used as a control strategy to make the modules move in formation and to reduce the tracking problem. In this approach, the first module is the leader and the second and third modules follow it. A Matlab program is written to control the robot by using the constructed mathematical model of the robot. The reaction forces between the wheels and the ground are calculated through using the Matlab program written. Moreover to make the simulations of the robot for some cases, a model is constructed in ADAMS program.

Dizertační práce se zabývá problematikou kinematického modelování a řízení mobliních kolových robotů. Přináší sumarizaci problematiky kinematického modelování mobilních robotů obecně a popis vlastností kolových mobilních robotů s několika řízenými koly. Použitý aparát z matematiky, fyziky je vysvětlován s důrazem na pohled teorie řízení. Dále je prezentován nový řídicí algoritmus pro mobilní kolové roboty s více řízenými koly, vhodný pro úlohu stabilizace v bodě i sledování trajektorie, tedy obě nejčastěji řešené úlohy pohybu mobilních robotů.

Este trabalho apresenta o projeto de dois controladores robustos, baseados no critério H∞ não linear, para o acompanhamento de trajetória de robôs móveis com rodas (RMRs). Estes controladores estabilizam o sistema em malha fechada e garantem que a norma L2 induzida entre os sinais de entrada (distúrbios) e saída seja limitada por um nível de atenuação &#947 > 0. Para o projeto, as equações dinâmicas não lineares do robô são descritas na forma quase linear a parâmetros variantes (quase-LPV), sendo os parâmetros parte do estado. Os controladores são resolvidos via desigualdades matriciais lineares (DMLs) e equações algébricas de Ricatti (EAR). Resultados em simulação com um estudo comparativo entre essas duas estratégias de controle e um controlador proporcional derivativo (PD) em conjunto com um controlador do tipo torque calculado são apresentados. Além disso, a implementação de dois métodos de localização de RMRs através de imagens é realizada. / This work presents the design of two robust controllers, based on nonlinear H∞ approach, for tracking trajectory of wheeled mobile robots (WMRs). These controllers stabilize the close-loop system and guarantee that induced L2 norm between input (disturbances) and output signals be bounded by an attenuation level &#947 > 0. For the design, the nonlinear dynamic equations of the robot are described in quasi linear parameter varying (quasi-LPV) form being the parameters part of the states. The controllers are solved via linear matrix inequalities (LMIs) and algebraic Riccati equation (ARE). Simulation results with a comparison study among these two control strategies and a proportional-derivative (PD) controller plus calculated torque are presented. Moreover, implementation of two methods of localization of WMRs based on images is accomplished.

Advances in hardware design have made wheeled mobile robots (WMRs) exceptionally mobile. To fully exploit this mobility, WMR planning, control, and estimation systems require motion models that are fast and accurate. Much of the published theory on WMR modeling is limited to 2D or kinematics, but 3D dynamic (or force-driven) models are required when traversing challenging terrain, executing aggressive maneuvers, and manipulating heavy payloads. This thesis advances the state of the art in both the formulation and calibration of WMR models We present novel WMR model formulations that are high-fidelity, general, modular, and fast. We provide a general method to derive 3D velocity kinematics for any WMR joint configuration. Using this method, we obtain constraints on wheel ground contact point velocities for our differential algebraic equation (DAE)-based models. Our “stabilized DAE” kinematics formulation enables constrained, drift free motion prediction on rough terrain. We also enhance the kinematics to predict nonzero wheel slip in a principled way based on gravitational, inertial, and dissipative forces. Unlike ordinary differential equation (ODE)-based dynamic models which can be very stiff, our constrained dynamics formulation permits large integration steps without compromising stability. Some alternatives like Open Dynamics Engine also use constraints, but can only approximate Coulomb friction at contacts. In contrast, we can enforce realistic, nonlinear models of wheel-terrain interaction (e.g. empirical models for pneumatic tires, terramechanics-based models) using a novel force-balance optimization technique. Simulation tests show our kinematic and dynamic models to be more functional, stable, and efficient than common alternatives. Simulations run 1K-10K faster than real time on an ordinary PC, even while predicting articulated motion on rough terrain and enforcing realistic wheel-terrain interaction models. In addition, we present a novel Integrated Prediction Error Minimization (IPEM) method to calibrate model parameters that is general, convenient, online, and evaluative. Ordinarily system dynamics are calibrated by minimizing the error of instantaneous output predictions. IPEM instead forms predictions by integrating the system dynamics over an interval; benefits include reduced sensing requirements, better observability, and accuracy over a longer horizon. In addition to calibrating out systematic errors, we simultaneously calibrate a model of stochastic error propagation to quantify the uncertainty of motion predictions. Experimental results on multiple platforms and terrain types show that parameter estimates converge quickly during online calibration, and uncertainty is well characterized. Under normal conditions, our enhanced kinematic model can predict nonzero wheel slip as accurately as a full dynamic model for a fraction of the computation cost. Finally, odometry is greatly improved when using IPEM vs. manual calibration, and when using 3D vs. 2D kinematics. To facilitate their use, we have released open source MATLAB and C++ libraries implementing the model formulation and calibration methods in this thesis.

Este trabalho apresenta o projeto de dois controladores robustos, baseados no critério H∞ não linear, para o acompanhamento de trajetória de robôs móveis com rodas (RMRs). Estes controladores estabilizam o sistema em malha fechada e garantem que a norma L2 induzida entre os sinais de entrada (distúrbios) e saída seja limitada por um nível de atenuação &#947 > 0. Para o projeto, as equações dinâmicas não lineares do robô são descritas na forma quase linear a parâmetros variantes (quase-LPV), sendo os parâmetros parte do estado. Os controladores são resolvidos via desigualdades matriciais lineares (DMLs) e equações algébricas de Ricatti (EAR). Resultados em simulação com um estudo comparativo entre essas duas estratégias de controle e um controlador proporcional derivativo (PD) em conjunto com um controlador do tipo torque calculado são apresentados. Além disso, a implementação de dois métodos de localização de RMRs através de imagens é realizada. / This work presents the design of two robust controllers, based on nonlinear H∞ approach, for tracking trajectory of wheeled mobile robots (WMRs). These controllers stabilize the close-loop system and guarantee that induced L2 norm between input (disturbances) and output signals be bounded by an attenuation level &#947 > 0. For the design, the nonlinear dynamic equations of the robot are described in quasi linear parameter varying (quasi-LPV) form being the parameters part of the states. The controllers are solved via linear matrix inequalities (LMIs) and algebraic Riccati equation (ARE). Simulation results with a comparison study among these two control strategies and a proportional-derivative (PD) controller plus calculated torque are presented. Moreover, implementation of two methods of localization of WMRs based on images is accomplished.

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