In most robot applications, the control of the manipulators end-effector along a specified desired trajectory is the main concern. In these applications, the end-effector (tip) of the manipulator is required to follow a given trajectory. Several methods have been so far proposed for the motion control of robot manipulators. However, most of these control methods ignore either joint friction or joint elasticity which can be caused by the transmission systems (e.g. belts and gearboxes). This study aims at development of a comprehensive control strategy for the tip-trajectory tracking of flexible-joint robot manipulators. While the proposed control strategy takes into account the effect of the friction and the elasticity in the joints, it also provides a highly accurate motion for the manipulators end-effector. During this study several approaches have been developed, implemented and verified experimentally/numerically for the tip trajectory tracking of robot manipulators. To compensate for the elasticity of the joints two methods have been proposed; they are a composite controller whose design is based on the singular perturbation theory and integral manifold concept, and a swarm controller which is a novel biologically-inspired controller and its concept is inspired by the movement of real biological systems such as flocks of birds and schools of fishes. To compensate for the friction in the joints two new approaches have been also introduced. They are a composite compensation strategy which consists of the non-linear dynamic LuGre model and a Proportional-Derivative (PD) compensator, and a novel friction compensation method whose design is based on the Work-Energy principle. Each of these proposed controllers has some advantages and drawbacks, and hence, depending on the application of the robot manipulator, they can be employed. For instance, the Work-Energy method has a simpler form than the LuGre-PD compensator and can be easily implemented in industrial applications, yet it provides less accuracy in friction compensation. In addition to design and develop new controllers for flexible-joint manipulators, another contribution of this work lays in the experimental verification of the proposed control strategies. For this purpose, experimental setups of a two-rigid-link flexible-joint and a single-rigid-link flexible-joint manipulators have been employed. The proposed controllers have been experimentally tested for different trajectories, velocities and several flexibilities of the joints. This ensures that the controllers are able to perform effectively at different trajectories and speeds. Besides developing control strategies for the flexible-joint manipulators, dynamic modeling and vibration suppression of flexible-link manipulators are other parts of this study. To derive dynamic equations for the flexible-link flexible-joint manipulators, the Lagrange method is used. The simulation results from Lagrange method are then confirmed by the finite element analysis (FEA) for different trajectories. To suppress the vibration of flexible manipulators during the manoeuvre, a collocated sensor-actuator is utilized, and a proportional control method is employed to adjust the voltage applied to the piezoelectric actuator. Based on the controllability of the states and using FEA, the optimum location of the piezoelectric along the manipulator is found. The effect of the controllers gain and the delay between the input and output of the controller are also analyzed through a stability analysis.

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. <p>The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. <p>A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. <p>A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.<p>Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan.

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. <p>The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. <p>A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. <p>A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.<p>Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan.

In most robot applications, the control of the manipulators end-effector along a specified desired trajectory is the main concern. In these applications, the end-effector (tip) of the manipulator is required to follow a given trajectory. Several methods have been so far proposed for the motion control of robot manipulators. However, most of these control methods ignore either joint friction or joint elasticity which can be caused by the transmission systems (e.g. belts and gearboxes). This study aims at development of a comprehensive control strategy for the tip-trajectory tracking of flexible-joint robot manipulators. While the proposed control strategy takes into account the effect of the friction and the elasticity in the joints, it also provides a highly accurate motion for the manipulators end-effector. During this study several approaches have been developed, implemented and verified experimentally/numerically for the tip trajectory tracking of robot manipulators. To compensate for the elasticity of the joints two methods have been proposed; they are a composite controller whose design is based on the singular perturbation theory and integral manifold concept, and a swarm controller which is a novel biologically-inspired controller and its concept is inspired by the movement of real biological systems such as flocks of birds and schools of fishes. To compensate for the friction in the joints two new approaches have been also introduced. They are a composite compensation strategy which consists of the non-linear dynamic LuGre model and a Proportional-Derivative (PD) compensator, and a novel friction compensation method whose design is based on the Work-Energy principle. Each of these proposed controllers has some advantages and drawbacks, and hence, depending on the application of the robot manipulator, they can be employed. For instance, the Work-Energy method has a simpler form than the LuGre-PD compensator and can be easily implemented in industrial applications, yet it provides less accuracy in friction compensation. In addition to design and develop new controllers for flexible-joint manipulators, another contribution of this work lays in the experimental verification of the proposed control strategies. For this purpose, experimental setups of a two-rigid-link flexible-joint and a single-rigid-link flexible-joint manipulators have been employed. The proposed controllers have been experimentally tested for different trajectories, velocities and several flexibilities of the joints. This ensures that the controllers are able to perform effectively at different trajectories and speeds. Besides developing control strategies for the flexible-joint manipulators, dynamic modeling and vibration suppression of flexible-link manipulators are other parts of this study. To derive dynamic equations for the flexible-link flexible-joint manipulators, the Lagrange method is used. The simulation results from Lagrange method are then confirmed by the finite element analysis (FEA) for different trajectories. To suppress the vibration of flexible manipulators during the manoeuvre, a collocated sensor-actuator is utilized, and a proportional control method is employed to adjust the voltage applied to the piezoelectric actuator. Based on the controllability of the states and using FEA, the optimum location of the piezoelectric along the manipulator is found. The effect of the controllers gain and the delay between the input and output of the controller are also analyzed through a stability analysis.

"Recent works on the control of wheeled mobile robots have shifted from the use of the kinematic model to the use of the dynamic model. Since theoretical results typically treat the inputs to the dynamic model as torques, few experimental results have been provided, as torque is typically not the input to most commercially available robots. Few papers have implemented controllers based on the dynamic model, and those that have did not address the issue of identifying the parameters of the dynamic model. This work focuses on a method for identifying the parameters of the dynamic model of a wheeled mobile robot. The method is shown to be both effective and easy to implement, and requires no prior knowledge of what the parameters may be. Experimental results on two mobile robots of different scale demonstrate its effectiveness. The estimates of the parameters created by the proposed method are then used in an adaptive controller to verify their accuracy. For future work, this method should be completed autonomously in a two-part manner, onboard the mobile robot. First, the robot should perform the method proposed here to generate an initial parameter estimate, and then use adaptive control to update the estimates."

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / This work proposes a study and application of advanced controller to trajectory tracking of wheeled mobile robots. This kind of problem is a challenger for controllers once its models has two inputs and three outputs and is a non-linear model. In the literature there are various solutions to wheeled mobile robots trajectory tracking, among them the Model Predictive Control (MPC) with linearization model and a non linear control which in this work will be nominated as Klancar Controller. The Predictive Controllers can be applied efficiently in plants which has multiple inputs an multiple outputs, in situation that a future reference trajectory is known and systems with input and output constraints . However, the main disadvantage of MPC is the high computational effort which limits its practical application. Thus, this specific controller uses the plants linearization model. On the other hand, the Klancar Controller may be more efficient than the ones based on linear models, once the model is non linear. However, its solution, by definition, does not match the optimized criteria which can be a disadvantage mainly in systems that has constrains and a known future reference. Furthermore, this work proposes the application of the Predictive Control Extended Prediction Self Adaptive Control (EPSAC) to wheeled mobile robot trajectory tracking. This control strategy uses explicitly the non linear robot model, future reference, constraints on the variables and has a optimized solution. And, to the matter of this work, it has not been found reports of the EPSAC applied in mobile robotics, and is thus an unprecedented application. Simulation results are presented comparing the controllers studied using performance indices. Else, the controllers were applied in a mobile robot. / Este trabalho propÃe o estudo e aplicaÃÃo de controladores avanÃados ao seguimento de trajetÃrias de robÃs mÃveis com rodas. Este tipo de problema à bastante desafiador do ponto de vista de controle uma vez que o modelo tem duas entradas e trÃs saÃdas, alÃm disso, trata-se de um modelo nÃo linear. Na literatura existem diversas soluÃÃes para o controle de trajetÃria de robÃs mÃveis, dentre eles tem-se o Controle Preditivo Baseado em Modelo (MPC) por meio de modelos linearizados e um controlador nÃo linear denominado neste trabalho de controlador de Klancar. Os controladores preditivos podem ser aplicados de forma eficiente em plantas com modelos multivariÃveis, em situaÃÃes na qual a trajetÃria futura de referÃncia à conhecida e em sistemas com restriÃÃes nas vaiÃveis de entrada e de saÃda. PorÃm, a principal desvantagem do MPC linearizado à o alto custo computacional o que limita as aplicaÃÃes prÃticas. AlÃm disso, esse controlador especÃfico utiliza um modelo linearizado da planta. Por outro lado, o controlador de Klancar pode ser mais eficiente que os baseados em modelos lineares, devido Ãs nÃo linearidades inerentes do modelo. No entanto, a sua soluÃÃo, por definiÃÃo, nÃo corresponde a critÃrios Ãtimos o que pode representar uma desvantagem principalmente em sistemas com restriÃÃes e referÃncia futura conhecida. AlÃm disso, neste trabalho à proposta a aplicaÃÃo do controle preditivo EPSAC (Extended Prediction Self Adaptive Control) para o controle de seguimento de trajetÃrias. Esta estratÃgia utiliza de forma explÃcita o modelo nÃo linear do robÃ, a referÃncia futura, as restriÃÃes nas variÃveis do robà e soluÃÃo corresponde a um critÃrio Ãtimo. Atà onde foi pesquisado pelo autor deste trabalho, nÃo existem relatos da utilizaÃÃo do EPSAC na robÃtica mÃvel, sendo desta forma uma aplicaÃÃo inÃdita. Resultados de simulaÃÃo sÃo apresentados comparando os controladores estudados, utilizando Ãndices de desempenhos. AlÃm disso, os mesmo foram implementados em um robà mÃvel.

Aujourd'hui, l'inspection des ouvrages d'art est réalisée de façon visuelle par des contrôleurs sur l'ensemble de la structure. Cette procédure est couteuse et peut être particulièrement dangereuse pour les intervenants. Pour cela, le développement du système de vision embarquée sur des drones est privilégié ces jours-ci afin de faciliter l'accès aux zones dangereuses.Dans ce contexte, le travail de cette thèse porte sur l'obtention des méthodes originales permettant la planification, la génération des trajectoires de référence, et le suivi de ces trajectoires par une plate-forme aéroportée stationnaire autonome. Ces méthodes devront habiliter une automatisation du vol en présence de perturbations aérologiques ainsi que des obstacles. Dans ce cadre, nous nous sommes intéressés à deux types de véhicules aériens capable de vol stationnaire : le dirigeable et le quadri-rotors.Premièrement, la représentation mathématique du véhicule volant en présence du vent a été réalisée en se basant sur la deuxième loi de Newton. Deuxièmement, la problématique de génération de trajectoire en présence de vent a été étudiée : le problème de temps minimal est formulé, analysé analytiquement et résolu numériquement. Ensuite, une stratégie de planification de trajectoire basée sur les approches de recherche opérationnelle a été développée.Troisièmement, le problème de suivi de trajectoire a été abordé. Une loi de commande non-linéaire robuste basée sur l'analyse de Lyapunov a été proposée. En outre, un pilote automatique basée sur les fonctions de saturations pour un quadri-rotors a été développée.Les méthodes et algorithmes proposés dans cette thèse ont été validés par des simulations. / Today, the inspection of structures is carried out through visual assessments effected by qualified inspectors. This procedure is very expensive and can put the personal in dangerous situations. Consequently, the development of an unmanned aerial vehicle equipped with on-board vision systems is privileged nowadays in order to facilitate the access to unreachable zones.In this context, the main focus in the thesis is developing original methods to deal with planning, reference trajectories generation and tracking issues by a hovering airborne platform. These methods should allow an automation of the flight in the presence of air disturbances and obstacles. Within this framework, we are interested in two kinds of aerial vehicles with hovering capacity: airship and quad-rotors.Firstly, the mathematical representation of an aerial vehicle in the presence of wind has been realized using the second law of newton.Secondly, the question of trajectory generation in the presence of wind has been studied: the problem of minimal time was formulated, analyzed analytically and solved numerically. Then, a strategy of trajectory planning based on operational research approaches has been developed.Thirdly, the problem of trajectory tracking was carried out. A nonlinear robust control law based on Lyapunov analysis has been proposed. In addition, an autopilot based on saturation functions for quad-rotor crafts has been developed.All methods and algorithms proposed in this thesis have been validated through simulations.

<p>Reversing with a trailer is very difficult and many drivers hesitate to even try it. This thesis examines if active steering, particularly AFS (Active Front Steering), can be used to provide assistance.</p><p>For analysis and controller design a simple geometric model of car and trailer is used. The model seems to be accurate enough at the low speeds relevant for trailer reversing. It is shown that the only trailer dependent model parameter can be estimated while driving. This enables use with different trailers.</p><p>Different schemes to control the system are tested. The main approach is to use the steering wheel as reference for some appropriate output signal, for example the angle between car and trailer. This makes reversing with a trailer more like reversing without a trailer. To turn left, the driver simply turns the steering wheel left and drives. Test driving, as well as theoretical analysis, shows that the resulting system is stable. Of the eight drivers that have tested this type of control, five found it to be a great advantage while two considered it more confusing than helpful.</p><p>A major problem with this control approach has to do with the way AFS is constructed. With AFS, the torque required to turn the front wheels results in a reaction torque in the steering wheel. Together with the reference tracking controllers, this makes the steering wheel unstable. Theoretical analysis implies that this problem has to be solved mechanically. One solution would be to combine AFS with electric power steering.</p><p>This thesis also presents a trajectory tracking scheme to autonomously reverse with a trailer. Starting from the current trailer position and the desired trajectory an appropriate turning radius for the trailer is decided. Within certain limits, this will stabilize the car as well. The desired trajectory can be programmed beforehand, but it can also be saved while driving forward. Both variants have been tested with good results.</p>

Underwater vehicles that use differential thrust for surge and yaw motion control have the advantage of increased maneuverability. Unfortunately, such vehicles usually don’t have thrusters/actuators to control the lateral movements. Hence, they fall into the underactuated vehicle category. The goal of the work in this thesis is to develop an autonomous control system for a differential thrust underwater remotely operated vehicle (ROV) to track predefined position trajectories. This is challenging because the mathematical model for underwater vehicles is highly nonlinear and the environmental disturbances are usually strong and unpredictable. These factors make the design of the control system very difficult. In this work, we use the VideoRay Pro III micro ROV as the test platform, on which we design an autonomous control system. We first present the development and analysis of a hydrodynamic model of the VideoRay Pro III using both analytical and experimental approaches. Based on this model, a state estimator is then designed using the unscented Kalman filter, which yields better estimates of the system states and their uncertainty level in a highly nonlinear system than the commonly used extended Kalman filter. In the controller design, the integrator backstepping technique is used to achieve a Lyapunov stable trajectory tracking controller based on the work by A. P. Aguiar et al. We extended their work by further considering the quadratic drag terms in the vehicle’s hydrodynamic model. The sliding mode control is used to design the bearing and depth controller. Finally, the autonomous control system is validated by simulation and experimental tests. It is shown that the VideoRay Pro III is able to track the predefined trajectory within error range of 0.5 meters.

Underwater vehicles that use differential thrust for surge and yaw motion control have the advantage of increased maneuverability. Unfortunately, such vehicles usually don’t have thrusters/actuators to control the lateral movements. Hence, they fall into the underactuated vehicle category. The goal of the work in this thesis is to develop an autonomous control system for a differential thrust underwater remotely operated vehicle (ROV) to track predefined position trajectories. This is challenging because the mathematical model for underwater vehicles is highly nonlinear and the environmental disturbances are usually strong and unpredictable. These factors make the design of the control system very difficult. In this work, we use the VideoRay Pro III micro ROV as the test platform, on which we design an autonomous control system. We first present the development and analysis of a hydrodynamic model of the VideoRay Pro III using both analytical and experimental approaches. Based on this model, a state estimator is then designed using the unscented Kalman filter, which yields better estimates of the system states and their uncertainty level in a highly nonlinear system than the commonly used extended Kalman filter. In the controller design, the integrator backstepping technique is used to achieve a Lyapunov stable trajectory tracking controller based on the work by A. P. Aguiar et al. We extended their work by further considering the quadratic drag terms in the vehicle’s hydrodynamic model. The sliding mode control is used to design the bearing and depth controller. Finally, the autonomous control system is validated by simulation and experimental tests. It is shown that the VideoRay Pro III is able to track the predefined trajectory within error range of 0.5 meters.