The goal of the research of this Dissertation is using actuation redundancy to reduce backlash in parallel manipulators (PMs.) Initially, 3-RRR and 3-RPR PM layouts where 3 is the number of branches, R is a revolute joint and P is a prismatic joint, are introduced. Actuated joints will later be underlined in the PM desciptions. A method for determining PM working area for rotated payload platforms, based on a mechanism inversion, is presented. Force solutions for non-redundantly actuated 3-RRR, 3-RRR, 3-RPR and 3-RPR PMs are formulated in terms of screw coordinates. The reciprocal product of screw coordinates is demonstrated to be invarient under changes in reference location and orientation. As examples, the PMs execute basic circle, logarithmic spiral and arc displacement and force trajectories. All non-redundantly-actuated PMs, encounter two backlash-prone zero-actuator-output configurations when executing any of the trajectories. Therefore, non-redundantly actuated PMs are found inadequate for precision applications. Force-uncertainties, where PMs cannot sustain or apply forces in uncertain directions, are examined. For typically actuated 3-RRR and 3-RPR PMs, force uncertainties are identified using screw system arguments based on the existance of 3 actuated forces forming degenerate (rank = 2) planar pencils of forces. These degenerate force pose make arbitrary force and moment application impossible and cause singularities in the force solutions. The working area of the 3-RRR PM is found compatible with all trajectories. This compatibility is due to zero minimum branch length being possible with the limitless angular displacements possible with stacked R joints. In comparison, the 3-RPR PM with minimum joint lengthes imposed on the P joints, has a smaller working area, and is not compatible with any of the trajectories. A P joint modification allowing relative length minimums of zero and a compatible working area identical to the 3-RRR PM, is considered. To address inadequacies, symmetric actuation-redundant 3-RRR and 3-RPR PMs are considered. Pseudo (right Moore-Penrose) inverse of the 3×6 ARS (associated reciprocal screw) matrix is considered to solve for the required actuation. This solution, while providing a minimum 2-norm of the vector of required actuator outputs, does not reduce backlash-prone configurations with all actuators still having two backlash-prone zero-output configurations. An algorithm for reducing backlash, using MATLAB’s constrained optimization routine FMINCON is applied. Minimizing the 2-norm of the vector of actuator outputs, subject to the backlash-free constraint of having outputs ≥ 0 or ≤ 0 depending on the initial values, is considered. Actuators providing the best conditioned ARS matices are utilized for the particular solutions. / Graduate

Propõe-se, com este trabalho, estudar numericamente se a redundância cinemática e a redundância de atuação podem ser boas alternativas para que manipuladores planares de cinemática paralela atinjam altas acelerações. Sabe-se que estes tipos de redundância promovem uma redução de singularidades do sistema robótico entre outros benefícios. No entanto, a avaliação comparativa do desempenho dinâmico de manipuladores redundantes ainda é pouco estudada. Este estudo não é trivial pois a redundância significa não somente o aumento do torque disponível, mas também que a inércia do sistema foi aumentada. A avaliação numérica deste trabalho se dará por meio do desenvolvimento de modelos cinemáticos e dinâmicos das possíveis configurações de manipuladores paralelos planares com redundância cinemática e redundância de atuação. Esta avaliação pode ser feita pela comparação entre os manipuladores redundantes e o não-redundante para desenvolver uma mesma trajetória do end-effector. Entretanto, esta avaliação é dependente da trajetória, logo esse trabalho também propõe uma avaliação através de um índice dinâmico em toda a área de trabalho dos manipuladores. / The aim of this work is to study numerically if the kinematic redundancy and the actuation redundancy can be good alternatives for parallel planar manipulators to achieve high accelerations. It is known that types of redundancy promote, among other benefits, a significant reduction in the singularities. However, the evaluation of the redundancy as a good solution to increase the dynamic performance was not studied. This study is not trivial because the redundancy means not only that there is more torque available, but also that the inertia of the system has been considerably increased. Different configurations of the redundant manipulator will be evaluated numerically through kinematic and dynamic models. This evaluation can be performed by the comparison among the non redundant manipulator and the redundant manipulators to execute the same task. This evaluation is task dependent, so this work proposes a dynamic index to desing dynamic maps over the workspace.

Propõe-se, com este trabalho, estudar numericamente se a redundância cinemática e a redundância de atuação podem ser boas alternativas para que manipuladores planares de cinemática paralela atinjam altas acelerações. Sabe-se que estes tipos de redundância promovem uma redução de singularidades do sistema robótico entre outros benefícios. No entanto, a avaliação comparativa do desempenho dinâmico de manipuladores redundantes ainda é pouco estudada. Este estudo não é trivial pois a redundância significa não somente o aumento do torque disponível, mas também que a inércia do sistema foi aumentada. A avaliação numérica deste trabalho se dará por meio do desenvolvimento de modelos cinemáticos e dinâmicos das possíveis configurações de manipuladores paralelos planares com redundância cinemática e redundância de atuação. Esta avaliação pode ser feita pela comparação entre os manipuladores redundantes e o não-redundante para desenvolver uma mesma trajetória do end-effector. Entretanto, esta avaliação é dependente da trajetória, logo esse trabalho também propõe uma avaliação através de um índice dinâmico em toda a área de trabalho dos manipuladores. / The aim of this work is to study numerically if the kinematic redundancy and the actuation redundancy can be good alternatives for parallel planar manipulators to achieve high accelerations. It is known that types of redundancy promote, among other benefits, a significant reduction in the singularities. However, the evaluation of the redundancy as a good solution to increase the dynamic performance was not studied. This study is not trivial because the redundancy means not only that there is more torque available, but also that the inertia of the system has been considerably increased. Different configurations of the redundant manipulator will be evaluated numerically through kinematic and dynamic models. This evaluation can be performed by the comparison among the non redundant manipulator and the redundant manipulators to execute the same task. This evaluation is task dependent, so this work proposes a dynamic index to desing dynamic maps over the workspace.

La popularité des robots parallèles s’est considérablement accrue lors des dernières décennies. Cette popularité a été stimulée par les nombreux avantages qu’offrent les robots parallèles par rapport à leurs homologues traditionnels sériels concernant certaines applications industrielles nécessitant de fortes accélérations et une bonne précision. Toutefois, afin d'exploiter pleinement leur potentiel et de tirer le meilleur de leurs capacités, un long chemin reste encore à parcourir. En plus de la conception mécanique, l'étalonnage et l'optimisation de la structure, le développement d’une commande efficace joue un rôle primordial dans l’amélioration de la performance globale des robots parallèles. Cependant, ces derniers sont connus par leur dynamique fortement non linéaire qui s’accroît considérablement lorsque de fortes accélérations sont sollicitées conduisant à des vibrations mécaniques. En outre, les incertitudes sont abondantes dans ces systèmes en raison des hypothèses simplificatrices de modélisation, l'usure des composants du robot et les variations de l'environnement. De plus, leur dynamique couplée et la redondance d'actionnement dans certains mécanismes donnent lieu à des problèmes de commande complexes et difficiles à gérer. Par conséquent, les stratégies de commande développées pour les robots parallèles devraient tenir compte de tous les enjeux et défis mentionnées précédemment. L'objectif principal de cette thèse réside dans la proposition de nouvelles stratégies de commande adaptatives pour les robots parallèles tenant compte de leurs caractéristiques et particularités afin d'améliorer leurs performances de suivi de trajectoires. En outre, les stratégies de commande développées devraient être validées d'abord en simulation, puis à travers des expérimentations temps-réel sur les robots parallèles à notre disposition. Dans ce contexte, trois contributions majeures sont proposées dans le cadre de cette thèse. Tout d'abord, une nouvelle classe de contrôleurs adaptatifs avec des gains de retour non linéaires temps-variant est proposée. La deuxième contribution réside dans le développement d’une version adaptative de la commande robuste RISE. Pour la troisième contribution, la stratégie de commande adaptative L1, récemment développée, est appliquée pour la première fois sur un robot parallèle, suivie de deux nouvelles extensions basées-modèle. Des simulations numériques ainsi que des expérimentations temps-réel sur différents prototypes de robots parallèles sont présentées et discutées. Tous les contrôleurs proposés sont validés pour différents scénarios permettant ainsi de montrer leur pertinence et efficacité. / Parallel Kinematic Manipulators (PKMs) have gained an increased popularity in the last few decades. This interest has been stimulated by the significant advantages of PKMs compared to their traditional serial counterparts, with respect to some specific industrial tasks requiring high accelerations and accuracy. However, to fully exploit their potential and to get the most of their capabilities, a long path is still to be covered. In addition to mechanical design, calibration and optimization of the structure, efficient control development plays an essential role in improving the overall performance of PKMs. However, PKMs are known for their highly nonlinear dynamics which increases considerably when operating at high accelerations leading to mechanical vibrations. Moreover, uncertainties are abundant in such systems due to model simplifications, the wear of the components of the robot and the variations of the environment. Furthermore, their coupled dynamics and actuation redundancy in some mechanisms give rise to complex and challenging control issues. Consequently, the developed control schemes should take into account all the previously mentioned issues and challenges. The main goal of this thesis lies in the proposal of new adaptive control schemes for PKMs while considering their characteristics and particularities in order to improve their tracking capabilities. Moreover, the developed control strategies should be first validated through numerical simulations, then through real-time experiments on available PKMs. Within this context, three main contributions are proposed in this thesis. First, a new class of adaptive controllers with nonlinear time-varying feedback gains is proposed. The second contribution lies in an adaptive-based extended version of RISE robust feedback control strategy. For the third contribution, the recently developed L1 adaptive control strategy is applied for the first time on a PKM, followed by two novel model-based extensions. Numerical simulations as well as real-time experiments on various PKMs prototypes are provided and discussed. All the proposed controllers are validated for different operating conditions in order to show their relevance and efficiency.

At a platform singularity, a parallel manipulator loses constraint. Adding redundant actuation in an existing leg or new leg can eliminate these types of singularities. However, redundant manipulators have been designed with little attention to frame invariant techniques. In this dissertation, physically meaningful measures for closeness to singularities in non-redundant manipulators are developed. Two such frameworks are constructed. The first framework is a constrained optimization problem that unifies seemingly unrelated existing measures and facilitates development of new measures. The second is a clearance propagation technique based on workspace generation. These closeness measures are expanded to include redundancy and thus can be used as objective functions for designing redundant actuation. The constrained optimization framework is applied to a planar three degree of freedom redundant parallel manipulator to show feasibility of the technique.

L'objectif principal de ce travail est de proposer des approches de commande performantes et robustes aux incertitudes pour les robots parallèles de type Delta, qui sont conçus pour effectuer des tâches industriels importantes et exigeantes comme l'emballage en agroalimentaire, la découpe laser, etc. Les difficultés les plus importantes pour garantir une bonne performance de suivi de trajectoires de ces manipulateurs pour les hautes accélérations avec la meilleure précision possible, tout en conservant de telle performance indépendamment des conditions d'opération (par exemple avec différentes conditions de charge, différentes trajectoires, etc.) sont leur actionnement couplé, l'augmentation de leurs dynamiques non-linéaires et le problème de vibrations mécaniques avec l'augmentation des accélérations envisagées, la présence d'incertitudes sur le modèle/environnement et la redondance d'actionnement si elle existe. Dans cette thèse, différentes approches de commande et observateurs d'état ont été proposés et implémentés expérimentalement sur deux robots de type Delta, à savoir le Par2 (non-redondant) et le R4 (à redondance d'actionnement). Pour le premier, une commande non linéaire/adaptative à mode Dual a été proposée en espace articulaire, synthétisé avec trois différents observateurs d'état pour la estimation des vitesses articulaires: un observateur lead-lag, un observateur Alpha-bêta-gamma et un observateur à grand gain. Pour le robot R4, un commande à feedforward en espace-dual avec a été proposée pour la compensation de sa dynamique (avec laquelle une aaccélération maximale de 100G a été atteinte), puis un contrôleur adaptatif dans l'espace-dual a été proposé afin de garantir une estimation et mise à jours automatique des paramètres du système en temps réel, garantissant ainsi sa bonne performance indépendamment du scénario expérimental. L'analyse de stabilité du robot Par2 bouclé avec la commande adaptative à Mode Dual et du robot R4 commandé avec le contrôleur adaptatif dans l'espace-dual sont fournies, des simulations ont été effectuées et les résultats expérimentaux confirment la bonne performance des approches de commande proposées. / The main objective of this work is to propose control strategies performant and robust towards uncertainties for Delta-like parallel robots, which are designed to perform important and demanding industrial tasks, such as packaging, laser cutting, etc. The most important difficulties to guarantee the good tracking performance of these manipulators for very high accelerations with the best possible precision, while maintaining such performance independently of the operational case (e.g. with different load conditions, different trajectories, etc.) are their coupled actuation, the increase of their high nonlinear dynamics and the problem of mechanical vibrations with the increase of the involved accelerations, the presence of uncertainties in the model/environment and the redundant actuation when applicable. In this thesis, different control schemes and state observers were proposed and experimentally implemented on two Delta-like robots, namely the Par2 (non-redundant) and the R4 (redundantly actuated) parallel manipulators. For the former, a nonlinear/adaptive Dual Mode controller was proposed in the joint space, complied with three different state observers for the estimation of joint velocities: a Lead-lag based observer, an Alpha-beta-gamma observer and the High-gain observer. For the latter, firstly a dual-space feedforward controller was proposed for the compensation of its dynamics (with which a maximum of 100G of acceleration was reached), then a dual-space adaptive controller was proposed in order to automatically estimate the parameters of the system in real-time, thus guaranteeing its good performance independently of the experimental scenario. The stability analysis of Par2 robot under the control of the Dual Mode controller and the R4 robot under the control of the dual-space adaptive controller are provided, simulations were performed and the experimental results confirm the good performance of the proposed control schemes.