Industrial robot manipulators are general-purpose machines used for industrial automation in order to increase productivity, flexibility, and product quality. Other reasons for using industrial robots are cost saving, and elimination of hazardous and unpleasant work. Robot motion control is a key competence for robot manufacturers, and the current development is focused on increasing the robot performance, reducing the robot cost, improving safety, and introducing new functionalities.  Therefore, there is a need to continuously improve the mathematical models and control methods in order to fulfil conflicting requirements, such as increased performance of a weight-reduced robot, with lower mechanical stiffness and more complicated vibration modes. One reason for this development of the robot mechanical structure is of course cost-reduction, but other benefits are also obtained, such as lower environmental impact, lower power consumption, improved dexterity, and higher safety. This thesis deals with different aspects of modeling and control of flexible, i.e., elastic, manipulators. For an accurate description of a modern industrial manipulator, this thesis shows that the traditional flexible joint model, described in literature, is not sufficient. An improved model where the elasticity is described by a number of localized multidimensional spring-damper pairs is therefore proposed. This model is called the extended flexible joint model. The main contributions of this work are the design and analysis of identification methods, and of inverse dynamics control methods, for the extended flexible joint model. The proposed identification method is a frequency-domain non-linear gray-box method, which is evaluated by the identification of a modern six-axes robot manipulator. The identified model gives a good description of the global behavior of this robot. The inverse dynamics problem is discussed, and a solution methodology is proposed. This methodology is based on the solution of a differential algebraic equation (DAE). The inverse dynamics solution is then used for feedforward control of both a simulated manipulator and of a real robot manipulator. The last part of this work concerns feedback control. First, a model-based nonlinear feedback control (feedback linearization) is evaluated and compared to a model-based feedforward control algorithm. Finally, two benchmark problems for robust feedback control of a flexible manipulator are presented and some proposed solutions are analyzed.

The objective of this study is to develop a high-fidelity physics-based flexible tire model that can be fully integrated into multibody dynamics computer algorithms for use in on-road and off-road vehicle dynamics simulation without ad-hoc co-simulation techniques. Despite the fact detailed finite element tire models using explicit finite element software have been widely utilized for structural design of tires by tire manufactures, it is recognized in the tire industry that existing state-of-the-art explicit finite element tire models are not capable of predicting the transient tire force characteristics accurately under severe vehicle maneuvering conditions due to the numerical instability that is essentially inevitable for explicit finite element procedures for severe loading scenarios and the lack of transient (dynamic) tire friction model suited for FE tire models. Furthermore, to integrate the deformable tire models into multibody full vehicle simulation, co-simulation technique could be an option for commercial software. However, there exist various challenges in co-simulation for the transient vehicle maneuvering simulation in terms of numerical stability and computational efficiency. The transient tire dynamics involves rapid changes in contact forces due to the abrupt braking and steering input, thus use of co-simulation requires very small step size to ensure the numerical stability and energy balance between two separate simulation using different solvers. In order to address these essential and challenging issues on the high-fidelity flexible tire model suited for multibody vehicle dynamics simulation, a physics-based tire model using the flexible multibody dynamics approach is proposed in this study. To this end, a continuum mechanics based shear deformable laminated composite shell element is developed based on the finite element absolute nodal coordinate formulation for modeling the complex fiber reinforced rubber tire structure. The assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches are introduced for alleviating element lockings exhibited in the element. Use of the concept of the absolute nodal coordinate formulation leads to various advantages for tire dynamics simulation in that (1) constant mass matrix can be obtained for fully nonlinear dynamics simulation; (2) exact modeling of rigid body motion is ensured when strains are zero; and (3) non-incremental solution procedure utilized in the general multibody dynamics computer algorithm can be directly applied without specialized updating schemes for finite rotations. Using the proposed shear deformable laminated composite shell element, a physics-based flexible tire model is developed. To account for the transient tire friction characteristics including the friction-induced hysteresis that appears in severe maneuvering conditions, the distributed parameter LuGre tire friction model is integrated into the flexible tire model. To this end, the contact patch predicted by the structural tire model is discretized into small strips across the tire width, and then each strip is further discretized into small elements to convert the partial differential equations of the LuGre tire friction model to the set of first-order ordinary differential equations. By doing so, the structural deformation of the flexible tire model and the LuGre tire friction force model are dynamically coupled in the final form of the equations, and these equations are integrated simultaneously forward in time at every time step. Furthermore, a systematic and automated procedure for parameter identification of LuGre tire friction model is developed. Since several fitting parameters are introduced to account for the nonlinear friction characteristics, the correlation of the model parameters with physical quantities are not clear, making the parameter identification of the LuGre tire friction model difficult. In the procedure developed in this study, friction parameters in terms of slip-dependent friction characteristics and adhesion parameter are estimated separately, and then all the parameters are identified using the nonlinear least squares fitting. Furthermore, the modified friction characteristic curve function is proposed for wet road conditions, in which the linear decay in friction is exhibited in the large slip velocity range. It is shown that use of the proposed numerical procedure leads to an accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Furthermore, the fundamental tire properties including the load-deflection curve, the contact patch lengths, contact pressure distributions, and natural frequencies are validated against the test data. Several numerical examples for hard braking and cornering simulation are presented to demonstrate capabilities of the physics-based flexible tire model developed in this study. Finally, the physics-based flexible tire model is further extended for application to off-road mobility simulation. To this end, a locking-free 9-node brick element with the curvature coordinates at the center node is developed and justified for use in modeling a continuum soil with the capped Drucker-Prager failure criterion. Multiplicative finite strain plasticity theory is utilized to consider the large soil deformation exhibited in the tire/soil interaction simulation. In order to identify soil parameters including cohesion and friction angle, the triaxial soil test is conducted. Using the soil parameters identified including the plastic hardening parameters by the compression soil test, the continuum soil model developed is validated against the test data. Use of the high-fidelity physics-based tire/soil simulation model in off-road mobility simulation, however, leads to a very large computational model to consider a wide area of terrains. Thus, the computational cost dramatically increases as the size of the soil model increases. To address this issue, the component soil model is proposed such that soil elements far behind the tire can be removed from the equations of motion sequentially, and then new soil elements are added to the portion that the tire is heading to. That is, the soil behavior only in the vicinity of the rolling tire is solved in order to reduce the overall model dimensionality associated with the finite element soil model. It is shown that use of the component soil model leads to a significant reduction in computational time while ensuring the accuracy, making the use of the physics-based deformable tire/soil simulation capability feasible in off-road mobility simulation.

Large displacement and large strain problems of mechanical systems can be solved mainly by four methods. These are Floating Frame of Reference, Incremental Finite Element, Large Rotation Vector and Absolute Nodal Coordinate Formulations (ANCF). Due to exact rigid body representation, simple mass matrix structure and non-incremental formulation, ANCF is more convenient in analyzing flexible multibody systems. However, it is limited to problems with regular boundaries, currently. The aim of the thesis is to improve the current ANCF in order to handle various problems with irregular boundaries. For this purpose, firstly meshfree ANCF has been developed to analyze flexible multibody systems. Verification of the developed meshfree formulation has been performed for beam type structures and accurate results have been obtained. Then, &ldquo / ANCF with Virtual Element Mapping Method&rdquo / has been proposed to overcome the boundary problems of the current formulations. The proposed method has been implemented to plane stress, plane strain, plate/shell and 3D solid finite elements. Verification of the proposed method has been performed by using the patch test problems available in the literature. Besides, it has been verified by various flexible multibody problems with large deformations. Additionally, shape function polynomials for thin plate assumption have been derived. It is observed that developed formulations and methods can be useful not only for flexible multibody systems but also for structural mechanics problems subjected to large deformations and/or rotations. The proposed methods and formulations are more efficient than the current formulations in the literature due to extended shape limits of finite elements.

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis presents a comprehensive study of the effects of material, geometric and operational parameters on flat belt-drives steady-state belt stresses, belt slip, and belt-drive efficiency. The belt stresses include: belt rubber shear, normal, axial and lateral stresses; reinforcements tension force; and tangential and normal belt-pulley contact stresses. Belt slip is measured using the driven over driver pulleys’ angular velocity ratio. Each parameter was varied over a range to understand its impact on the steady-state belt-drive response. The material parameters studied are belt axial stiffness and damping, belt bending stiffness and damping, and belt-pulley friction coefficient. The geometric parameters studied are pulley center distance, pulleys diameter ratio, and belt thickness. The operational parameters studied are the driver pulley angular velocity and the driven pulley opposing torque (load). A high-fidelity flexible multibody dynamics parametric model of a two-pulley belt-drive system was created using a commercial multibody dynamics code. In the model the belt’s rubber matrix is represented using three-dimensional brick elements and the belt’s reinforcements are represented using one dimensional beam elements at the top surface of the belt. An asperity-based Coulomb friction model is used for the friction forces between the pulley and belt. The pulleys are modeled as rigid bodies with a cylindrical contact surface. The equations of motion are integrated using an explicit solution procedure. Unlike prior models which use one-dimensional truss or beam elements for the belt, the present model uses a three-dimensional belt model which introduces the effect of the thickness of the belt rubber matrix (modeled using brick elements). This enables a more accurate prediction of the belt stresses and slip than prior models. This thesis resolves in more details the complex stick-slip friction behavior of an axially flexible belt coupled with the shear effects of a flexible rubber cushion and at the same time shows the effect of the main system parameters on this stick-slip behavior. Some of the important conclusions of the thesis include: (1) the driver pulley has two distinct contact zones - a negative traction zone and a positive traction zone - while only one traction zone is present over the driven pulley; (2) the width of the negative traction zone on the driver pulley increases with the belt-pulley coefficient of friction and decreases with the belt axial stiffness; (3) the maximum belt tension and normal contact stress occur on the driver pulley and increase with the belt thickness, belt axial stiffness, and coefficient of friction; (4) belt-drive energy efficiency increases with the belt axial stiffness, and decreases with belt thickness, belt bending damping, belt operating speed, and operating torque load. The belt-drive modeling methodology presented in this thesis which enables accurate prediction of the belt stresses and slip can in turn be used to more accurately predict the fatigue life, wear life, and energy efficiency of belt-drives.

This thesis is concerned with the efficient numerical simulation of finite element based flexible multibody systems. Scaling operations are systematically applied to the governing index-3 differential algebraic equations in order to solve the problem of ill conditioning for small time step sizes. The importance of augmented Lagrangian terms is demonstrated. The use of fast sparse solvers is justified for the solution of the linearized equations of motion resulting in significant savings of computational costs. Three time stepping schemes for the integration of the governing equations of flexible multibody systems are discussed in detail. These schemes are the two-stage Radau IIA scheme, the energy decaying scheme, and the generalized-α method. Their formulations are adapted to the specific structure of the governing equations of flexible multibody systems. The efficiency of the time integration schemes is comprehensively evaluated on a series of test problems. Formulations for structural and constraint elements are reviewed and the problem of interpolation of finite rotations in geometrically exact structural elements is revisited. This results in the development of a new improved interpolation algorithm, which preserves the objectivity of the strain field and guarantees stable simulations in the presence of arbitrarily large rotations. Finally, strategies for the spatial discretization of beams in the presence of steep variations in cross-sectional properties are developed. These strategies reduce the number of degrees of freedom needed to accurately analyze beams with discontinuous properties, resulting in improved computational efficiency.

Les systèmes d'entraînement de bandes flexibles sont utilisés dans la production d'une très grande variété de produits du quotidien mais également dans la métallurgie et dorénavant pour la production des nouvelles technologies. L'amélioration des systèmes industriels d'entraînement de bandes est un problème difficile car ils sont de grande dimension, non-linéaires, à paramètres variant et incertains. Ils possèdent un fort couplage entre les différentes parties (mécanique et commande) à cause de la bande qui relie les éléments. Il faut donc améliorer la chaîne de production par une approche pluridisciplinaire. Les objectifs sont de maîtriser les paramètres clés de ces systèmes afin de garantir les cadences de production et les précisions demandées de plus en plus importantes. Il faut également réduire les défauts les plus récurrents, notamment les plis de bande. Or jusqu'à présent seuls des modèles 1D étaient utilisés. Ils sont indispensables pour la synthèse de commande et les études fréquentielles mais ne permettent pas d'étudier des phénomènes complexes tels que les plis de bande. Une nouvelle approche d'étude de ces systèmes est développée. Dans un premier temps, des améliorations de structures de commandes sont proposées. Dans un second temps un modèle 3D par éléments finis utilisant un algorithme de dynamique multicorps flexibles est développé et utilisé pour étudier les plis de bande par comparaison à la théorie classique de prédiction de ces défauts. Dans un troisième temps un simulateur complet est développé comprenant le modèle 3D mécanique par élément finis couplé à la partie commande (co-simulation). / Roll-to-Roll systems are used in the manufacturing of a wide variety of everyday products as well as in metallurgy and for the manufacturing of new technologies. The improvement of Roll-to-Roll systems is a difficult problem because they are large, non-linear, with varying and uncertain parameters. They have a coupling between the different parts (mechanical and control) with the help of the web connecting the elements. It is therefore necessary to improve the process line through a multidisciplinary approach. The objectives are to master the key parameters of these systems in order to guarantee the manufacturing rates and the more important accuracies requested. It is also necessary to reduce or remove the most recurring defects such as web wrinkles. Until now, only 1D models were used. They are essential for control synthesis and frequency studies but they do not allow to study complex phenomena such as web wrinkles. A new approach for studying these systems is developed. First, improvements of control structures are proposed. Secondly, a 3D finite element model using a flexible multibody dynamics algorithm is developed, used in this work to study web wrinkles and compared to the classical prediction theory of these defects. Finally, a complete simulator is developed including the mechanical 3D model by finite element coupled to the control part (co-simulation).