The goal of this thesis is to explore different control strategies to execute rhythmic movements. This issue is covered both with design perspectives (implementation in a robot) and analysis perspectives. Indeed we aim at analyzing both our robot behavior, and the behavior of human subjects executing the same task. Interesting parallels between these data sets are raised, illustrating for instance the ubiquitous trade-off of control theory between performance and robustness. / L'objectif de cette thèse est d'explorer différentes stratégies d'exécution des mouvements rythmiques. Cet objectif est couvert à la fois dans des perspectives d'implémentation (sur un robot) et d'analyse. En effet, nous souhaitons analyser à la fois le comportement de notre robot, et le comportement de sujets humains exécutant la même tâche. Des parallèles intéressants, entre les deux ensemble de données, sont proposés et illustrent, par exemple, le compromis entre la robustesse et la performance, souvent utilisé dans la thèorie du contrôle.

A mechatronic system is an assembly of technological components, such as a mechanism, sensors, actuators, and a control unit. Recently, a number of researchers and industrial manufacturers have highlighted the potential advantages of lightweight parallel mechanisms with respect to the accuracy, dynamic performances, construction cost, and transportability issues. The design of a mechatronic system with such a mechanism requires a multidisciplinary approach, where the mechanical deformations have to be considered. This thesis proposes two original contributions in this framework. (i) First, a modular and systematic method is developed for the integrated simulation of mechatronic systems, which accounts for the strongly coupled dynamics of the mechanical and non-mechanical components. The equations of motion are formulated using the nonlinear Finite Element approach for the mechanism, and the block diagram language for the control system. The time integration algorithm relies on the generalized-alpha method, known in structural dynamics. Hence, well-defined concepts from mechanics and from system dynamics are combined in a unified formulation, with guaranteed convergence and stability properties. Several applications are treated in the fields of robotics and vehicle dynamics. (ii) Usual methods in flexible multibody dynamics lead to complex nonlinear models, not really suitable for control design. Therefore, a systematic nonlinear model reduction technique is presented, which transforms an initial high-order Finite Element model into a low-order and explicit model. The order reduction is obtained using the original concept of Global Modal Parameterization: the motion of the assembled mechanism is described in terms of rigid and flexible modes, which have a global physical interpretation in the configuration space. The reduction procedure involves the component-mode technique and an approximation strategy in the configuration space. Two examples are presented: a four-bar mechanism, and a parallel kinematic machine-tool. Finally, both simulation and modeling tools are exploited for the dynamic analysis and the control design of an experimental lightweight manipulator with hydraulic actuators. A Finite Element model is first constructed and validated with experimental data. A reduced model is derived, and an active vibration controller is designed on this basis. The simulation of the closed-loop mechatronic system predicts remarkable performances. The model-based controller is also implemented on the test-bed, and the experimental results agree with the simulation results. The performances and the other advantages of the control strategy demonstrate the relevance of our developments in mechatronics.