Overactuated systems coordination

The economic growth inherent to our nowadays society pushes the industries toward better performances. In the mechatronic context, the increasing competition results in more and more stringent specifications. Thus, the multiple objectives to track become hard to achieve without compromises. A potential interesting solution to this problematic is overactuation, in the sense that, the considered system has more actuated degrees of freedom than the minimal number required to realize a task. Indeed, overactuation enables flexible and efficient responses to a high variety of tasks. Moreover, the coordinated combination of different subsystems enables both to combine their advantages and to cancel their disadvantages. However, the successful coordination of the supplementary degrees of freedom at our disposal, thanks to overactuation, is not trivial. As a matter of fact, the problem of unpredictable response of overactuated systems to a periodic excitation can be particularly critical. Furthermore, the flexibility brought by the overactuation is to be used efficiently in order to justify its corresponding complexity and higher costs. In this sense, the tracking of multiple simultaneous objectives are clearly enabled by the overactuation and thus constitutes a clear motivation for such a solution. As a consequence, the constructive coordination of overactuated systems, which can be very difficult, is very important to achieve stringent objectives. This thesis aims at contributing to the improvement of the coordination of such systems. In this context, three axis of research are considered: differential geometry, potential functions and closed-loop control. Each of these axis is to be taken as a separate insight on the overall coordination of overactuated systems. On the one hand, the formalism of differential geometry enables a solution to the unpredictability problem raised here above. An intelligent parameterization of the solution space to a periodic task enforces the predictability of the subsystem responses. Indeed, the periodicity of the task is transferred to the latter subsystem responses, thanks to an adequate coordination scheme. On the second hand, potential functions enable the coordination of multiple simultaneous objectives to track. A clear hierarchy in the tasks priority is achieved through their successive projections into reduced orthogonal subspaces. Moreover, the previously mentioned predictability problem is also re-examined in this context. Finally, in the frame of an international project in collaboration with the European Southern Observatory (ESO), an opto-mecatronic overactuated system, called Differential Delay Line, enables the consideration of closed-loop coordination. The successful coordination of the subsystems of the Differential Delay Line, combining their intrinsic advantages, is the key control-element ensuring the achievement of the stringent requirements. This thesis demonstrates that a constructive coordination of the supplementary degrees of freedom of overactuated systems enables to achieve, at least partly, the stringent requirements of nowadays mechatronics.