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