Modeling and optimal control of multibody systems with intermittent contacts

This thesis focuses on the application of numerical optimal control methods to the trajectory planning of multibody systems (MBS). The trajectory planning problem consists in determining a suitable sequence of control actions to be taken in order for a dynamic system to accomplish a specified task. The difficulties in planning trajectories for MBS are mainly due to their complex, nonlinear, fast dynamics. Moreover, in contexts such as robotic locomotion or manipulation, in which the system necessarily has to interact with the surrounding environment through intermittent contact forces, additional issues arise, due to the discontinuities caused by impacts and friction. Numerical optimal control offers the possibility to handle significantly complex models and, most notably, to exploit the richness of their dynamics in the accomplishment of the prescribed task. The thesis aims to investigate the modeling of the aforementioned complex systems, as well as their interactions with the environment, in order for the resulting model to be suitably dealt with by numerical optimal control techniques. The application of such methods to several benchmark systems is presented, that share the feature of being not easily - or at least not effectively - controllable by means other than numerical. Finally, the thesis addresses issues related to the presence of uncertainties that might compromise the applicability of the planned control trajectories to a real system. Rather than traditional control strategies based on feedback, alternative strategies are investigated that rely on a stochastic model of the disturbance in order to include considerations on its effects in the trajectory optimization problem. Such strategies allow to plan trajectories that provide certain guarantees of stability and robustness in the presence of uncertainties. Specifically, the applicability of an already existing framework for robust optimal control of periodic nonlinear system in general was extended to MBS with intermittent contacts.