Optimal control problems for mechanical systems arise in many applications and can be typically solved by numerical methods only. Approximated control strategies should maintain important properties of the original solution, though. This is why we focus on discrete mechanics to develop optimal control methods that are based on discrete variational principles in mechanics.
Theory and algorithms can be extended to hybrid mechanical systems in order to model impact and sudden changes in topology or in the environment. Motion Planning with Motion Primitives is another approach whereby inherent system structures, which have been extensively studied in geometric mechanics, can be exploited for the design of optimal control strategies.