  We present a reformulation of a contact-implicit optimization (CIO) approach
that computes optimal trajectories for rigid-body systems in contact-rich
settings. A hard-contact model is assumed, and the unilateral constraints are
imposed in the form of complementarity conditions. Newton's impact law is
adopted for enhanced physical correctness. The optimal control problem is
formulated as a multi-staged program through a multiple-shooting scheme. This
problem structure is exploited within the FORCES Pro framework to retrieve
optimal motion plans, contact sequences and control inputs with increased
computational efficiency. We investigate our method on a variety of dynamic
object manipulation tasks, performed by a six degrees of freedom robot. The
dynamic feasibility of the optimal trajectories, as well as the repeatability
and accuracy of the task-satisfaction are verified through simulations and real
hardware experiments on one of the manipulation problems.
