  Planning a time-optimal trajectory for aerial robots is critical in many
drone applications, such as rescue missions and package delivery, which have
been widely researched in recent years. However, it still involves several
challenges, particularly when it comes to incorporating special task
requirements into the planning as well as the aerial robot's dynamics. In this
work, we study a case where an aerial manipulator shall hand over a parcel from
a moving mobile robot in a time-optimal manner. Rather than setting up the
approach trajectory manually, which makes it difficult to determine the optimal
total travel time to accomplish the desired task within dynamic limits, we
propose an optimization framework, which combines discrete mechanics and
complementarity constraints (DMCC) together. In the proposed framework, the
system dynamics is constrained with the discrete variational Lagrangian
mechanics that provides reliable estimation results also according to our
experiments. The handover opportunities are automatically determined and
arranged based on the desired complementarity constraints. Finally, the
performance of the proposed framework is verified with numerical simulations
and hardware experiments with our self-designed aerial manipulators.
