  Approaching a set goal for a UAV comprises a trajectory plan and a controller
design (control after plan problems). The optimal trajectory (reference) is
calculated before being tracked with a proper controller. It is believed that
the quadrotor will follow the designed trajectory totally in the trajectory
plan process. However, the dynamic state error usually, for a mismatched
feed-forward, spoils this assumption, making the unwanted sacrifice in the
objective function defined in the trajectory plan process. We base the target
problem in this research on a second-order system model which widely exists in
the dynamics of vehicles. Specially, the unavoidable dynamic state error is
considered in the trajectory plan process, assuming the LQR without the
feed-forward is applied in the subsequent control after plan problems. The
Copenhagen Limit provides the possibility of estimating the dynamic state error
in an analytical solution. The trade-off results are provided in multiobjective
Pareto front solutions and the mapped pseudo Pareto fronts. We explore the
relationship between the controller and the corresponding pseudo Pareto fronts.
