  Controllability, a basic property of various networked systems, has gained
profound theoretical applications in complex social, technological, biological,
and brain networks. Yet, little attention has been given to the control
trajectory (route), along which a controllable system can be controlled from
any initial to any final state, hampering the implementation of practical
control. Here we systematically uncover the fundamental relations between
control trajectory and several other key factors, such as the control distance
between initial and final states ($\delta$), number of driver nodes, and the
control time. The length ($\mathcal{L}$) and maximum distance to the initial
state ($\mathcal{R}$) are employed to quantify the locality and globality of
control trajectories. We analyze how the scaling behavior of the averaged
$\mathcal{L}$ and $\mathcal{R}$ changes with increasing $\delta$ for different
initial states. After showing the scaling behavior for each trajectory, we also
provide the distributions of $\mathcal{L}$ and $\mathcal{R}$. Further attention
is given to the control time $t_{f}$ and its influence on $\mathcal{L}$ and
$\mathcal{R}$. Our results provide comprehensive insights in understanding
control trajectories for complex networks, and pave the way to achieve
practical control in various real systems.
