This paper presents a non-linear optimization method for trajectory planning of tethered aerial robots. Particularly, the paper addresses the planning problem of an unmanned aerial vehicle (UAV) linked to an unmanned ground vehicle (UGV) by means of a tether. The result is a collision-free trajectory for UAV and tether, assuming the UGV position is static. The optimizer takes into account constraints related to the UAV, UGV and tether positions, obstacles and temporal aspects of the motion such as limited robot velocities and accelerations, and finally the tether state, which is not required to be tense. The problem is formulated in a weighted multi-objective optimization framework. Results from simulated scenarios demonstrate that the approach is able to generate obstacle-free and smooth trajectories for the UAV and tether.