Wireless communications is nowadays an important aspect of robotics. There are many applications in which a robot must move to a certain goal point while transmitting information through a wireless channel which depends on the particular trajectory chosen by the robot to reach the goal point. In this context, we develop a method to generate optimum trajectories which allow the robot to reach the goal point using little mechanical energy while transmitting as much data as possible. This is done by optimizing the trajectory (path and velocity profile) so that the robot consumes less energy while also offering good wireless channel conditions. We consider a realistic wireless channel model as well as a realistic dynamic model for the mobile robot (considered here to be a drone). Simulations results illustrate the merits of the proposed method.