—For the first time, the problem of optimizing energy for communication and motion is investigated. We consider a single mobile robot with continuous high bandwidth wireless communication, e.g. caused by a multimedia application like video surveillance. This robot is connected to a radio base station and moves with constant speed from a given starting point on the plane to a target point. The task is to find the best path such that the energy consumption for mobility and the communication is optimized. This is motivated by the fact that the energy consumption of radio devices increases polynomially (at least to the power of two) with the transmission distance. We introduce efficient approximation algorithms finding the optimal path given the starting point, the target point and the position of the radio stations. We exemplify the influence of the communication cost by a starting scenario with one radio station. We study the performance of the proposed algorithm in simulation, co...