Mobile Energy Harvesting Nodes: Offline and Online Optimal Policies

We consider a mobile energy harvesting transmitter where movement is motivated by trying to find better energy harvesting locations. Movement comes with an energy cost expenditure, and hence there exists a throughput-movement tradeoff. On one hand, the transmitter may opt not to move and use all its available energy for transmission; on the other hand, it can choose to move to a potentially better location, spending some of its available energy during the movement process, and yet harvest larger amounts of energy at the new location and achieve higher throughput. In this paper, we characterize this tradeoff by designing throughput optimal power allocation policies subject to energy causality constraints and moving costs. In our setup, the transmitter moves along a straight line, where two energy sources are located at the opposite ends of the line. We first study the offline version of this problem where the goal is to maximize the throughput by a given deadline. We find a closed form solution for the case of single energy arrival at each source, and provide an iterative solution for the case of multiple energy arrivals. Then, we study the online version of this problem with independent and identically distributed (i.i.d.) energy arrivals at each source, and the goal is to maximize the long term average throughput. We propose an optimal move-then-transmit scheme where the transmitter first moves towards the source with higher mean energy arrival, stays at that source, and then starts transmission.