  We consider distributed systems of identical autonomous computational
entities, called robots, moving and operating in the plane in synchronous
Look-Compute-Move (LCM) cycles. The algorithmic capabilities of these systems
have been extensively investigated in the literature under four distinct models
(OBLOT, FSTA, FCOM, LUMI), each identifying different levels of memory
persistence and communication capabilities of the robots. Despite their
differences, they all always assume that robots have unlimited amounts of
energy.
  In this paper, we remove this assumption and start the study of the
computational capabilities of robots whose energy is limited, albeit renewable.
We first study the impact that memory persistence and communication
capabilities have on the computational power of such energy-constrained systems
of robots; we do so by analyzing the computational relationship between the
four models under this energy constraint. We provide a complete
characterization of this relationship.
  We then study the difference in computational power caused by the energy
restriction and provide a complete characterization of the relationship between
energy-constrained and unrestricted robots in each model. We prove that within
LUMI there is no difference; an integral part of the proof is the design and
analysis of an algorithm that in LUMI allows energy-constrained robots to
execute correctly any protocol for robots with unlimited energy. We then show
the (apparently counterintuitive) result that in all other models, the energy
constraint actually provides the robots with a computational advantage.
