  In swarm robotics, a set of robots has to perform a given task with specified
internal capabilities (model) and under a given adversarial scheduler. Relation
between a model $M_1$ under scheduler $S_1$, and that of a model $M_2$ under
scheduler $S_2$ can be of four different types: not less powerful, more
powerful, equivalent and orthogonal. In literature there are four main models
of robots with lights: $\mathcal{LUMI}$, where robots have the power of
observing the lights of all the robots, $\mathcal{FSTA}$ , where each robot can
see only its own light, $\mathcal{FCOM}$, where each robot can observe the
light of all other robots except its own and $\mathcal{OBLOT}$, where the
robots do not have any light. In this paper, we investigate the computational
power of $\mathcal{FSTA}$ and $\mathcal{FCOM}$ model under asynchronous
scheduler by comparing it with other model and scheduler combinations. Our main
focus is to understand and compare the power of persistent memory and explicit
communication in robots under asynchronous scheduler.
