  Research on distributed computing by a team of identical mobile computational
entities, called robots, operating in a Euclidean space in
$\mathit{Look}$-$\mathit{Compute}$-$\mathit{Move}$ ($\mathit{LCM}$) cycles, has
recently focused on better understanding how the computational power of robots
depends on the interplay between their internal capabilities (i.e., persistent
memory, communication), captured by the four standard computational models
(OBLOT, LUMI, FSTA, and FCOM) and the conditions imposed by the external
environment, controlling the activation of the robots and their synchronization
of their activities, perceived and modeled as an adversarial scheduler.
  We consider a set of adversarial asynchronous schedulers ranging from the
classical semi-synchronous (SSYNCH) and fully asynchronous (ASYNCH) settings,
including schedulers (emerging when studying the atomicity of the combination
of operations in the $\mathit{LCM}$ cycles) whose adversarial power is in
between those two. We ask the question: what is the computational relationship
between a model $M_1$ under adversarial scheduler $K_1$ ($M_1(K_1)$) and a
model $M_2$ under scheduler $K_2$ ($M_2(K_2)$)? For example, are the robots in
$M_1(K_1)$ more powerful (i.e., they can solve more problems) than those in
$M_2(K_2)$?
  We answer all these questions by providing, through cross-model analysis, a
complete characterization of the computational relationship between the power
of the four models of robots under the considered asynchronous schedulers. In
this process, we also provide qualified answers to several open questions,
including the outstanding one on the proper dominance of SSYNCH over ASYNCH in
the case of unrestricted visibility.
