Research on distributed computing by a team of identical mobile computational entities, called robots, operating in a Euclidean space in Look-Compute-Move (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 LCM cycles) whose adversarial power is in between those two. We ask the question: what is the computational relationship between a model M₁ under adversarial scheduler K₁ (M₁(K₁)) and a model M₂ under scheduler K₂ (M₂(K₂))? For example, are the robots in M₁(K₁) more powerful (i.e., they can solve more problems) than those in M₂(K₂)?

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.