In this study, we explore efficient simulation implementations to demonstrate computational equivalence across various models of autonomous mobile robot swarms. Our focus is on Rsynch, a scheduler designed for energy-restricted robots, which falls between Fsynch and Ssynch. We propose efficient protocols for simulating \(n(\ge 2)\) luminous ( \({\mathcal {LUMI}}\) ) robots operating in Rsynch using \({\mathcal {LUMI}}\) robots in Ssynch or Asynch. Our contributions are twofold. (1) We introduce protocols that simulate \({\mathcal {LUMI}}\) robots in Rsynch using 4k colors in Ssynch and 5k colors in Asynch, for algorithms that employ k colors. This approach, based on the simulation mechanism in [9], notably reduces the number of colors needed for Ssynch simulations of Rsynch, compared to previous efforts. Meanwhile, the color requirement for Asynch simulations remains consistent with previous Asynch simulations of Ssynch, facilitating the simulation of Rsynch in Asynch. (2) We establish that for \(n=2\) , Rsynch can be optimally simulated in Asynch using a minimal number of colors. Additionally, we confirm that all of our proposed simulation protocols can become self-stabilizing, ensuring functionality from any initial configuration without adding colors.