Two-Robot Computational Landscape: A Complete Characterization of Model Power in Minimal Mobile Robot Systems

2025-12-27

AI Summary

Characterizing the computational power of two autonomous mobile robots under the Look-Compute-Move paradigm across diverse robot models (OBLOT, FSTA, FCOM, LUMI) and scheduler types (FSYNCH, SSYNCH, ASYNCH, and their atomic variants). Method: We introduce a simulation-free, unified constructive analysis framework to systematically compare expressive power across all model–scheduler combinations. Contribution/Results: We establish, for the first time, the equivalence of FSTA^F and LUMI^F under fully synchronous scheduling, and prove the orthogonality (i.e., incomparability) of FSTA and FCOM. We provide a complete characterization—covering all equivalences and separations—among all 16 model–scheduler pairs. This yields the first precise, exhaustive hierarchy of computational capabilities for two-robot systems. Our results reveal the fundamental coupling among synchrony, memory, and communication in minimal-scale distributed coordination and correct the applicability boundary of general n-robot theorems when n = 2.

Technology Category

• Planning, Routing, and Scheduling: Model-Based Reasoning
• Intelligent Robots: Multi-Robot Systems
• Multiagent Systems: Coordination and Collaboration

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

The computational power of autonomous mobile robots under the Look-Compute-Move (LCM) model has been widely studied through an extensive hierarchy of robot models defined by the presence of memory, communication, and synchrony assumptions. While the general n-robot landscape has been largely established, the exact structure for two robots has remained unresolved. This paper presents the first complete characterization of the computational power of two autonomous robots across all major models, namely OBLOT, FSTA, FCOM, and LUMI, under the full spectrum of schedulers (FSYNCH, SSYNCH, ASYNCH, and their atomic variants). Our results reveal a landscape that fundamentally differs from the general case. Most notably, we prove that FSTA^F and LUMI^F coincide under full synchrony, a surprising collapse indicating that perfect synchrony can substitute both memory and communication when only two robots exist. We also show that FSTA and FCOM are orthogonal: there exists a problem solvable in the weakest communication model but impossible even in the strongest finite-state model, completing the bidirectional incomparability. All equivalence and separation results are derived through a novel simulation-free method, providing a unified and constructive view of the two-robot hierarchy. This yields the first complete and exact computational landscape for two robots, highlighting the intrinsic challenges of coordination at the minimal scale.

Problem

• Characterize computational power of two autonomous mobile robots
• Compare robot models OBLOT, FSTA, FCOM, LUMI across schedulers
• Determine equivalence and separation in two-robot coordination hierarchy

Innovation

• Complete characterization of two-robot computational power
• Simulation-free method for equivalence and separation results
• Proving synchrony substitutes memory and communication for two robots