On the Computational Power of Energy-Constrained Mobile Robots: Algorithms and Cross-Model Analysis

TL;DR

This paper investigates how energy constraints affect the computational capabilities of autonomous mobile robots across different models, revealing that energy limitations can sometimes enhance computational power.

Contribution

It provides a comprehensive analysis of the computational relationships between energy-constrained and unconstrained robots across four models, including algorithms and characterizations.

Findings

In LUMI, energy constraints do not reduce computational power.

In other models, energy constraints can increase computational capabilities.

The paper offers algorithms enabling energy-limited robots to simulate unlimited-energy protocols.

Abstract

We consider distributed systems of identical autonomous computational entities, called robots, moving and operating in the plane in synchronous Look-Compute-Move (LCM) cycles. The algorithmic capabilities of these systems have been extensively investigated in the literature under four distinct models (OBLOT, FSTA, FCOM, LUMI), each identifying different levels of memory persistence and communication capabilities of the robots. Despite their differences, they all always assume that robots have unlimited amounts of energy. In this paper, we remove this assumption and start the study of the computational capabilities of robots whose energy is limited, albeit renewable. We first study the impact that memory persistence and communication capabilities have on the computational power of such energy-constrained systems of robots; we do so by analyzing the computational relationship between the four models under this energy constraint. We provide a complete characterization of this relationship. We then study the difference in computational power caused by the energy restriction and provide a complete characterization of the relationship between energy-constrained and unrestricted robots in each model. We prove that within LUMI there is no difference; an integral part of the proof is the design and analysis of an algorithm that in LUMI allows energy-constrained robots to execute correctly any protocol for robots with unlimited energy. We then show the (apparently counterintuitive) result that in all other models, the energy constraint actually provides the robots with a computational advantage.