On the fundamental limitations of performance for distributed decision-making in robotic networks

TL;DR

This paper investigates the fundamental limitations in performance metrics such as time and message complexity for distributed decision-making tasks in robotic networks, encompassing consensus, optimization, and voting problems.

Contribution

It introduces a formal model based on I/O automata for distributed computation in robotic networks and derives bounds on performance metrics, bridging computer science and control theory approaches.

Findings

Established bounds on time, message, and byte complexity for distributed decision problems.

Compared various approaches to assess their relative performance.

Provided insights into the relation between computer science and control community tools.

Abstract

This paper studies fundamental limitations of performance for distributed decision-making in robotic networks. The class of decision-making problems we consider encompasses a number of prototypical problems such as average-based consensus as well as distributed optimization, leader election, majority voting, MAX, MIN, and logical formulas. We first propose a formal model for distributed computation on robotic networks that is based on the concept of I/O automata and is inspired by the Computer Science literature on distributed computing clusters. Then, we present a number of bounds on time, message, and byte complexity, which we use to discuss the relative performance of a number of approaches for distributed decision-making. From a methodological standpoint, our work sheds light on the relation between the tools developed by the Computer Science and Controls communities on the topic of distributed algorithms.