Environmental Sensing Options for Robot Teams: A Computational Complexity Perspective

TL;DR

This paper compares the computational complexity of visual and scalar-field sensing in robot teams, revealing both intractability in general and tractability in restricted cases within a formal 2D grid model.

Contribution

It provides the first analysis of the computational complexity of verifying and designing robot teams using visual and scalar-field sensing in a formal setting.

Findings

Both sensing types lead to polynomial-time intractable problems in general.

Restricted scenarios can make these problems tractable.

Verification and design problems share similar complexity patterns.

Abstract

Visual and scalar-field (e.g., chemical) sensing are two of the options robot teams can use to perceive their environments when performing tasks. We give the first comparison of the computational characteristic of visual and scalar-field sensing, phrased in terms of the computational complexities of verifying and designing teams of robots to efficiently and robustly perform distributed construction tasks. This is done relative a basic model in which teams of robots with deterministic finite-state controllers operate in a synchronous error-free manner in 2D grid-based environments. Our results show that for both types of sensing, all of our problems are polynomial-time intractable in general and remain intractable under a variety of restrictions on parameters characterizing robot controllers, teams, and environments. That being said, these results also include restricted situations for each of our problems in which those problems are effectively polynomial-time tractable. Though there are some differences, our results suggest that (at least in this stage of our investigation) verification and design problems relative to visual and scalar-field sensing have roughly the same patterns and types of tractability and intractability results.