Approximation Algorithms for Robot Tours in Random Fields with Guaranteed Estimation Accuracy

TL;DR

This paper develops approximation algorithms for robot sampling and touring in random fields, improving theoretical guarantees and simulation results while disproving a prior lower bound claim.

Contribution

It introduces new approximation algorithms for sample placement and shortest tours in convex environments, with enhanced guarantees and validation through simulations.

Findings

Improved approximation algorithms with better guarantees

Simulation results demonstrating algorithm effectiveness

Disproof of a previous lower bound claim

Abstract

We study the sample placement and shortest tour problem for robots tasked with mapping environmental phenomena modeled as stationary random fields. The objective is to minimize the resources used (samples or tour length) while guaranteeing estimation accuracy. We give approximation algorithms for both problems in convex environments. These improve previously known results, both in terms of theoretical guarantees and in simulations. In addition, we disprove an existing claim in the literature on a lower bound for a solution to the sample placement problem.