Summary

This paper introduces some information-theoretic measures (not in the measure theoretic sense) that relates to dynamic coverage control and informative path planning. Their novel contribution is the introduction of somer metric called Clarity.

Introduction

The paper begins by introducing prior/relevant works. They note that these methods are useful but fail to address whether information can be gathered in the first place. The main objective of the paper is then stated: > Given a platform (e.g. a robot) with onboard sensors, and an environment in which information is to be collected: > 1. Does the overall system have sufficient actuation sensing capabilities to gather information in a specified time? > 2. What are the optimal control strategies to collect the information?

This paper’s two main contributions are the introduction of Clarity and perceivability.

Clarity

Definitions & Theorems

We begin by defining what a random variable is, then defining differential entropy. We then get our first novel contribution which is the definition of clarity: Clarity We then go on to define some properties of clarity: Clarity

Then, since in any information gathering task, our ultimate goal is to minimize our estimation error. Given some rv $X$ and it’s estimate $\hat{X}$ the expected estimation error is $$E_{}\left[ (X-\hat{X})^{2} \right]=D(X,\hat{X})$$ or the MSE Distortion. We then obtain a result that bounds the the expected MSE distortion: Clarity We then begin to explore the connection between this and coverage control:

Connection between Clarity and Dynamic Coverage Control