Explorability of a turbulent scalar field

Abstract

In this paper we extend the concept of explorability of noisy scalar fields to turbulent scalar fields. Since turbulent fields are prone to sporadic measurement, we use expected value of rate of measurements to estimate the rate of measurement at a location and use this estimate to define explorability of a turbulent scalar field. We define the notion of coherent steps in a turbulent field and prove that if the turbulent field is locally explorable the step taken by the robot will be coherent. We also present a method to compute the Cumulative Distribution Function of the error in estimation of rate of measurement and then show that the probability of a coherent step is inversely proportional to the variance in estimation error if the error has Gaussian distribution.