Coherent steps of mobile sensing agents in Gaussian scalar fields

This paper develops fundamental theoretical results to describe exploration behaviors of mobile sensing agents in a noisy scalar field. We introduce concepts of coherent steps and incoherent steps of the sensing agents and prove that a step of an agent is coherent if and only if the probability of a false-walk is less than a threshold determined by the explorable probability. Among all possible coherent steps, gradient climbing and level curve tracking are the steps that can achieve local supremum explorable probabilities. We also prove that by increasing the number of agents that are collaborating, the incoherent steps of the collaborating groups can become coherent. Based on estimates of the noise variance, we propose an algorithm that estimates the minimum number of agents required to guarantee coherent steps and implement a strategy that allows the sensing agents to self-organize into groups with the estimated minimum number of agents. Results are demonstrated in multi-robot experiments.