Performance Analysis of Chemotaxis-Inspired Stochastic Controllers for Multi-Agent Coverage

Abstract

In this study, we analyze the performance of stochastic coverage controllers inspired by the chemotaxis of bacteria. The control algorithm of bacteria to generate the chemotaxis switches between forward movement and random rotation based on the difference between the current and previous concentration of a chemical. The considered coverage controllers mimic this algorithm, where bacteria and the chemical concentration are regarded as agents and the achieved degree of coverage, respectively. Because the coverage controllers operate similar to the control algorithm of bacteria, they are potentially suitable for molecular robots. Molecular robots, which consist of biomolecules, are recognized as a key component in the development of future medical systems based on micro-robots working inside the human body. However, the performance of the controllers has not yet been analyzed, and no theoretical guarantee of coverage completion has been provided. We address this problem by determining whether a performance index that quantifies the achieved degree of coverage increases over time for the feedback system. We first show that the performance index is characterized by the distance between agents under certain conditions. Using this result, we prove that the performance index increases with probability 1 under some conditions although the controllers are stochastic. This provides partial evidence for coverage completion, which makes the controllers more reliable. The analysis result is validated by numerical experiments.