Recursive Averaging with Application to Bio-Inspired 3D Source Seeking

TL;DR

This paper develops a recursive averaging method for oscillatory systems and introduces a bio-inspired 3D source seeking algorithm for rigid bodies, proving its stability through advanced mathematical analysis.

Contribution

It presents a new recursive averaging approach for multi-scale oscillatory systems and a novel bio-inspired 3D source seeking algorithm with proven stability.

Findings

Convergence of oscillatory system trajectories to an averaged system.

Development of a practical stability proof for the source seeking algorithm.

Integration of averaging and singular perturbation techniques for stability analysis.

Abstract

We analyze a class of high-amplitude, high-frequency oscillatory systems in which periodicity occurs on two distinct time scales and establish the convergence of its trajectories to a suitably averaged system by recursively applying the averaging theorem. Moreover, we introduce a novel bio-inspired 3D source seeking algorithm for rigid bodies with a collocated sensor and prove its practical stability under typical assumptions on the source signal strength field by combining our averaging results with singular perturbation.