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

We analyze a class of high-frequency, high-amplitude 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 higher-order averaging. Moreover, we introduce a novel bio-inspired 3D source seeking algorithm for rigid bodies equipped 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.