A Functional Subnetwork Approach to Multistate Central Pattern Generator Phase Difference Control

Abstract

Central pattern generators (CPGs) are ubiquitous neural circuits that contribute to an eclectic collection of rhythmic behaviors across an equally diverse assortment of animal species. Due to their prominent role in many neuromechanical phenomena, numerous bioinspired robots have been designed to both investigate and exploit the operation of these neural oscillators. In order to serve as effective tools for these robotics applications, however, it is often necessary to be able to adjust the phase alignment of multiple CPGs during operation. To achieve this goal, we present the design of our phase difference control (PDC) network using a functional subnetwork approach (FSA) wherein subnetworks that perform basic mathematical operations are assembled such that they serve to control the relative phase lead/lag of target CPGs. Our PDC network operates by first estimating the phase difference between two CPGs, then comparing this phase difference to a reference signal that encodes the desired phase difference, and finally eliminating any error by emulating a proportional controller that adjusts the CPG oscillation frequencies. The architecture of our PDC network, as well as its various parameters, are all determined via analytical design rules that allow for direct interpretability of the network behavior. Simulation results for both the complete PDC network and a selection of its various functional subnetworks are provided to demonstrate the efficacy of our methodology.