Analysis and synthesis of central pattern generators via multivariable harmonic balance

The central pattern generator (CPG) provides a fundamental control mechanism underlying rhythmic motions in animal locomotion. We consider a class of CPGs modeled by a group of interconnected identical neurons. Based on the idea of multivariable harmonic balance, we show how the oscillation profile is related to the connectivity matrix that specifies the architecture and strengths of the interconnections. Specifically, the frequency, amplitudes, and phases are essentially encoded in terms of a pair of eigenvalue and eigenvector. This basic principle is used to estimate the oscillation profile of a given CPG and to determine the connectivity matrix that achieves a prescribed oscillation profile