Coupling-dependent convergence behavior of phase oscillators with tegotae-control

A bio-inspired way to model locomotion is using a network of coupled phase oscillators to create a Central Pattern Generator (CPG). The recently developed feedback control method tegotae includes exteroceptive force feedback into the governing phase update equations, leading to gait limit cycles. However, the oscillator coupling weights are often determined empirically. Here, we first investigate how the coupling coefficients influence the limit cycle convergence behavior on a 2- and 3-limbed structure in simulation. We find that the convergence with tegotae can be improved by introducing appropriate cross-couplings. This results in a smoother convergence and steady-state behavior where each individual oscillator drives the full network to a common convergence state in comparison to competing convergence states with ill-chosen cross-couplings. We then validate the findings in hardware and hypothesize how the appropriate couplings could be derived directly from the morphology, potentially eliminating the empiric determination.