Instability-based mechanism for body undulations in centipede locomotion

Centipedes have many body segments and legs and they generate body undulations during terrestrial locomotion. Centipede locomotion has the characteristic that body undulations are absent at low speeds but appear at faster speeds; furthermore, their amplitude and wavelength increase with increasing speed. There are conflicting reports regarding whether the muscles along the body axis resist or support these body undulations and the underlying mechanisms responsible for the body undulations remain largely unclear. In the present study, we investigated centipede locomotion dynamics using computer simulation with a body-mechanical model and experiment with a centipede-like robot and then conducted dynamic analysis with a simple model to clarify the mechanism. The results reveal that body undulations in these models occur due to an instability caused by a supercritical Hopf bifurcation. We subsequently compared these results with data obtained using actual centipedes. The model and actual centipedes exhibit similar dynamic properties, despite centipedes being complex, nonlinear dynamic systems. Based on our findings, we propose a possible passive mechanism for body undulations in centipedes, similar to a follower force or jackknife instability. We also discuss the roles of the muscles along the body axis in generating body undulations in terms of our physical model.