Mismatch of body undulation and limb waves enables robust centipede locomotion

Centipedes that use retrograde (head-to-tail) limb stepping waves display body undulation when locomoting at high speed (Manton et al. 1952). Yet, little is known of how centipedes coordinate body undulation with stepping patterns to locomote. We studied body-limb coordination in centipedes via a robophysical model (L=70 cm, 8 leg pairs), programmed to generate retrograde waves for both the body and limbs. This robot achieved effective gaits when body-limb waves had equal spatial frequency (i.e.,n_bdoy=n_leg). However, the gait efficacy was sensitive to body-limb coordination if n_bdoy=n_leg=1. Specifically, changes (e.g., ±π/3) in the body-leg wave phase lag led to a decrease (e.g., 40%) in speed. With n_bdoy=n_leg=1 the average speed across all body-leg phase lags (0 to 2π) was 8.6±17.1 cm/cycle. In contrast, by increasing n_leg while fixing n_bdoy, the robot’s locomotive performance was robust to changes in the body-leg wave phase lags. With n_bdoy=1 and n_leg=1.6, the average speed across all body-leg phase lags was 15.4±7.0 cm/cycle. A similar mismatch in body-leg spatial frequency (n_body=1.6±0.2, n_leg=2.2±0.2) was observed in the S. polymorpha (N=3, L=7.3±1.5cm, 19 leg pairs). This suggests robust centipede locomotion is achieved by distinct frequencies in the body and limb waves.