A Geometric Phase Approach to Body-Driven Steering in Multi-Legged Robots

Centipedes maneuver in diverse terradynamic environments using seemingly complex combinations of body undulation and limb stepping. While laboratory studies have focused on forward locomotion, few studies have quantified steering behaviors (defined as a combination of rotation and displacement). Prior work reconstructed C. elegans nematode turning using a reduced-order model of two superimposed traveling waves in body curvature (Wang, et al. IROS 2020). We investigated whether a similar approach could describe centipede turning. In preliminary trials, we recorded the midline trajectories of S. subspinipes turning (2 individuals, 24 trials) using high-speed cameras and kinematic analysis identified two traveling waves during turning. Thus, we posit the two-traveling wave template can be generalized to steering multi-legged, undulatory systems. Specifically, we hypothesize that the optimal phasing of the traveling waves can be determined using a geometric phase approach to produce turning behaviors. We test our hypothesis using a robophysical device (6 segment - 10 legs, body length=1m) and varied the amplitude (0 to 20 degrees) and spatial frequency (0 to 0.5 waves) of the second traveling wave, resulting in control over the angular (0 to 20 degree) and translational (.28 to .38 body length) displacement. These results show that the two-traveling wave template can be extended to multilegged locomotors providing a framework for centipede robot locomotion with performance comparable to animals.