Steering and turning control of <i>C. elegans</i>

Elongate animals (e.g., snakes, nematodes) propagate waves of body curvature to generate propulsion in dissipative environments. In particular, the nematode worm C. elegans lives in environments (e.g., rotting fruit) where maneuverability is crucial to overcome heterogeneities and post-interaction deformations. To search for steering control principles in undulatory locomotion, we studied C. elegans traversing both agar and liquid buffer. These worms generate a time-dependent omega-like shape for reorientation to achieve body rotation of 150±26° on agar and 84±39° in liquid buffer. Principal component analysis (PCA) revealed the worms use four principal components during turning, superimposing two body traveling waves with two spatial frequencies. A geometric mechanics framework rationalized the observed turning dynamics by properly coupling the amplitude and the phase of the two body traveling waves. Theory predicted omega turns can achieve rotation of 153° on agar and 89° in liquid buffer, in agreement with worm experiments. These results and robophysical experiments implementing the behavior suggest that omega turns are a robust strategy for turning in diverse environments.