Worm omega turn modeling and its limbless robot implementation via geometric mechanics

Reorientation plays a key role in limbless biological and robotic locomotion on different types of terrains. However, modeling the reorientation behaviors found in biological systems and implementing them on robotic platforms remain challenging. This work focuses on an omega shaped turning motion of the mm-long nematode worm C. elegans that allows large and rapid reorientation in natural environments (e.g., rotting fruit). By investigating body curvature dynamics with PCA analysis, we model omega turns as a superposition of two parametrized traveling waves: a forward wave, which drives forward motion, and an omega wave, which triggers turning. Using tools from geometric mechanics, we analyze the motion generated by the two-wave model with numerical simulations and determine the optimal coordination of parameters (e.g., the spatial frequencies) that maximizes the turning angle. Inspired by the C. elegans omega turning motion model, we develop controllers that enable limbless robots to exhibit omega shaped turning for reorientation. By geometric simulation and robophysical experiment, we demonstrate that the omega turn-inspired controller allows a limbless robot to produce effective and robust turning motion on challenging terrains, such as rigid lattices and granular media.