Model of metameric locomotion in smooth active directional filaments with curvature fluctuations

Locomotion in segmented animals, such as annelids and myriapods (centipedes millipedes), is generated by a coordinated movement known metameric locomotion, which can be also implemented robots designed to perform specific tasks. We introduce theoretical model, based on an active directional motion of the head segment passive trailing rest body segments, order formalize study locomotion. The model specifically formulated steered Ornstein-Uhlenbeck curvature process, preserving continuity along whole filament, thus supersedes simple Brownian would inapplicable this case. obtain probability density analytically solving Fokker-Planck equation pertinent model. calculate explicitly correlators, mean-square orientational fluctuations, correlation function separation between tail both either via or directly implementing it numerically from Langevin equations. analytical numerical results coincide. Our help understand locomotion animals instruct design robots.