Geometric Gait Analysis of Corkscrew Swimmers at Low Reynolds Regime

Abstract

Applying geometric mechanics to gait analysis stems from low Reynolds number swimming. However, geometric gait analysis tools have not played a prominent role in overcoming difficulties imposed by low Reynolds swimmer's necessity for time-symmetry destruction and transferred their mark to nature's successful swimming strategy, such as the bacteria's propulsion with a rotating corkscrew-shaped tail. For instance, the corkscrew swimming strategy has led to the development of micro/nano-scale corkscrew swimming robots for in vivo treatment. For designing and engineering a low Reynolds corkscrew swimming robot, it is crucial to understand how body deformation interacts with surrounding and generates net motion. Hence, we tried to find intuitive ways of controlling corkscrew swimming robots. This thesis presents applications of geometric tools, called connection vector fields and constraint curvature functions, to develop motion primitives for corkscrew swimming robots. First, we integrate Euler angle decomposition with geometric tools, an integration never tried. Moreover, by appropriately setting the variables, we could glimpse the effects of helix parameters. Our framework can expand to vehicles with asymmetric rotational inertia about three cartesian axes and to corkscrew swimming robots with soft tails. In addition, it can also offer biomechanical insights into swimming strategy in living systems, such as E. coli or spermatozoon.