Modelling and controllability of the motion of a slender, flexible micro-swimmer
This work provides a new modeling approach for flexible micro-swimmers, which may benefit biologists and engineers studying low Reynolds number locomotion, but the results are preliminary and incremental.
The paper develops a novel kinematic model for a slender flexible micro-swimmer in low Reynolds number flow, representing it as a rigid head and flexible tail, and derives a weak controllability result for the system. Simulation results show head velocity variation for a bump function moving along the swimmer.
The mechanism of swimming at very low Reynolds number conditions is a topic of interest to biologists and engineering community. We develop a novel kinematic model of a slender flexible swimmer which locomotes in a low Reynolds number regime. In contrast to existing techniques that model such systems as a connected set of straight, rigid links, the novelty of our technique stems from the fact that we model the swimmer with two components - one is a straight, rigid body (the head) and the other is a flexible member (the tail). Using Cox theory we model the gradient of the forces as a function of the instantaneous shape of the swimmer and its velocity. By virtue of the low inertia conditions, an expression for the translational and rotational velocity of the head is obtained for the planar motion in the form of a Lie algebra of the Special Euclidean group. We explain the principal fiber bundle structure of the configuration space of the swimmer and use that to show a weak controllability result for a type of slender flexible swimmer where the shape space is the space of all continuous curves of a given length. A set of simulation results is presented showing the variation of the swimmer head velocity for a bump function moving along the swimmer length.