Control and Locomotion of Hydrodynamically Coupled Rigid Spheres

Abstract

The coupling interactions between two spherical swimmers in an ideal fluid have known analytic approximations for certain types of motion. We apply these results to produce locomotion and coordination through the actuation of internal masses inside each swimmer. Through control of either both swimmers or one of them, the latter case taking advantage of compliance in the passive swimmer, desired motion along the spheres' line of centers can be achieved. We subsequently treat general 2D motion as a superposition of motion components along and perpendicular to the spheres' line of centers, leading to a derivation of a full model of controlled locomotion and coordination of two spheres in a planar fluid.