Controllability of a Pair of Swimming Microrotors in a Bounded Domain at Low Reynolds Number

We investigate the dynamics of a pair of spinning spheres or microrotors in a fluid at low Reynolds numbers. These microrotors are each approximated by a rotlet, a fundamental singularity of the Stokes equation. Singularities of Stokes flows serve as useful theoretical models for microswimmers and micro-robots. Rotlet models of microswimmers have received less attention since a rotlet cannot generate translation by itself if the only control input is the rate of spin or strength of the rotlet. However a pair of rotlets can interact and execute net motion. In an unbounded domain of fluid, the positions of a pair of rotlets are not fully controllable due to the existence of an invariant. However, in a confined domain, we show that the positions of the pair of spheres are small time locally controllable. We show how control inputs can be constructed based on combinations of Lie brackets to move the rotlets from one point to another in the domain.