Purcell's swimmers in pairs.

We investigate the effects of hydrodynamic interactions between microorganisms swimming at low Reynolds numbers, treating them as a control system. We employ Lie brackets analysis to examine the motion of two neighboring three-link swimmers interacting through the ambient fluid in which they propel themselves. Our analysis reveals that the hydrodynamic interaction has a dual consequence: on one hand, it diminishes the system's efficiency; on the other hand, it dictates that the two microswimmers must synchronize their motions to attain peak performance.