Controllability and Optimal Control of Microswimmers: Theory and Applications

The process of swimming at the microscopic scale is successfully described as a finite-dimensional, nonholonomic control system due to negligible inertia in the low-Reynolds number regime that holds for objects this size. The study of such systems from the point of view of mathematical control theory yields fundamental results on elementary swimmer models aimed at understanding the principles of microswimming, including theoretical controllability and optimal swimming cycles. In this review, we provide a description of the microswimmer control framework, a survey of the associated results and models as well as experimental validations, with the objective of highlighting current theoretical challenges and applications to microrobot design and guidance.