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In this paper, we analyze the inverse dynamics and control of abacteria-inspired uniflagellar robot in a fluid medium at low Reynolds number.Inspired by the mechanism behind the locomotion of flagellated bacteria, weconsider a robot comprised of a flagellum -- a flexible helical filament --attached to a spherical head. The flagellum rotates about the head at acontrolled angular velocity and generates a propulsive force that moves therobot forward. When the angular velocity exceeds a threshold value, thehydrodynamic force exerted by the fluid can cause the soft flagellum to buckle,characterized by a dramatic change in shape. In this computational study, afluid-structure interaction model that combines Discrete Elastic Rods (DER)algorithm with Lighthill's Slender Body Theory (LSBT) is employed to simulatethe locomotion and deformation of the robot. We demonstrate that the robot canfollow a prescribed path in three dimensional space by exploiting buckling ofthe flagellum. The control scheme involves only a single (binary) scalar input-- the angular velocity of the flagellum. By triggering the bucklinginstability at the right moment, the robot can follow an arbitrary path inthree dimensional space. We also show that the complexity of the dynamics ofthe helical filament can be captured using a deep neural network, from which weidentify the input-output functional relationship between the control inputsand the trajectory of the robot. Furthermore, our study underscores thepotential role of buckling in the locomotion of natural bacteria.

Control of uniflagellar soft robots at low Reynolds number using buckling instability