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