Buckling Instability to Control the Swimming Direction in Bacterial Flagella

We analyze the control of a uniflagellar soft robot in low Reynolds fluid. Inspired by the locomotion of 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 by the fluid can cause the flagellum to buckle, characterized by a dramatic change in shape. A fluid-structure interaction model that combines Discrete Elastic Rods algorithm with Lighthill's Slender Body Theory is employed to simulate the system. 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 scalar input - the angular velocity of the flagellum. We also show that the complexity of the dynamics 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. Our study underscores the potential role of buckling in the locomotion of natural bacteria.