Modeling, Characterization, and Control of Bacteria-Inspired Bi-Flagellated Mechanism with Tumbling

Multi-flagellated bacteria utilize the hydrodynamic interaction between their filamentary tails, known as flagella, to swim and change their swimming direction in low Reynolds number flow. Simplified hydrodynamics model, like Resistive Force Theories (RFT), lacks the capability to capture the dynamics of certain interactions known as bundling and tumbling. However, for the development of efficient and steerable robots inspired by bacteria, it becomes crucial to exploit this interaction. In this paper, we present the construction of a macroscopic bio-inspired robot featuring two rigid flagella arranged as right-handed helices, along with a cylindrical head. By rotating the flagella in opposite directions, the robot's body can reorient itself through repeatable and controllable tumbling. To accurately model this bi-flagellated mechanism in low Reynolds flow, we employ a coupling of rigid body dynamics and the method of Regularized Stokeslet Segments (RSS). Unlike RFT, RSS takes into account the hydrodynamic interaction between distant filamentary structures. Furthermore, we delve into the exploration of the parameter space in terms of the flagellum geometry to optimize the propulsion and torque of the system. To achieve the desired reorientation of the robot, we propose a tumble control scheme that involves modulating the rotation direction and speed of the two flagella. The scheme enhance the steerability by enabling the robot to attain the desired heading angle with high accuracy. Notably, the overall scheme boasts a simplified design and control as it only requires two control inputs. With our macroscopic framework serving as a foundation, we envision the eventual miniaturization of this technology to construct mobile and controllable micro-scale bacterial robots.