Modeling, Characterization, and Control of Bacteria-inspired Bi-flagellated Mechanism with Tumbling (2307.00155v1)
Abstract: 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. This interaction, referred to as bundling and tumbling, is often overlooked in simplified hydrodynamic models such as Resistive Force Theories (RFT). 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 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. By implementing this scheme, the robot can effectively reorient itself to attain the desired attitude. 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.
- C. Brennen and H. Winet, “Fluid mechanics of propulsion by cilia and flagella,” Annual Review of Fluid Mechanics, vol. 9, pp. 339–398, 1977.
- E. Lauga and T. R. Powers, “The hydrodynamics of swimming microorganisms,” Reports on progress in physics, vol. 72, no. 9, p. 096601, 2009.
- A. Dolev, M. Kaynak, and M. S. Sakar, “On-board mechanical control systems for untethered microrobots,” Advanced Intelligent Systems, vol. 3, no. 10, p. 2000233, 2021.
- M. Dvoriashyna and E. Lauga, “Hydrodynamics and direction change of tumbling bacteria,” Plos one, vol. 16, no. 7, p. e0254551, 2021.
- G. I. Taylor, “Analysis of the swimming of microscopic organisms,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 209, no. 1099, pp. 447–461, 1951.
- S. Lim, Y. Du, Y. Lee, S. K. Panda, D. Tong, and M. K. Jawed, “Fabrication, control, and modeling of robots inspired by flagella and cilia,” Bioinspiration & Biomimetics, 2022.
- R. Vogel and H. Stark, “Motor-driven bacterial flagella and buckling instabilities,” The European Physical Journal E, vol. 35, no. 2, pp. 1–15, 2012.
- M. K. Jawed, N. K. Khouri, F. Da, E. Grinspun, and P. M. Reis, “Propulsion and instability of a flexible helical rod rotating in a viscous fluid,” Physical review letters, vol. 115, no. 16, p. 168101, 2015.
- Y. Du, J. Lam, K. Sachanandani, and M. K. Jawed, “Modeling the locomotion of articulated soft robots in granular medium,” IEEE Robotics and Automation Letters, vol. 7, no. 3, pp. 6495–6502, 2022.
- K. Son, J. S. Guasto, and R. Stocker, “Bacteria can exploit a flagellar buckling instability to change direction,” Nature physics, vol. 9, no. 8, pp. 494–498, 2013.
- H. C. Berg, “The rotary motor of bacterial flagella,” Annual review of biochemistry, vol. 72, no. 1, pp. 19–54, 2003.
- H. C. Berg and D. A. Brown, “Chemotaxis in escherichia coli analysed by three-dimensional tracking,” nature, vol. 239, no. 5374, pp. 500–504, 1972.
- S. Lim, A. Yadunandan, and M. K. Jawed, “Bacteria inspired multi-flagella propelled soft robot at low reynolds number,” arXiv preprint arXiv:2111.12793, 2021.
- Z. Ye, S. Régnier, and M. Sitti, “Rotating magnetic miniature swimming robots with multiple flexible flagella,” IEEE Transactions on Robotics, vol. 30, no. 1, pp. 3–13, 2013.
- J. Lighthill, “Flagellar hydrodynamics,” SIAM review, vol. 18, no. 2, pp. 161–230, 1976.
- R. Cortez, “Regularized stokeslet segments,” Journal of Computational Physics, vol. 375, pp. 783–796, 2018.
- M. Kim, J. C. Bird, A. J. Van Parys, K. S. Breuer, and T. R. Powers, “A macroscopic scale model of bacterial flagellar bundling,” Proceedings of the National Academy of Sciences, vol. 100, no. 26, pp. 15481–15485, 2003.
- S. Koyasu and Y. Shirakihara, “Caulobacter crescentus flagellar filament has a right-handed helical form,” Journal of molecular biology, vol. 173, no. 1, pp. 125–130, 1984.
- N. C. Darnton, L. Turner, S. Rojevsky, and H. C. Berg, “On torque and tumbling in swimming escherichia coli,” Journal of bacteriology, vol. 189, no. 5, pp. 1756–1764, 2007.
- B. Scharf, “Real-time imaging of fluorescent flagellar filaments of rhizobium lupini h13-3: flagellar rotation and ph-induced polymorphic transitions,” Journal of bacteriology, vol. 184, no. 21, pp. 5979–5986, 2002.
- R. M. Macnab and M. K. Ornston, “Normal-to-curly flagellar transitions and their role in bacterial tumbling. stabilization of an alternative quaternary structure by mechanical force,” Journal of molecular biology, vol. 112, no. 1, pp. 1–30, 1977.
- S. Chattopadhyay and X.-L. Wu, “The effect of long-range hydrodynamic interaction on the swimming of a single bacterium,” Biophysical Journal, vol. 96, no. 5, pp. 2023–2028, 2009.