UCLA

Bacteria, one of the most common prokaryotic germs, typically move through fluids by rotating one or more slender helical structures called flagella. Flagellar propulsion results from a complicated fluid-structure interaction (FSI), between the structural flexbility of flagella and the hydrydynamic forces generated by the surrounding flow. This FSI can result in geometrically nonlinear deformation and structural instability. The former generally happens in compliant structures, such as soft robots, but is challenging to model and simulate while the latter is conventionally avoided because they normally causes structural failure. However, bacteria were recently discovered to utilize structural instability to change their movement direction, and this mechanism is called ``buckling-to-turn". This mechanism can be used to control the moving direction of microrobots that can potentially revolutionize in-vivo targeted drug delivery or minimally invasive surgeries. Nonetheless, there is no released work that developed soft robots that are able to replicate this mechanism. This is due to experimental challenges: flagellum is difficult to be controlled precisely on generic soft robots that are actuated by external fields while self-actuated soft robots have a surprisingly low energy efficiency (mostly below 0.1%).

Recently, the hydrodynamic force model - Resistive Force Theory (RFT) that was original defined in viscous fluids only accounting for the local force around each segment have been also found valid in granular media (GM), such as sand, chia seeds, snow. This amazing discovery is a milestone to the exploration of locomotion in GM because it reveals a validated theory for movements in granules for the first time, and enables fast simulation of these movements thanks to the simplicity of RFT. Although previous work performed experiments on animals in the nature to comprehend their locomotion, work that employs soft robots as experimental platform to replicate the locomotion for practice is very few because of challenges in both experiments and simulations.

Our work solve the above problems by combining model experiments with state-of-the-art computational tools in computer graphics, and theoretical analysis towards developing predictive physical understanding of untethered flagellar propulsion in viscous fluids and granular media.We scale up the flagellar bacterial propulsion to desktop-scale soft flagellated robots. This allows for systematic experimental exploration of parameter space. In parallel, we conduct numerical simulations using the Discrete Differential Geometry (DDG)-based method, which was originally produced for special effects of the visually dramatic dynamics of slender structures, e.g., hair and fur in the animation industry. We adapt DDG-based simulator into engineering as a predictive computational tool and test it against our experiments. Overall, this dissertation makes four major contributions: First, we introduce arguably the simplest soft multi-flagellated robot with a single binary control signal, which can move along an arbitrary 2D trajectory near air-fluid interface and at the interface between two fluids. Our work explores the performance of multi-flagellar propulsion near an open boundary as opposed to closed boundaries such as walls, as the former is much less studied but has numerous applications, such as flagellated robots used as baits, and tools for oil spill cleanup, water quality monitoring, and infrastructure inspection. We investigate the performance of the robot versus the number of flagella. In the end, we briefly propose the idea of incorporating machine learning with our fast-running simulator as a handy inverse design tool of flagellated robots.

Secondly, we use the same robot as experimental platform to explore the locomotion in granular media (GM). Numerically, the same DDG-RFT-Stokes' framework is applied again to model the hydrodynamics of locomotion moving through GM. Numerical and experimental results match quantitatively with each other when the number of flagella is two or three, validating the applicability of RFT in GM. However, ``stick-slip" or ``jamming", i.e., the robot randomly gets stuck at the same position with time passing, happens when the number of flagella turns four or five. The simulator fails to capture this, which proves the limitation of RFT in GM. Moreover, our main finding is that increasing the number of flagella from two to three decreases the speed of the robot. This is kind of counter intuitive, proving the complexity of flexible flagellar locomotion, the competition between the drag and propulsion. This indicates that our simulator is potentiallyapplicable for unknown physics exploration. We find that there is an optimal rotational speed at which maximum efficiency is achieved. This highlights that our validated simulator can be used as a design tool for soft robots. Our third contribution is the implementation of an Euler-Bernoulli beam-based analytical framework that is both simple and capable of capturing the performance of the robot in GM.

Our forth contribution is developing the first untethered underwater robot with a flexible polymeric flagellum that can replicate bacterial ``buckling-to-turn" mechanism. Additionally, we show the effect of flagellar geometrical properties on the performance of flagellar propulsion. Moreover, we prove that while bacteria utilize buckling to steer, flagellar buckling is probably not ample for a robust robotic system to follow any 3D prescribed trajectory. As a result, we develop a ``mass-transformer" mechanism to make the robot system robust and be able to reach a destination in the 3D space. Additionally, we are the first to demonstrate that the state-of-the-art continuous hydrodynamic model Regularized Stokeslet Segment (RSS) method can accurately model the hydrodynamic force on a rotating flagellum on an untethered robot (with a rigid head). We develop a numerical framework that incorporates (i) DDG to account for the elasticity of soft flagellum, (ii) RSS for the long term hydrodynamic flow by the rotating helical flagellum, and (iii) Stokes' law for the hydrodynamics induced by a spherical head. Our modular robot design enables researchers to use it as testbeds for studying generic flagellar propulsion. The ``mass-transformer" mechanism together with simple flagellar buckling control scheme can be used for developing autonomous underwater robots for exploration and and exploitation of new environments.