Robots on a microscopic scale, especially soft robots, are actively being developed for their potential in in-vivo therapeutic usage. Initially inspired by nature displayed through microscopes (e.g. bacteria, respiratory cilia), the physics of the robots at a low Reynolds number differentiates itself from the physics of the human scale. Traditional modeling and experimental methods for microbots require advanced microfabrication facilities and computationally expensive finite element methods due to innate objectives to interact with bodily fluids. Moreover, precise control and conclusive verification on a microscopic scale are often unfeasible due to technological limitations in manufacturing, control, and modeling. We resolve these challenges by combining discrete differential geometry-based modeling with embedded external force models and active material properties. We verify our modeling methods through experiments in various scales including desktop scale experiments, as well as millimeter and micrometer robot experiments, and exploit our model’s operability independent of the scale. The prominence of scale-independence of our model and desktop experiments enables us to analyze the characteristics of the behavior of the robots operating in a low Reynolds number at a low-cost viable scale with less challenge in microfabrication and control. The form factor choices for our robots are bacterial flagella, cilia, and functional ferromagnetic soft robots, which share a common ultrastructure of rod and beam. A collection of modeling problems of ferromagnetic soft robots and bio-inspired locomotion at disparate length scales are explored.\First, we conduct a desktop-scale experiment, which resembles the propulsion mechanism of bacteria, using two artificial elastic flagella. The locomotion of the near straight-line motion of bacteria called bundling occurs when both flagella are rotating in the same direction. A 3D-printed robotic prototype with a palm-sized body was submerged in glycerine for the experiment. We implemented the discrete elastic rod (DER) method with Regularized Stokeslet Segments (RSS) method for hydrodynamics and a constraint-based contact model to verify our model against the experiment. Dimensionless analysis was conducted for the results to enable adaptation for robots of the same form factor with different scales. Furthermore, a comparison of propulsion due to single flagellum and preliminary findings on cyclic bundling and unbundling sequence is reported.

We then investigate the directional change mechanism of bacteria referred to as tumbling. Using a rigid robot experiment with RSS method and numerical simulation accounting for the righting moment of the head due to center of gravity, the tumbling behavior could be analyzed for controllability. The reults on attitude control of the robot inside a viscous medium using tumbling mechanism is reported. Furthermore, a non dimensional analysis enabled generalization of our results to microscale as well as help optimizing the design space of flagella for the best turn over ability.

Next using the programmable ferromagnetic soft robot of a rod, cilium, and functional robot configuration, we introduced a ferromagnetic coupling into the DER method. Our model shows excellent quantitative agreement with the experiment. The model could capture the dynamic buckling of the soft robot, the motion of an mm-scale ciliary robot in glycerol, and the microscale functional robot with walking, jumping, and rolling gait modes. Our modeling method is the fastest for ferromagnetic soft robots with frictional contact known thus far. With the rod model with fixed boundary conditions, faster than real-time simulation was achieved.

Lastly, a coordinate invariant, machine learning (ML)-based, reduced-order hydrodynamics model suited for helical form factors was developed. The ML-based hydrodynamics model shows the accuracy of a high-fidelity hydrodynamics model (RSS) with the speed of an empirical coefficient-based local hydrodynamics model for a low Reynolds number flow.