Validated reduced order models for simulating trajectories of bio-inspired artificial micro-swimmers

Autonomous micro-swimming robots can be utilized to perform specialized procedures such as in vitro or in vivo medical tasks as well as chemical surveillance or micro manipulation. Maneuverability of the robot is one of the requirements that ensure successful completion of its task. In micro fluidic environments, dynamic trajectories of active micro-swimming robots must be predicted reliably and the response of control inputs must be well-understood. In this work, a reduced-order model, which is based on the resistive force theory, is used to predict the transient, coupled rigid body dynamics and hydrodynamic behavior of bio-inspired artificial micro-swimmers. Conceptual design of the micro-swimmer is biologically inspired: it is composed of a body that carries a payload, control and actuation mechanisms, and a long flagellum either such as an inextensible whip like tail-actuator that deforms and propagates sinusoidal planar waves similar to spermatozoa, or of a rotating rigid helix similar to many bacteria, such as E. Coli. In the reduced-order model of the microswimmer, fluid’s resistance to the motion of the body and the tail are computed from resistive force theory, which breaks up the resistance coefficients to local normal and tangential components. Using rotational transformations between a fixed world frame, body frame and the local Frenet-Serret coordinates on the helical tail we obtain the full 6 degrees-of-freedom relationship between the resistive forces and torques and the linear and rotational motions of the swimmer. In the model, only the tail’s frequency (angular velocity for helical tail) is used as a control input in the dynamic equations of the micro-swimming robot. The reduced-order model is validated by means of direct observations of natural micro swimmers presented earlier in the literature and against; results show very good agreement. Three-dimensional, transient CFD simulations of a single degree of freedom swimmer is used to predict resistive force coefficients of a micro-swimmer with a spherical body and flexible tail actuator that uses traveling plane wave deformations for propulsion. Modified coefficients show a very good agreement between the predicted and actual time-dependent swimming speeds, as well as forces and torques along all axes.