Micro- and nanorobots operating in low Reynolds number fluid environments require specialized swimming strategies for efficient locomotion. Prior research has focused on designs mimicking the rotary corkscrew motion of bacterial flagella or the planar beating motion of eukaryotic flagella. These biologically inspired designs are typically of uniform construction along their flagellar axis. This work demonstrates for the first time planar undulations of composite multilink nanowire-based chains (diameter 200 nm) induced by a planar-oscillating magnetic field. Those chains comprise an elastic eukaryote-like polypyrrole tail and rigid magnetic nickel links connected by flexible polymer bilayer hinges. The multilink design exhibits a high swimming efficiency. Furthermore, the manufacturing process enables tuning the geometrical and material properties to specific applications.

One of the most efficient actuation methods of robotic microswimmers for biomedical applications is by applying time-varying external magnetic fields. In order to improve the design of the swimmer and optimize its performance, one needs to develop simple theoretical models that enable explicit analysis of the swimmer's dynamics. This paper studies the dynamics of a simple microswimmer model with two magnetized links connected by an elastic joint, which undergoes planar undulations induced by an oscillating magnetic field. The nonlinear dynamics of the microswimmer is formulated by assuming Stokes flow and using resistive force theory to calculate the viscous drag forces. Key effects that enable the swimmer to overcome the scallop theorem and generate net propulsion are identified, including violation of front-back symmetry. Assuming small oscillation amplitude, approximate solution is derived by using perturbation expansion, and leading-order expressions for the swimmer's displacement per cycle X and average speed V are obtained. Optimal actuation frequencies that maximize X or V are found for given swimmer's parameters. An ultimate optimal choice of swimmer's parameters and actuation frequency is found, for which the average swimming speed V attains a global maximum. Finally, the theoretical predictions of optimal performance values are validated by comparison to reported experimental results of magnetic microswimmers.

Robotic locomotion typically involves using gaitsperiodic changes of kinematic shape, which induce net motion of the body in a desired direction. An example is robotic microswimmers, which are inspired by motion of swimming microorganisms. One of the most famous theoretical models of a microswimmer is Purcell's planar three-link swimmer, whose structure possesses two axes of symmetry. Several works analyzed gaits for robotic three-link systems based on body-fixed velocity integrals. Using this approach, finite motion in desired directions can only be obtained approximately. In this study, we propose gaits which are based on analysis of the system's structural symmetries, and generate exact motion along principal directions without net rotation. Another gait that produces almost pure rotation is presented, and bounds on the small-amplitude residual translation are obtained by using perturbation expansion. Next, the theory is extended to more realistic swimmers which have only one symmetry axis. Gaits for such swimmers which generate net translation are proposed, and their small-amplitude motion is analyzed using perturbation expansion. The theoretical results are demonstrated by using numerical simulations and conducting controlled motion experiments with a robotic macroswimmer prototype in a highly viscous fluid.

One of the promising capabilities of magnetic microswimmers is towing a cargo, which can be used for targeted drug delivery or performing tissue biopsy. A key question is what should be the optimal size ratio between the cargo and the swimmer's flexible tail. This question is addressed here for the simplest theoretical model of a magnetic microswimmer undergoing planar undulations-a spherical load connected by a torsion spring to a rigid slender link. The swimmer's dynamic is formulated and leading-order expressions for its motion are obtained explicitly under small-amplitude approximation. Optimal combinations of magnetic actuation frequency, torsion stiffness, and tail length for maximizing displacement, average speed, or energetic efficiency are obtained. The theoretical results are compared with reported experiments in several types of cargo-towing magnetic microswimmers.

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