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 few possible mechanisms for self-propulsion at low Reynolds number is undulations of a passive elastic tail, as proposed in the classical work of Purcell (1977). This effect is studied here by investigating a variant of Purcell's three-link swimmer model where the front joint angle is periodically actuated while the rear joint is driven by a passive torsional spring. The dynamic equations of motion are formulated and explicit expressions for the leading-order solution are derived by using perturbation expansion. The dependence of the motion on the actuation amplitude and frequency is analyzed, and optimization with respect to the swimmer's geometry is conducted.

This paper studies a simple two-dimensional model of a swimmer at low-Reynolds-number near a no-slip wall by utilizing methods of complex analysis. The swimmer is propelled by purely tangential surface deformations and is modeled by moving point singularities. The nonlinear dynamics of the swimmer is formulated explicitly, and its motion near the wall is fully characterized. The results show qualitative agreement with predictions of three-dimensional models and with motion experiments on a robotic swimmer. The success and simplicity of the model suggest that it will provide a simple way to study the dynamics of low-Reynolds-number swimmers in more complicated geometries.

This paper studies Lagrangian hybrid systems, which are a special class of hybrid systems modeling mechanical systems with unilateral constraints that are undergoing impacts. This class of systems naturally display Zeno behavior-an infinite number of discrete transitions that occur in finite time, leading to the convergence of solutions to limit sets called Zeno equilibria. This paper derives simple conditions for stability of Zeno equilibria. Utilizing these results and the constructive techniques used to prove them, the paper introduces the notion of a completed hybrid system which is an extended hybrid system model allowing for the extension of solutions beyond Zeno points. A procedure for practical simulation of completed hybrid systems is outlined, and conditions guaranteeing upper bounds on the incurred numerical error are derived. Finally, we discuss an application of these results to the stability of unilaterally constrained motion of mechanical systems under perturbations that violate the constraint.Index Terms-Langrangian hybrid systems, stability, unilateral contact constraints, Zeno behavior.

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.