Optimal actuation of flagellar magnetic microswimmers

The N -Link Swimmer in Three Dimensions: Controllability and Optimality Results

The controllability of a fully three-dimensional N -link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2-link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2-link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all eight linearly independent directions in the combined configuration and shape space, leading to controllability; the swimmer can move from any starting configuration and shape to any target configuration and shape by operating on the two shape variables. The result is subsequently extended to the N -link swimmer. Finally, the minimal time optimal control problem and the minimization of the power expended are addressed and a qualitative description of the optimal strategies is provided.

Driving a Microswimmer with Wall-Induced Flow

Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby. Recent advances in artificial magnetic cilia carpets offer the potentiality to use a similar wall-generated background flow to steer bio-hybrid microrobots. In this paper, we provide some ground theoretical and numerical work assessing the viability of this novel means of swimmer guidance by setting up a simple model of a spherical swimmer in an oscillatory flow and analysing it from the control theory viewpoint. We show a property of local controllability around the reference free trajectories and investigate the bang-bang structure of the control for time-optimal trajectories, with an estimation of the minimal time for suitable objectives. By direct simulation, we have demonstrated that the wall actuation can improve the wall-following transport by nearly 50%, which can be interpreted by synchronous flow structure. Although an open-loop control with a periodic bang-bang actuation loses some robustness and effectiveness, a feedback control is found to improve its robustness and effective transport, even with hydrodynamic wall-swimmer interactions. The results shed light on the potentialities of flow control and open the way to future experiments on swimmer guidance.

Control and controllability of microswimmers by a shearing flow

With the continuing rapid development of artificial microrobots and active particles, questions of microswimmer guidance and control are becoming ever more relevant and prevalent. In both the applications and theoretical study of such microscale swimmers, control is often mediated by an engineered property of the swimmer, such as in the case of magnetically propelled microrobots. In this work, we will consider a modality of control that is applicable in more generality, effecting guidance via modulation of a background fluid flow. Here, considering a model swimmer in a commonplace flow and simple geometry, we analyse and subsequently establish the efficacy of flow-mediated microswimmer positional control, later touching upon a question of optimal control. Moving beyond idealized notions of controllability and towards considerations of practical utility, we then evaluate the robustness of this control modality to sources of variation that may be present in applications, examining in particular the effects of measurement inaccuracy and rotational noise. This exploration gives rise to a number of cautionary observations, which, overall, demonstrate the need for the careful assessment of both policy and behavioural robustness when designing control schemes for use in practice.

Particle actuation by rotating magnetic fields in microchannels: a numerical study

Magnetic particles confined in microchannels can be actuated to perform translation motion using a rotating magnetic field, but their actuation in such a situation is not yet well understood. Here, the actuation of a ferromagnetic particle confined in square microchannels is studied using immersed-boundary lattice Boltzmann simulations. In wide channels, when a sphere is positioned close to a side wall but away from channel corners, it experiences a modest hydrodynamic actuation force parallel to the channel walls. This force decreases as the sphere is shifted toward the bottom wall but the opposite trend is found when the channel is narrow. When the sphere is positioned midway between the top and bottom channel walls, the actuation force decreases as the channel width decreases and can reverse its direction. These phenomena are elucidated by studying the flow and pressure fields in the channel-particle system and by analyzing the viscous and pressure components of the hydrodynamic force acting on different parts of the sphere.