Dynamics and Optimal Actuation of a Three-Sphere Low-Reynolds-Number Swimmer with Muscle-Like Arms

  title={Dynamics and Optimal Actuation of a Three-Sphere Low-Reynolds-Number Swimmer with Muscle-Like Arms},
  author={Alessandro Montino and Antonio DeSimone},
  journal={Acta Applicandae Mathematicae},
The three-sphere swimmer by Najafi and Golestanian is composed of three spheres connected by two arms. The case in which the swimmer can control the lengths of the two arms has been studied in detail. Here we study a variation of the model in which the swimmer’s arms are constructed according to Hill’s model of muscular contraction. The swimmer is able to control the tension developed in the active components of the arms. The two shape parameters and the tensions acting on the two arms are then… 

Elastic three-sphere microswimmer in a viscous fluid

We discuss the dynamics of a generalized three-sphere microswimmer in which the spheres are connected by two elastic springs. The natural length of each spring is assumed to undergo a prescribed

Swimming trajectories of a three-sphere microswimmer near a wall.

The general three-dimensional motion can be mapped onto a quasi-two-dimensional representational model by an appropriate redefinition of the order parameters governing the transition between the swimming states and allow for an accurate description of the swimming behavior near a wall.

Boosting micromachine studies with Stokesian dynamics

Artificial microswimmers, nano- and microrobots, are essential in many applications from engineering to biology and medicine. We present a Stokesian dynamics study of the dynamical properties and

State diagram of a three-sphere microswimmer in a channel

The resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge.

Rate-independent soft crawlers

  • P. Gidoni
  • Mathematics
    The Quarterly Journal of Mechanics and Applied Mathematics
  • 2018
This paper applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how the various strategies

On the optimal control of rate-independent soft crawlers



Three-sphere low-Reynolds-number swimmer with a passive elastic arm

A variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring is investigated, showing that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one.

Optimal Strokes for Low Reynolds Number Swimmers: An Example

It is shown how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).

On self-propulsion of micro-machines at low Reynolds number: Purcell's three-link swimmer

Using slender-body hydrodynamics in the inertialess limit, we examine the motion of Purcell's swimmer, a planar, fore–aft-symmetric three-link flagellum or propulsive mechanism that translates by

Dynamics of Purcell’s three-link microswimmer with a passive elastic tail

  • E. PassovY. Or
  • Physics, Engineering
    The European physical journal. E, Soft matter
  • 2012
This effect is studied 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.

Optimally Swimming Stokesian Robots

Self-propelled stokesian robots composed of assemblies of assembly of balls, in dimensions 2 and 3, are proved to be able to control their position and orientation as a result of controllability, and Chow's theorem is applied.

Analytic results for the three-sphere swimmer at low Reynolds number.

The simple model of a low Reynolds number swimmer made from three spheres that are connected by two arms is considered in its general form and analyzed and the role of noise and coherence in the stroke cycle is discussed.

Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers

We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct

Optimal stroke patterns for Purcell's three-link swimmer.

Stroke patterns for Purcell's three-link swimmer are optimized and are significantly more efficient than those previously suggested by authors who only consider geometric design rather than kinematic criteria.

Natural locomotion in fluids and on surfaces : swimming, flying, and sliding

This volume developed from a Workshop on Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding which was held at the Institute for Mathematics and its Applications (IMA) at the