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Optimal motion control of three-sphere based low-Reynolds number swimming microrobot. ROBOTICA 2021. [DOI: 10.1017/s0263574721000953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
AbstractMicrorobots with their promising applications are attracting a lot of attention currently. A microrobot with a triangular mechanism was previously proposed by scientists to overcome the motion limitations in a low-Reynolds number flow; however, the control of this swimmer for performing desired manoeuvres has not been studied yet. Here, we have proposed some strategies for controlling its position. Considering the constraints on arm lengths, we proposed an optimal controller based on quadratic programming. The simulation results demonstrate that the proposed optimal controller can steer the microrobot along the desired trajectory as well as minimize fluctuations of the actuators length.
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Shanbrom C, Balisacan J, Wilkens G, Chyba M. Geometric Methods for Efficient Planar Swimming of Copepod Nauplii. MICROMACHINES 2021; 12:mi12060706. [PMID: 34208685 PMCID: PMC8268059 DOI: 10.3390/mi12060706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Revised: 05/31/2021] [Accepted: 06/02/2021] [Indexed: 11/28/2022]
Abstract
Copepod nauplii are larval crustaceans with important ecological functions. Due to their small size, they experience an environment of low Reynolds number within their aquatic habitat. Here we provide a mathematical model of a swimming copepod nauplius with two legs moving in a plane. This model allows for both rotation and two-dimensional displacement by the periodic deformation of the swimmer’s body. The system is studied from the framework of optimal control theory, with a simple cost function designed to approximate the mechanical energy expended by the copepod. We find that this model is sufficiently realistic to recreate behavior similar to those of observed copepod nauplii, yet much of the mathematical analysis is tractable. In particular, we show that the system is controllable, but there exist singular configurations where the degree of non-holonomy is non-generic. We also partially characterize the abnormal extremals and provide explicit examples of families of abnormal curves. Finally, we numerically simulate normal extremals and observe some interesting and surprising phenomena.
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Affiliation(s)
- Corey Shanbrom
- Department of Mathematics and Statistics, Sacramento State University, 6000 J St., Sacramento, CA 95819, USA;
| | - Jonas Balisacan
- Department of Mathematics, University of Hawai’i at Mānoa, 2565 McCarthy Mall, Honolulu, HI 96822, USA; (J.B.); (G.W.)
| | - George Wilkens
- Department of Mathematics, University of Hawai’i at Mānoa, 2565 McCarthy Mall, Honolulu, HI 96822, USA; (J.B.); (G.W.)
| | - Monique Chyba
- Department of Mathematics, University of Hawai’i at Mānoa, 2565 McCarthy Mall, Honolulu, HI 96822, USA; (J.B.); (G.W.)
- Correspondence:
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Sukhov A, Hubert M, Grosjean G, Trosman O, Ziegler S, Collard Y, Vandewalle N, Smith AS, Harting J. Regimes of motion of magnetocapillary swimmers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:59. [PMID: 33895914 PMCID: PMC8068718 DOI: 10.1140/epje/s10189-021-00065-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 03/31/2021] [Indexed: 05/26/2023]
Abstract
The dynamics of a triangular magnetocapillary swimmer is studied using the lattice Boltzmann method. We extend on our previous work, which deals with the self-assembly and a specific type of the swimmer motion characterized by the swimmer's maximum velocity centred around the particle's inverse viscous time. Here, we identify additional regimes of motion. First, modifying the ratio of surface tension and magnetic forces allows to study the swimmer propagation in the regime of significantly lower frequencies mainly defined by the strength of the magnetocapillary potential. Second, introducing a constant magnetic contribution in each of the particles in addition to their magnetic moment induced by external fields leads to another regime characterized by strong in-plane swimmer reorientations that resemble experimental observations.
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Affiliation(s)
- Alexander Sukhov
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Straße 248, 90429, Nuremberg, Germany.
| | - Maxime Hubert
- PULS Group, Department of Physics, Interdisciplinary Center for Nanostructured Films, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058, Erlangen, Germany
| | - Galien Grosjean
- GRASP Lab, CESAM Research Unit, Université de Liège, Allée du 6 Août 19, 4000, Liège, Belgium
- IST Austria, Lab Building West, Am Campus 1, 3400, Klosterneuburg, Austria
| | - Oleg Trosman
- PULS Group, Department of Physics, Interdisciplinary Center for Nanostructured Films, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058, Erlangen, Germany
| | - Sebastian Ziegler
- PULS Group, Department of Physics, Interdisciplinary Center for Nanostructured Films, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058, Erlangen, Germany
| | - Ylona Collard
- GRASP Lab, CESAM Research Unit, Université de Liège, Allée du 6 Août 19, 4000, Liège, Belgium
| | - Nicolas Vandewalle
- GRASP Lab, CESAM Research Unit, Université de Liège, Allée du 6 Août 19, 4000, Liège, Belgium
| | - Ana-Sunčana Smith
- PULS Group, Department of Physics, Interdisciplinary Center for Nanostructured Films, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058, Erlangen, Germany
- Group for Computational Life Sciences, Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička cesta 54, P.P. 180, Zagreb, 10002, Croatia
| | - Jens Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Straße 248, 90429, Nuremberg, Germany
- Department of Chemical and Biological Engineering and Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429, Nuremberg, Germany
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Abdi H, Nejat Pishkenari H. Controlled swarm motion of self-propelled microswimmers for energy saving. JOURNAL OF MICRO-BIO ROBOTICS 2021. [DOI: 10.1007/s12213-021-00142-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Dynamic Modeling and Optimal Control of a Novel Microswimmer with Gimbal Based Disks. ROBOTICA 2021. [DOI: 10.1017/s0263574720001289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
SUMMARY
We have introduced a new low-Reynolds-number microrobot with high 3D maneuverability. Our novel proposed microrobot has a higher rank of the controllability matrix with respect to the previous microswimmers which makes it capable of performing complex motions in space. In this study, governing equations of the microswimmer’s motion have been derived and simulated. Subsequently, we have proposed a cascade optimal control technique to control the swimmer trajectory. In the proposed control scheme, the actuation is provided in a way that an exponential stability on the system trajectory error as well as minimum fluctuations of control signals are achieved.
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Wischnewski C, Kierfeld J. Snapping elastic disks as microswimmers: swimming at low Reynolds numbers by shape hysteresis. SOFT MATTER 2020; 16:7088-7102. [PMID: 32657319 DOI: 10.1039/d0sm00741b] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We illustrate a concept for shape-changing microswimmers, which exploits the hysteresis of a shape transition of an elastic object, by an elastic disk undergoing cyclic localized swelling. Driving the control parameter of a hysteretic shape transition in a completely time-reversible manner gives rise to a non-time-reversible shape sequence and a net swimming motion if the elastic object is immersed into a viscous fluid. We prove this concept with a microswimmer which is a flat circular elastic disk that undergoes a transition into a dome-like shape by localized swelling of an inner disk. The control parameter of this shape transition is a scalar swelling factor of the disk material. With a fixed outer frame with an additional attractive interaction in the central region, the shape transition between flat and dome-like shape becomes hysteretic and resembles a hysteretic opening and closing of a scallop. Employing Stokesian dynamics simulations of a discretized version of the disk we show that the swimmer is effectively moving into the direction of the opening of the dome in a viscous fluid if the swelling parameter is changed in a time-reversible manner. The swimming mechanism can be qualitatively reproduced by a simple 9-bead model.
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Abstract
Copepods are agile microcrustaceans that are capable of maneuvering freely in water. However, the physical mechanisms driving their rotational motion are not entirely clear in small larvae (nauplii). Here we report high-speed video observations of copepod nauplii performing acrobatic feats with three pairs of appendages. Our results show rotations about three principal axes of the body: yaw, roll, and pitch. The yaw rotation turns the body to one side and results in a circular swimming path. The roll rotation consists of the body spiraling around a nearly linear path, similar to an aileron roll of an airplane. We interpret the yaw and roll rotations to be facilitated by appendage pronation or supination. The pitch rotation consists of flipping on the spot in a maneuver that resembles a backflip somersault. The pitch rotation involved tail bending and was not observed in the earliest stages of nauplii. The maneuvering strategies adopted by plankton may inspire the design of microscopic robots, equipped with suitable controls for reorienting autonomously in three dimensions.
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Sukhov A, Ziegler S, Xie Q, Trosman O, Pande J, Grosjean G, Hubert M, Vandewalle N, Smith AS, Harting J. Optimal motion of triangular magnetocapillary swimmers. J Chem Phys 2019; 151:124707. [DOI: 10.1063/1.5116860] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Alexander Sukhov
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Straße 248, 90429 Nürnberg, Germany
| | - Sebastian Ziegler
- Institute for Theoretical Physics, Friedrich-Alexander University Erlangen-Nürnberg, 91054 Erlangen, Germany
| | - Qingguang Xie
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Oleg Trosman
- Institute for Theoretical Physics, Friedrich-Alexander University Erlangen-Nürnberg, 91054 Erlangen, Germany
| | - Jayant Pande
- Department of Physics, Bar-Ilan University, 52900 Ramat Gan, Israel
| | - Galien Grosjean
- Université de Liège, GRASP Lab, CESAM Research Unit, Allée du 6 Août 19, Liège 4000, Belgium
| | - Maxime Hubert
- Université de Liège, GRASP Lab, CESAM Research Unit, Allée du 6 Août 19, Liège 4000, Belgium
| | - Nicolas Vandewalle
- Université de Liège, GRASP Lab, CESAM Research Unit, Allée du 6 Août 19, Liège 4000, Belgium
| | - Ana-Sunčana Smith
- Institute for Theoretical Physics, Friedrich-Alexander University Erlangen-Nürnberg, 91054 Erlangen, Germany
| | - Jens Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Straße 248, 90429 Nürnberg, Germany
- Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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Abstract
Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and/or their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler–Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.
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Daddi-Moussa-Ider A, Lisicki M, Mathijssen AJTM, Hoell C, Goh S, Bławzdziewicz J, Menzel AM, Löwen H. State diagram of a three-sphere microswimmer in a channel. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:254004. [PMID: 29757157 DOI: 10.1088/1361-648x/aac470] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that 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. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.
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Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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Daddi-Moussa-Ider A, Lisicki M, Hoell C, Löwen H. Swimming trajectories of a three-sphere microswimmer near a wall. J Chem Phys 2018; 148:134904. [DOI: 10.1063/1.5021027] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Maciej Lisicki
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd., Cambridge CB3 0WA, United Kingdom
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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