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Tek Mıknatıs aracığılı ile bir Manyetotaktik Bakterinin Adaptif Manevra Kontrolü için Bağımsız Eklem Kontrol Simulasyonları

Year 2020, Ejosat Special Issue 2020 (ISMSIT), 50 - 59, 30.11.2020
https://doi.org/10.31590/ejosat.818986

Abstract

Mikro robotik sistemlerin invaziv olmayan tıptaki muhtemel uygulamaları son on yıldır literatürde yoğun bir şekilde gösterilmektedir. Yayınlanan çalışmalar büyük oranda bilgisayar kontrollü bir harici elektromanyetik alan içerisinde hareket eden farklı tiplerdeki yapay veya biyo-hibrid mikro yüzücülerin performansına odaklanmıştır. Mikro yüzücülerin tamamen canlı doku içinde veya harici ortamlarda yüzme ve hareket kontrol performansı ile ilgili çalışmalar yaygındır, ancak biyo-hibrid bir mikro yüzücünün başka bir robot yardımı ile hareket kontrolü şu ana kadar literatürde hiç detaylı olarak gösterilmemiştir. Bu çalışmada, gerçek bir manyeto taktik bakteri hücresinin (Magnetospirillum Gryphiswaldens) belirli bir mesafeden hareket ve manevra kontrolünün simülasyonu yapılmıştır. Seçilen canlı hücrenin yüzme yönü, mıknatıs yerleştirilmiş bir robot kolunun hareketi ve bu mıknatısın manyetik alanı sonucu ortaya çıkan manyetik tork yardımı ile kontrol edilmektedir. Kontrol performansı, süreksiz fonsksiyon olarak tanımlanmış oryantasyon referansına karşın ortaya çıkan pozisyon takip hatasının oransal – integral – türev (PID) denetleyicisi yardımı ile minimize edilmesine dayanmaktadır. Ayrıca, integral katsayısı anlık hataya bağlı olarak değişecek şekilde, yani adaptif olarak, modellenmiştir. Tüm sistemin dinamik ve kinematik davranışı için nümerik çözümler zamana bağlı olarak gerçekleştirilmiştir. Hareket kontrol sisteminin performansı, mikro robotun düzlemsel hareketindeki her bir serbestlik derecesi için ayrı ayrı incelenmiştir. Simülasyon çalışmaları göstermektedir ki; bağımsız eklem kontrolü metodu ile hareket ettirilen düzlemsel bir robot kol, aynı anda canlı hücrenin düz bir katı yüzeyine yakın olarak hareketini takip ederken, yüzme yönünü tayin etmek için de başarılı bir şekilde kullanılabilir. Ayrıca, yapılan simülasyonlar, manyetik alandaki efektif atalet ve mikro robot üzerinde hissedilen sıvı direncinin kontrol reaksiyonunda küçük fakat hissedilir bir gecikmeye neden olduğuna işaret etmektedir.

References

  • François, Q., André, A., Duplat, B., Haliyo, S., & Régnier, S. (2019) Tracking systems for intracranial medical devices: a review, Medical Devices and Sensors, 2(2), e10033. https://doi.org/10.1002/mds3.10033
  • Ceylan, H., Giltinan, J., Kozielski, K., & Sitti, M. (2017) Mobile microrobots for bioengineering applications, Lab on a Chip, 17(10), 1705-1724. https://doi.org/10.1039/C7LC00064B
  • Sitti, M., Ceylan, H., Hu, W., Giltinan, J., Turan, M., Yim, S., & Diller, E. (2015) Biomedical applications of untethered mobile milli/microrobots, Proceedings of the IEEE, 103(2), 205-224. https://doi.org/10.1109/JPROC.2014.2385105
  • Nelson, B.J., Kaliakatsos, I.K., & Abbott, J.J. (2010) Microrobots for minimally invasive medicine, Annual Review of Biomedical Engineering, 12, 55-85. https://doi.org/10.1146/annurev-bioeng-010510-103409
  • Tabak, A.F. (2019) Bioinspired and biomimetic micro-robotics for therapeutic applications, in Handbook of Biomechatronics, 1. Ed., J. Segil, Eds., Academic Press, U.K. https://doi.org/10.1016/b978-0-12-812539-7.00010-6
  • Singh, A.V., Ansari, M.H.D., Laux, P., & Luch, A., (2019) Micronanorobots: important considerations when developing novel drug delivery platforms, Expert Opinion on Drug Delivery, 16(11), 1259-1275. https://doi.org/10.1080/17425247.2019.1676228
  • Soto, F., & Chrostowski, R. (2018) Frontiers of medical micro/nanorobotics: in vivo applications and commercialization perspectives toward clinical uses, Frontiers in Bioengineering and Biotechnology, 6, 170. https://doi.org/10.3389/fbioe.2018.00170
  • Dreyfus, R., Baudry, J., Roper, M.L., Fermigier, M., Stone, H.A., & Bibette, J. (2005) Microscopic artificial swimmers, Nature, 437, 862-865. https://doi.org/10.1038/nature04090
  • Alapan, Y., Yasa, O., Schauer, O., Giltinan, J., Tabak, A.F., Sourjik, V., & Sitti, M. (2018) Soft erythrocyte-based bacterial microswimmers for cargo delivery, Science Robotics, 3(17), eaar4423. https://doi.org/10.1126/scirobotics.aar4423
  • Medina-Sánchez, M., Schwarz, L., Meyer, A.K., Hebenstreit, F., & Schmidt, O.G. (2016) Cellular Cargo Delivery: toward assisted fertilization by sperm-carrying micromotors, Nano Letters, 16(1), 555-561. https://doi.org/10.1021/acs.nanolett.5b04221
  • Nagai, M., Hirano, T., & Shibata, T. (2019) Phototactic algae-driven unidirectional transport of submillimeter-sized cargo in a microchannel, Micromachines, vol. 10(2), 130. https://doi.org/10.3390/mi10020130
  • Belharet, K., Folio, D., & Ferreira, A. (2010) Endovascular navigation of a ferromagnetic microrobot using MRI-based predictive control, IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, 2804-2809. https://doi.org/10.1109/IROS.2010.5650803
  • Tamaz, S., Gourdeau, R., Chanu, A., Mathieu, J.-B., & Martel, S. (2008) Real-time MRI-based control of a ferromagnetic core for endovascular navigation, IEEE Transactions on Bio-Medical Engineering, 55(7), 1854-1863. https://doi.org/10.1109/TBME.2008.919720
  • Khalil, I.S.M., Alfar, A., Tabak, A.F., Klingner, A., Stramigioli, S., & Sitti, M. (2017a) Positioning of drug carriers using permanent magnet-based robotic system in three-dimensional space, IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Munich, Germany, 1117-1122. https://doi.org/10.1109/AIM.2017.8014168
  • Servant, A., Qiu, F., Mazza, M., Kostarelos, K., & Nelson, B.J. (2015) Controlled in vivo swimming of a swarm of bacteria-like microrobotic flagella, Advanced Materials, 27(19), 2981-2988. https://doi.org/10.1002/adma.201404444
  • Wu, Z., Troll, J., Jeong, H.-H., Wei, Q., Stang, M., Ziemssen, F., Wang, Z., Dong, M., Schnichels, S., Qui, T., & Fischer, P. (2018) A swarm of slippery micropropellers penetrates the vitreous body of the eye, Science Advances, vol. 4(11), eaat4388. https://doi.org/10.1126/sciadv.aat4388
  • Ceylan, H., Yasa, I.C., Yasa, O., Tabak, A.F., Giltinan J., Sitti, M. (2018) 3D-printed biodegradable microswimmer for drug delivery and targeted cell labeling, bioRxiv, 1, 379024. https://doi.org/10.1101/379024
  • Ghosh, A., & Fischer, P. (2009) Controlled propulsion of artificial magnetic nanostructured propellers, Nano Letters, 9(6), 2243-2245. https://doi.org/10.1021/nl900186w
  • Felfoul, O., & Martel, S. (2013) Assessment of navigation control strategy for magnetotactic bacteria in microchannel: toward targeting solid tumours, Biomedical Microdevices, 15(6), 1015-1024. https://doi.org/10.1007/s10544-013-9794-4
  • Kummer, M.P., Abbott, J.J., Kratochvil, B.E., Borer, R., Sengul, A., & Nelson, B.J. (2010) OctoMag: an electromagnetic system for 5-dof wireless micromanipulation, IEEE Transactions on Robotics, 26(6), 1006-1017. https://doi.org/10.1109/TRO.2010.2073030
  • Fountain, T.W.R., Kailat, P.V., Abbott, J.J., (2010) Wireless control of magnetic helical microrobots using a rotating-permanent-magnet manipulator, International Conference on IEEE Robotics and Automation, Anchorage, AK, USA, 576-581. https://doi.org/10.1109/ROBOT.2010.5509245
  • Petruska, A.J., & Abbott, J.J. (2013) Optimal permanent-magnet geometries for dipole field approximation, IEEE Transactions on Magnetics, 49(2), 811–819. https://doi.org/10.1109/TMAG.2012.2205014
  • Akçura, N., Çetin, L., Kahveci, A., Alasli, A.K., Can, F.C., & Tamer, Ö. (2018) Guided motion control methodology for microrobots, 6th International Conference on Control Engineering & Information Technology, Istanbul, Turkey. https://doi.org/10.1109/CEIT.2018.8751803
  • Khalil, I.S.M., Pichel, M.P., Abelmann, L., & Misra, S., (2013) Closed-loop control of magnetotactic bacteria, International Journal of Robotics Research, 32(6), 637-649. https://doi.org/10.1177/0278364913479412
  • Khalil, I.S.M., Tabak, A.F., Hageman, T., Ewis, M., Pichel, M., Mitwally, M.E., El-Din, N.S., Abelmann, L., & Sitti, M. (2017b) Near-surface effects on the controlled motion of magnetotactic bacteria, IEEE International Conference on Robotics and Automation, Singapore, 5976-5982. https://doi.org/10.1109/ICRA.2017.7989705
  • Spong, M.W., & Vidyasagar, M. (1989) Robot Dynamics and Control. John Wiley and Sons, Inc., New Jersey.
  • Othayoth, R.S., Chittawadigi, R.G., Joshi, R.P., & Saha, S.K. (2017) Robot kinematics made easy using RoboAnalyzer software, Computer Applications in Engineering Education, 25(5), 669-680. https://doi.org/10.1002/cae.21828
  • Raibert, M.H., & Craig, J.J. (1981) Hybrid position/force control of manipulators, Journal of Dynamic Systems, Measurement, and Control, 102, 126-133. https://doi.org/10.1115/1.3139652
  • Purcell, E.M. (1977) Life at low Reynolds number, American Journal of Physics, 45(1), 3-11, https://doi.org/10.1119/1.10903
  • Keller, J.B., & Rubinow, S.I. (1976) Swimming of flagellated microorganisms, Biophysical Journal, 16(2), 151-170. https://doi.org/10.1016/s0006-3495(76)85672-x
  • Tabak, A.F. (2018) Hydrodynamic impedance of bacteria and bacteria-inspired micro-swimmers: a new strategy to predict power consumption of swimming micro-robots for real-time applications, Advanced Theory and Simulations, 1(4), 1700013. https://doi.org/10.1002/adts.201700013
  • Rengifo, C., Aoustin, Y., Chevallereau, C., & Plestan, F. (2009) A penalty-based approach for contact forces computation in bipedal robots, IEEE-RAS International Conference on Humanoid Robots, Paris, France, 121-127. https://doi.org/10.1109/ICHR.2009.5379590
  • M. Denai, M., Linkens, D.A., Asbury, A.J., & Gray, W.M. (1990) Self tuning PID control of atracurium-induced muscle relaxation in surgical patients, IEE Proceedings D – Control Theory and Applications, 137(5), 261-272. https://doi.org/10.1049/ip-d.1990.0032
  • Lugmair, M., Froriep, R., Kuplent, F., & Langhans, L. (2003) Tempo beim laser im griff, F&M Elektronik Jahrgang, 111(5), 32-35.
  • Dong, F., Huang, Z., Qiu, D., Hao, L., Wu, W., & Jin, Z. (2019) Design and analysis of a small-scale linear propulsion system for maglev applications (1) – the overall design process, IEEE Transactions on Applied Superconductivity, 29(2), 5201005. https://doi.org/10.1109/TASC.2019.2895312
  • Maxon Group (2019) EC 45 flat Ø42.8 mm, brushless, 70 Watt, Maxon Catalogue Page. Retrieved from WWW https://www.maxongroup.com/maxon/view/product/397172 on 10.01.2019.
  • Eaton, J.W., Bateman, D., Hauberg, S., & Wehbring, R. (2019) GNU Octave version 5.1.0 manual: a high level interactive language for numerical computations.
  • Shampine, L.F., & Gordon, M.K. (1975) Computer Solution of Ordinary Differential Equations, W. H. Freeman and Company, San Francisco.
  • Lauga, E., DiLuzio, W.R., Whitesides, G.M., & Stone, H.A. (2006) Swimming in circles: Motion of bacteria in near solid boundaries, Biophysical Journal, 90, 400-412. https://doi.org/10.1529/biophysj.105.069401
  • Constantino, M.A., Jabbarzadeh, M., Fu, H.C., Bansil, R. (2016) Helical and rod-shaped bacteria swim in helical trajectories with little additional propulsion from helical shape, Science Advances, 2(11), e1601661. https://doi.org/10.1126/sciadv.1601661

Independent Joint Control Simulations on Adaptive Maneuvering of a Magnetotactic Bacterium via a Single Permanent Magnet

Year 2020, Ejosat Special Issue 2020 (ISMSIT), 50 - 59, 30.11.2020
https://doi.org/10.31590/ejosat.818986

Abstract

The use of micro-robotic systems in non-invasive medicine has been heavily promoted in the literature for the last decade. The studies usually focus on artificial or biohybrid microswimmers of various origins subject to the effect of an external electromagnetic field controlled by a computer. Although there exist several motion control studies shared to date, control of a bio-hybrid microswimmer has rarely been demonstrated employing an open kinematic chain, in detail. In this work, motion control of an isolated magnetotactic bacterium cell (Magnetospirillum Gryphiswaldens) is presented via a magnetic field actively positioned by an open kinematic chain. The cell is modeled with its complete environment to make it as realistic as possible along with the magnetic torque, which is induced by a single magnet attached at the end effector of a robotic arm, exerted on it for maneuvering control. The control is based on a proportional – integral – derivative (PID) gain scheme with adaptive integral gain to focus on a particular steady-state error with discontinuous reference signals. The control signal is transformed into pulse width modulation (PWM) signals to drive the motors articulating the joints of the open kinematic chain, the inverse kinematics of which is designed to be simple enough to achieve independent joint control. A numerical analysis of the coupled system is carried out in the time domain. The performance of the said motion control approach is investigated for each degree of freedom for the planar motion of the microswimmer. Simulations demonstrate a planar open kinematic chain is capable of control the gait of the microswimmer while following its trajectory near a planar boundary via independent joint control. Furthermore, simulations demonstrate that the effective magnetic inertia and the shear stress results in a small but certain lag in the motion control performance of the overall system.

References

  • François, Q., André, A., Duplat, B., Haliyo, S., & Régnier, S. (2019) Tracking systems for intracranial medical devices: a review, Medical Devices and Sensors, 2(2), e10033. https://doi.org/10.1002/mds3.10033
  • Ceylan, H., Giltinan, J., Kozielski, K., & Sitti, M. (2017) Mobile microrobots for bioengineering applications, Lab on a Chip, 17(10), 1705-1724. https://doi.org/10.1039/C7LC00064B
  • Sitti, M., Ceylan, H., Hu, W., Giltinan, J., Turan, M., Yim, S., & Diller, E. (2015) Biomedical applications of untethered mobile milli/microrobots, Proceedings of the IEEE, 103(2), 205-224. https://doi.org/10.1109/JPROC.2014.2385105
  • Nelson, B.J., Kaliakatsos, I.K., & Abbott, J.J. (2010) Microrobots for minimally invasive medicine, Annual Review of Biomedical Engineering, 12, 55-85. https://doi.org/10.1146/annurev-bioeng-010510-103409
  • Tabak, A.F. (2019) Bioinspired and biomimetic micro-robotics for therapeutic applications, in Handbook of Biomechatronics, 1. Ed., J. Segil, Eds., Academic Press, U.K. https://doi.org/10.1016/b978-0-12-812539-7.00010-6
  • Singh, A.V., Ansari, M.H.D., Laux, P., & Luch, A., (2019) Micronanorobots: important considerations when developing novel drug delivery platforms, Expert Opinion on Drug Delivery, 16(11), 1259-1275. https://doi.org/10.1080/17425247.2019.1676228
  • Soto, F., & Chrostowski, R. (2018) Frontiers of medical micro/nanorobotics: in vivo applications and commercialization perspectives toward clinical uses, Frontiers in Bioengineering and Biotechnology, 6, 170. https://doi.org/10.3389/fbioe.2018.00170
  • Dreyfus, R., Baudry, J., Roper, M.L., Fermigier, M., Stone, H.A., & Bibette, J. (2005) Microscopic artificial swimmers, Nature, 437, 862-865. https://doi.org/10.1038/nature04090
  • Alapan, Y., Yasa, O., Schauer, O., Giltinan, J., Tabak, A.F., Sourjik, V., & Sitti, M. (2018) Soft erythrocyte-based bacterial microswimmers for cargo delivery, Science Robotics, 3(17), eaar4423. https://doi.org/10.1126/scirobotics.aar4423
  • Medina-Sánchez, M., Schwarz, L., Meyer, A.K., Hebenstreit, F., & Schmidt, O.G. (2016) Cellular Cargo Delivery: toward assisted fertilization by sperm-carrying micromotors, Nano Letters, 16(1), 555-561. https://doi.org/10.1021/acs.nanolett.5b04221
  • Nagai, M., Hirano, T., & Shibata, T. (2019) Phototactic algae-driven unidirectional transport of submillimeter-sized cargo in a microchannel, Micromachines, vol. 10(2), 130. https://doi.org/10.3390/mi10020130
  • Belharet, K., Folio, D., & Ferreira, A. (2010) Endovascular navigation of a ferromagnetic microrobot using MRI-based predictive control, IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, 2804-2809. https://doi.org/10.1109/IROS.2010.5650803
  • Tamaz, S., Gourdeau, R., Chanu, A., Mathieu, J.-B., & Martel, S. (2008) Real-time MRI-based control of a ferromagnetic core for endovascular navigation, IEEE Transactions on Bio-Medical Engineering, 55(7), 1854-1863. https://doi.org/10.1109/TBME.2008.919720
  • Khalil, I.S.M., Alfar, A., Tabak, A.F., Klingner, A., Stramigioli, S., & Sitti, M. (2017a) Positioning of drug carriers using permanent magnet-based robotic system in three-dimensional space, IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Munich, Germany, 1117-1122. https://doi.org/10.1109/AIM.2017.8014168
  • Servant, A., Qiu, F., Mazza, M., Kostarelos, K., & Nelson, B.J. (2015) Controlled in vivo swimming of a swarm of bacteria-like microrobotic flagella, Advanced Materials, 27(19), 2981-2988. https://doi.org/10.1002/adma.201404444
  • Wu, Z., Troll, J., Jeong, H.-H., Wei, Q., Stang, M., Ziemssen, F., Wang, Z., Dong, M., Schnichels, S., Qui, T., & Fischer, P. (2018) A swarm of slippery micropropellers penetrates the vitreous body of the eye, Science Advances, vol. 4(11), eaat4388. https://doi.org/10.1126/sciadv.aat4388
  • Ceylan, H., Yasa, I.C., Yasa, O., Tabak, A.F., Giltinan J., Sitti, M. (2018) 3D-printed biodegradable microswimmer for drug delivery and targeted cell labeling, bioRxiv, 1, 379024. https://doi.org/10.1101/379024
  • Ghosh, A., & Fischer, P. (2009) Controlled propulsion of artificial magnetic nanostructured propellers, Nano Letters, 9(6), 2243-2245. https://doi.org/10.1021/nl900186w
  • Felfoul, O., & Martel, S. (2013) Assessment of navigation control strategy for magnetotactic bacteria in microchannel: toward targeting solid tumours, Biomedical Microdevices, 15(6), 1015-1024. https://doi.org/10.1007/s10544-013-9794-4
  • Kummer, M.P., Abbott, J.J., Kratochvil, B.E., Borer, R., Sengul, A., & Nelson, B.J. (2010) OctoMag: an electromagnetic system for 5-dof wireless micromanipulation, IEEE Transactions on Robotics, 26(6), 1006-1017. https://doi.org/10.1109/TRO.2010.2073030
  • Fountain, T.W.R., Kailat, P.V., Abbott, J.J., (2010) Wireless control of magnetic helical microrobots using a rotating-permanent-magnet manipulator, International Conference on IEEE Robotics and Automation, Anchorage, AK, USA, 576-581. https://doi.org/10.1109/ROBOT.2010.5509245
  • Petruska, A.J., & Abbott, J.J. (2013) Optimal permanent-magnet geometries for dipole field approximation, IEEE Transactions on Magnetics, 49(2), 811–819. https://doi.org/10.1109/TMAG.2012.2205014
  • Akçura, N., Çetin, L., Kahveci, A., Alasli, A.K., Can, F.C., & Tamer, Ö. (2018) Guided motion control methodology for microrobots, 6th International Conference on Control Engineering & Information Technology, Istanbul, Turkey. https://doi.org/10.1109/CEIT.2018.8751803
  • Khalil, I.S.M., Pichel, M.P., Abelmann, L., & Misra, S., (2013) Closed-loop control of magnetotactic bacteria, International Journal of Robotics Research, 32(6), 637-649. https://doi.org/10.1177/0278364913479412
  • Khalil, I.S.M., Tabak, A.F., Hageman, T., Ewis, M., Pichel, M., Mitwally, M.E., El-Din, N.S., Abelmann, L., & Sitti, M. (2017b) Near-surface effects on the controlled motion of magnetotactic bacteria, IEEE International Conference on Robotics and Automation, Singapore, 5976-5982. https://doi.org/10.1109/ICRA.2017.7989705
  • Spong, M.W., & Vidyasagar, M. (1989) Robot Dynamics and Control. John Wiley and Sons, Inc., New Jersey.
  • Othayoth, R.S., Chittawadigi, R.G., Joshi, R.P., & Saha, S.K. (2017) Robot kinematics made easy using RoboAnalyzer software, Computer Applications in Engineering Education, 25(5), 669-680. https://doi.org/10.1002/cae.21828
  • Raibert, M.H., & Craig, J.J. (1981) Hybrid position/force control of manipulators, Journal of Dynamic Systems, Measurement, and Control, 102, 126-133. https://doi.org/10.1115/1.3139652
  • Purcell, E.M. (1977) Life at low Reynolds number, American Journal of Physics, 45(1), 3-11, https://doi.org/10.1119/1.10903
  • Keller, J.B., & Rubinow, S.I. (1976) Swimming of flagellated microorganisms, Biophysical Journal, 16(2), 151-170. https://doi.org/10.1016/s0006-3495(76)85672-x
  • Tabak, A.F. (2018) Hydrodynamic impedance of bacteria and bacteria-inspired micro-swimmers: a new strategy to predict power consumption of swimming micro-robots for real-time applications, Advanced Theory and Simulations, 1(4), 1700013. https://doi.org/10.1002/adts.201700013
  • Rengifo, C., Aoustin, Y., Chevallereau, C., & Plestan, F. (2009) A penalty-based approach for contact forces computation in bipedal robots, IEEE-RAS International Conference on Humanoid Robots, Paris, France, 121-127. https://doi.org/10.1109/ICHR.2009.5379590
  • M. Denai, M., Linkens, D.A., Asbury, A.J., & Gray, W.M. (1990) Self tuning PID control of atracurium-induced muscle relaxation in surgical patients, IEE Proceedings D – Control Theory and Applications, 137(5), 261-272. https://doi.org/10.1049/ip-d.1990.0032
  • Lugmair, M., Froriep, R., Kuplent, F., & Langhans, L. (2003) Tempo beim laser im griff, F&M Elektronik Jahrgang, 111(5), 32-35.
  • Dong, F., Huang, Z., Qiu, D., Hao, L., Wu, W., & Jin, Z. (2019) Design and analysis of a small-scale linear propulsion system for maglev applications (1) – the overall design process, IEEE Transactions on Applied Superconductivity, 29(2), 5201005. https://doi.org/10.1109/TASC.2019.2895312
  • Maxon Group (2019) EC 45 flat Ø42.8 mm, brushless, 70 Watt, Maxon Catalogue Page. Retrieved from WWW https://www.maxongroup.com/maxon/view/product/397172 on 10.01.2019.
  • Eaton, J.W., Bateman, D., Hauberg, S., & Wehbring, R. (2019) GNU Octave version 5.1.0 manual: a high level interactive language for numerical computations.
  • Shampine, L.F., & Gordon, M.K. (1975) Computer Solution of Ordinary Differential Equations, W. H. Freeman and Company, San Francisco.
  • Lauga, E., DiLuzio, W.R., Whitesides, G.M., & Stone, H.A. (2006) Swimming in circles: Motion of bacteria in near solid boundaries, Biophysical Journal, 90, 400-412. https://doi.org/10.1529/biophysj.105.069401
  • Constantino, M.A., Jabbarzadeh, M., Fu, H.C., Bansil, R. (2016) Helical and rod-shaped bacteria swim in helical trajectories with little additional propulsion from helical shape, Science Advances, 2(11), e1601661. https://doi.org/10.1126/sciadv.1601661
There are 40 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ahmet Fatih Tabak 0000-0003-3311-6942

Publication Date November 30, 2020
Published in Issue Year 2020 Ejosat Special Issue 2020 (ISMSIT)

Cite

APA Tabak, A. F. (2020). Independent Joint Control Simulations on Adaptive Maneuvering of a Magnetotactic Bacterium via a Single Permanent Magnet. Avrupa Bilim Ve Teknoloji Dergisi50-59. https://doi.org/10.31590/ejosat.818986