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2019


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Bistability of magnetic states in Fe-Pd nanocap arrays

Aravind, P. B., Heigl, M., Fix, M., Groß, F., Gräfe, J., Mary, A., Rajgowrav, C. R., Krupiński, M., Marszałek, M., Thomas, S., Anantharaman, M. R., Albrecht, M.

Nanotechnology, 30, pages: 405705, 2019 (article)

Abstract
Magnetic bistability between vortex and single domain states in nanostructures are of great interest from both fundamental and technological perspectives. In soft magnetic nanostructures, the transition from a uniform collinear magnetic state to a vortex state (or vice versa) induced by a magnetic field involves an energy barrier. If the thermal energy is large enough for overcoming this energy barrier, magnetic bistability with a hysteresis-free switching occurs between the two magnetic states. In this work, we tune this energy barrier by tailoring the composition of FePd alloys, which were deposited onto self-assembled particle arrays forming magnetic vortex structures on top of the particles. The bifurcation temperature, where a hysteresis-free transition occurs, was extracted from the temperature dependence of the annihilation and nucleation field which increases almost linearly with Fe content of the magnetic alloy. This study provides insights into the magnetization reversal process associated with magnetic bistability, which allows adjusting the bifurcation temperature range by the material properties of the nanosystem.

mms

link (url) [BibTex]

2019


link (url) [BibTex]


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An international laboratory comparison study of volumetric and gravimetric hydrogen adsorption measurements

Hurst, K. E., Gennett, T., Adams, J., Allendorf, M. D., Balderas-Xicohténcatl, R., Bielewski, M., Edwards, B., Espinal, L., Fultz, B., Hirscher, M., Hudson, M. S. L., Hulvey, Z., Latroche, M., Liu, D., Kapelewski, M., Napolitano, E., Perry, Z. T., Purewal, J., Stavila, V., Veenstra, M., White, J. L., Yuan, Y., Zhou, H., Zlotea, C., Parilla, P.

{ChemPhysChem}, 20(15):1997-2009, Wiley-VCH, Weinheim, Germany, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Hydrogen Energy

Hirscher, M., Autrey, T., Orimo, S.

{ChemPhysChem}, 20, pages: 1153-1411, Wiley-VCH, Weinheim, Germany, 2019 (misc)

mms

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Superior magnetic performance in FePt L10 nanomaterials

Son, K., Ryu, G. H., Jeong, H., Fink, L., Merz, M., Nagel, P., Schuppler, S., Richter, G., Goering, E., Schütz, G.

{Small}, 15(34), Wiley, Weinheim, Germany, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


Mobile microrobots for active therapeutic delivery
Mobile microrobots for active therapeutic delivery

Erkoc, P., Yasa, I. C., Ceylan, H., Yasa, O., Alapan, Y., Sitti, M.

Advanced Therapeutics, Wiley Online Library, 2019 (article)

pi

[BibTex]

[BibTex]


Shape-encoded dynamic assembly of mobile micromachines
Shape-encoded dynamic assembly of mobile micromachines

Alapan, Y., Yigit, B., Beker, O., Demirörs, A. F., Sitti, M.

Nature, 18, 2019 (article)

pi

[BibTex]

[BibTex]


Microfluidics Integrated Lithography‐Free Nanophotonic Biosensor for the Detection of Small Molecules
Microfluidics Integrated Lithography‐Free Nanophotonic Biosensor for the Detection of Small Molecules

Sreekanth, K. V., Sreejith, S., Alapan, Y., Sitti, M., Lim, C. T., Singh, R.

Advanced Optical Materials, 2019 (article)

pi

[BibTex]

[BibTex]


ENGINEERING Bio-inspired robotic collectives
ENGINEERING Bio-inspired robotic collectives

Sitti, M.

Nature, 567, pages: 314-315, Macmillan Publishers Ltd., London, England, 2019 (article)

pi

[BibTex]

[BibTex]


Peptide-Induced Biomineralization of Tin Oxide (SnO2) Nanoparticles for Antibacterial Applications
Peptide-Induced Biomineralization of Tin Oxide (SnO2) Nanoparticles for Antibacterial Applications

Singh, A. V., Jahnke, T., Xiao, Y., Wang, S., Yu, Y., David, H., Richter, G., Laux, P., Luch, A., Srivastava, A., Saxena, P. S., Bill, J., Sitti, M.

Journal of nanoscience and nanotechnology, 19, American Scientific Publishers, 2019 (article)

pi

[BibTex]

[BibTex]


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Vizualizing nanoscale spin waves using MAXYMUS

Gräfe, J., Weigand, M., Van Waeyenberge, B., Gangwar, A., Groß, F., Lisiecki, F., Rychly, J., Stoll, H., Träger, N., Förster, J., Stobiecki, F., Dubowik, J., Klos, H., Krwaczyk, M., Back, C. H., Goering, E. J., Schütz, G.

{Proceedings of SPIE}, 11090, SPIE, Bellingham, Washington, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Niobium near-surface composition during nitrogen infusion relevant for superconducting radio-frequency cavities

Semione, G. D. L., Dangwal Pandey, A., Tober, S., Pfrommer, J., Poulain, A., Drnec, J., Schütz, G., Keller, T. F., Noei, H., Vonk, V., Foster, B., Stierle, A.

{Physical Review Accelerators and Beams}, 22(10), American Physical Society, Ridge, NY, USA, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Electromechanical actuation of dielectric liquid crystal elastomers for soft robotics

Davidson, Z., Shahsavan, H., Guo, Y., Hines, L., Xia, Y., Yang, S., Sitti, M.

Bulletin of the American Physical Society, APS, 2019 (article)

pi

[BibTex]

[BibTex]


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A rational reinterpretation of dual process theories

Milli, S., Lieder, F., Griffiths, T.

2019 (article)

re

DOI [BibTex]

DOI [BibTex]


Probabilistic Linear Solvers: A Unifying View
Probabilistic Linear Solvers: A Unifying View

Bartels, S., Cockayne, J., Ipsen, I. C. F., Hennig, P.

Statistics and Computing, 2019 (article) Accepted

pn

link (url) [BibTex]

link (url) [BibTex]


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Systematic experimental study on quantum sieving of hydrogen isotopes in metal-amide-imidazolate frameworks with narrow 1-D channels

Mondal, S. S., Kreuzer, A., Behrens, K., Schütz, G., Holdt, H., Hirscher, M.

{ChemPhysChem}, 20(10):1311-1315, Wiley-VCH, Weinheim, Germany, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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The route to supercurrent transparent ferromagnetic barriers in superconducting matrix

Ivanov, Y. P., Soltan, S., Albrecht, J., Goering, E., Schütz, G., Zhang, Z., Chuvilin, A.

{ACS Nano}, 13(5):5655-5661, American Chemical Society, Washington, DC, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


Learning to Navigate Endoscopic Capsule Robots
Learning to Navigate Endoscopic Capsule Robots

Turan, M., Almalioglu, Y., Gilbert, H. B., Mahmood, F., Durr, N. J., Araujo, H., Sarı, A. E., Ajay, A., Sitti, M.

IEEE Robotics and Automation Letters, 4, 2019 (article)

pi

[BibTex]

[BibTex]


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Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces

Klus, S., Schuster, I., Muandet, K.

Journal of Nonlinear Science, 2019, First Online: 21 August 2019 (article)

ei

DOI [BibTex]

DOI [BibTex]


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Real-space imaging of confined magnetic skyrmion tubes

Birch, M. T., Cortés-Ortuño, D., Turnbull, L. A., Wilson, M. N., Groß, F., Träger, N., Laurenson, A., Bukin, N., Moody, S. H., Weigand, M., Schütz, G., Popescu, H., Fan, R., Steadman, P., Verezhak, J. A. T., Balakrishnan, G., Loudon, J. C., Twitchett-Harrison, A. C., Hovorka, O., Fangohr, H., Ogrin, F., Gräfe, J., Hatton, P. D.

2019 (misc)

mms

link (url) [BibTex]

link (url) [BibTex]


Order and Information in the Phases of a Torque-driven Artificial Collective System
Order and Information in the Phases of a Torque-driven Artificial Collective System

Wang, W., Gardi, G., Kishore, V., Koens, L., Son, D., Gilbert, H., Harwani, P., Lauga, E., Sitti, M.

arXiv preprint arXiv:1910.11226, 2019 (article)

pi

[BibTex]

[BibTex]


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Exploiting dynamic opening of apertures in a partially fluorinated MOF for enhancing H2 desorption temperature and isotope separation

Zhang, L., Jee, S., Park, J., Jung, M., Wallcher, D., Franz, A., Lee, W., Yoon, M., Choi, K., Hirscher, M., Oh, H.

{Journal of the American Chemical Society}, 141(50):19850-19858, American Chemical Society, Washington, DC, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Speeding up the extended Kalman filter approach for denoising XMCD movies of fast magnetization dynamics

Fähnle, M., Schütz, G.

{Ultramicroscopy}, 206, North-Holland, Amsterdam, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Artifacts from manganese reduction in rock samples prepared by focused ion beam (FIB) slicing for X-ray microspectroscopy

Macholdt, D. S., Förster, J., Müller, M., Weber, B., Kappl, M., Kilcoyne, A. L. D., Weigand, M., Leitner, J., Jochum, K. P., Pöhlker, C., Andreae, M. O.

{Geoscientific instrumentation, methods and data systems}, 8(1):97-111, Copernicus Publ., Göttingen, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Magnetic field dependence of mangetotransport properties of MgB2/CrO2 bilayer thin films

Alzayed, N. S., Shahabuddin, M., Ramey, S. M., Soltan, S.

{Journal of Superconductivity and Novel Magnetism}, 32(8):2447-2455, Springer Science + Business Media B.V., New York, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Mixed-state magnetotransport properties of MgB2 thin film prepared by pulsed laser deposition on an Al2O3 substrate

Alzayed, N. S., Shahabuddin, M., Ramey, S. M., Soltan, S.

{Journal of Materials Science: Materials in Electronics}, 30(2):1547-1552, Springer, Norwell, MA, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Comparison of theories of fast and ultrafast magnetization dynamics

Fähnle, M.

{Journal of Magnetism and Magnetic Materials}, 469, pages: 28-29, NH, Elsevier, Amsterdam, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Concepts for improving hydrogen storage in nanoporous materials

Broom, D. P., Webb, C. J., Fanourgakis, G. S., Froudakis, G. E., Trikalitis, P. N., Hirscher, M.

{International Journal of Hydrogen Energy}, 44(15):7768-7779, Elsevier, Amsterdam, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Controlling dislocation nucleation-mediatd plasticity in nanostructures via surface modification

Shin, J., Chen, L. Y., Sanli, U. T., Richter, G., Labat, S., Richard, M., Cornelius, T., Thomas, O., Gianola, D. S.

{Acta Materialia}, 166, pages: 572-586, Elsevier Science, Kidlington, 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]


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Reprogrammability and scalability of magnonic Fibonacci quasicrystals

Lisiecki, F., Rychly, J., Kuswik, P., Glowinski, H., Klos, J. W., Groß, F., Bykova, I., Weigand, M., Zelent, M., Goering, E. J., Schütz, G., Gubbiotti, G., Krawczyk, M., Stobiecki, F., Dubowik, J., Gräfe, J.

{Physical Review Applied}, 11(5), American Physical Society, College Park, Md. [u.a.], 2019 (article)

mms

DOI [BibTex]

DOI [BibTex]

2018


Role of symmetry in driven propulsion at low Reynolds number
Role of symmetry in driven propulsion at low Reynolds number

Sachs, J., Morozov, K. I., Kenneth, O., Qiu, T., Segreto, N., Fischer, P., Leshansky, A. M.

Phys. Rev. E, 98(6):063105, American Physical Society, December 2018 (article)

Abstract
We theoretically and experimentally investigate low-Reynolds-number propulsion of geometrically achiral planar objects that possess a dipole moment and that are driven by a rotating magnetic field. Symmetry considerations (involving parity, $\widehat{P}$, and charge conjugation, $\widehat{C}$) establish correspondence between propulsive states depending on orientation of the dipolar moment. Although basic symmetry arguments do not forbid individual symmetric objects to efficiently propel due to spontaneous symmetry breaking, they suggest that the average ensemble velocity vanishes. Some additional arguments show, however, that highly symmetrical ($\widehat{P}$-even) objects exhibit no net propulsion while individual less symmetrical ($\widehat{C}\widehat{P}$-even) propellers do propel. Particular magnetization orientation, rendering the shape $\widehat{C}\widehat{P}$-odd, yields unidirectional motion typically associated with chiral structures, such as helices. If instead of a structure with a permanent dipole we consider a polarizable object, some of the arguments have to be modified. For instance, we demonstrate a truly achiral ($\widehat{P}$- and $\widehat{C}\widehat{P}$-even) planar shape with an induced electric dipole that can propel by electro-rotation. We thereby show that chirality is not essential for propulsion due to rotation-translation coupling at low Reynolds number.

pf

link (url) DOI Project Page [BibTex]

2018


link (url) DOI Project Page [BibTex]


Swimming Back and Forth Using Planar Flagellar Propulsion at Low Reynolds Numbers
Swimming Back and Forth Using Planar Flagellar Propulsion at Low Reynolds Numbers

Khalil, I. S. M., Tabak, A. F., Hamed, Y., Mitwally, M. E., Tawakol, M., Klingner, A., Sitti, M.

Advanced Science, 5(2):1700461, 2018 (article)

Abstract
Abstract Peritrichously flagellated Escherichia coli swim back and forth by wrapping their flagella together in a helical bundle. However, other monotrichous bacteria cannot swim back and forth with a single flagellum and planar wave propagation. Quantifying this observation, a magnetically driven soft two‐tailed microrobot capable of reversing its swimming direction without making a U‐turn trajectory or actively modifying the direction of wave propagation is designed and developed. The microrobot contains magnetic microparticles within the polymer matrix of its head and consists of two collinear, unequal, and opposite ultrathin tails. It is driven and steered using a uniform magnetic field along the direction of motion with a sinusoidally varying orthogonal component. Distinct reversal frequencies that enable selective and independent excitation of the first or the second tail of the microrobot based on their tail length ratio are found. While the first tail provides a propulsive force below one of the reversal frequencies, the second is almost passive, and the net propulsive force achieves flagellated motion along one direction. On the other hand, the second tail achieves flagellated propulsion along the opposite direction above the reversal frequency.

pi

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Parallel and functionally segregated processing of task phase and conscious content in the prefrontal cortex

Kapoor, V., Besserve, M., Logothetis, N. K., Panagiotaropoulos, T. I.

Communications Biology, 1(215):1-12, December 2018 (article)

ei

link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


Optical and Thermophoretic Control of Janus Nanopen Injection into Living Cells
Optical and Thermophoretic Control of Janus Nanopen Injection into Living Cells

Maier, C. M., Huergo, M. A., Milosevic, S., Pernpeintner, C., Li, M., Singh, D. P., Walker, D., Fischer, P., Feldmann, J., Lohmüller, T.

Nano Letters, 18, pages: 7935–7941, November 2018 (article) Accepted

Abstract
Devising strategies for the controlled injection of functional nanoparticles and reagents into living cells paves the way for novel applications in nanosurgery, sensing, and drug delivery. Here, we demonstrate the light-controlled guiding and injection of plasmonic Janus nanopens into living cells. The pens are made of a gold nanoparticle attached to a dielectric alumina shaft. Balancing optical and thermophoretic forces in an optical tweezer allows single Janus nanopens to be trapped and positioned on the surface of living cells. While the optical injection process involves strong heating of the plasmonic side, the temperature of the alumina stays significantly lower, thus allowing the functionalization with fluorescently labeled, single-stranded DNA and, hence, the spatially controlled injection of genetic material with an untethered nanocarrier.

pf

link (url) DOI [BibTex]

link (url) DOI [BibTex]


A swarm of slippery micropropellers penetrates the vitreous body of the eye
A swarm of slippery micropropellers penetrates the vitreous body of the eye

Wu, Z., Troll, J., Jeong, H. H., Wei, Q., Stang, M., Ziemssen, F., Wang, Z., Dong, M., Schnichels, S., Qiu, T., Fischer, P.

Science Advances, 4(11):eaat4388, November 2018 (article)

Abstract
The intravitreal delivery of therapeutic agents promises major benefits in the field of ocular medicine. Traditional delivery methods rely on the random, passive diffusion of molecules, which do not allow for the rapid delivery of a concentrated cargo to a defined region at the posterior pole of the eye. The use of particles promises targeted delivery but faces the challenge that most tissues including the vitreous have a tight macromolecular matrix that acts as a barrier and prevents its penetration. Here, we demonstrate novel intravitreal delivery microvehicles slippery micropropellers that can be actively propelled through the vitreous humor to reach the retina. The propulsion is achieved by helical magnetic micropropellers that have a liquid layer coating to minimize adhesion to the surrounding biopolymeric network. The submicrometer diameter of the propellers enables the penetration of the biopolymeric network and the propulsion through the porcine vitreous body of the eye over centimeter distances. Clinical optical coherence tomography is used to monitor the movement of the propellers and confirm their arrival on the retina near the optic disc. Overcoming the adhesion forces and actively navigating a swarm of micropropellers in the dense vitreous humor promise practical applications in ophthalmology.

pf

Video: Nanorobots propel through the eye link (url) DOI [BibTex]

Video: Nanorobots propel through the eye link (url) DOI [BibTex]


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Reducing 3D Vibrations to 1D in Real Time

Park, G., Kuchenbecker, K. J.

Hands-on demonstration (4 pages) presented at AsiaHaptics, Incheon, South Korea, November 2018 (misc)

Abstract
For simple and realistic vibrotactile feedback, 3D accelerations from real contact interactions are usually rendered using a single-axis vibration actuator; this dimensional reduction can be performed in many ways. This demonstration implements a real-time conversion system that simultaneously measures 3D accelerations and renders corresponding 1D vibrations using a two-pen interface. In the demonstration, a user freely interacts with various objects using an In-Pen that contains a 3-axis accelerometer. The captured accelerations are converted to a single-axis signal, and an Out-Pen renders the reduced signal for the user to feel. We prepared seven conversion methods from the simple use of a single-axis signal to applying principal component analysis (PCA) so that users can compare the performance of each conversion method in this demonstration.

hi

Project Page [BibTex]

Project Page [BibTex]


A Large-Scale Fabric-Based Tactile Sensor Using Electrical Resistance Tomography
A Large-Scale Fabric-Based Tactile Sensor Using Electrical Resistance Tomography

Lee, H., Park, K., Kim, J., Kuchenbecker, K. J.

Hands-on demonstration (3 pages) presented at AsiaHaptics, Incheon, South Korea, November 2018 (misc)

Abstract
Large-scale tactile sensing is important for household robots and human-robot interaction because contacts can occur all over a robot’s body surface. This paper presents a new fabric-based tactile sensor that is straightforward to manufacture and can cover a large area. The tactile sensor is made of conductive and non-conductive fabric layers, and the electrodes are stitched with conductive thread, so the resulting device is flexible and stretchable. The sensor utilizes internal array electrodes and a reconstruction method called electrical resistance tomography (ERT) to achieve a high spatial resolution with a small number of electrodes. The developed sensor shows that only 16 electrodes can accurately estimate single and multiple contacts over a square that measures 20 cm by 20 cm.

hi

Project Page [BibTex]

Project Page [BibTex]


Deep Inertial Poser: Learning to Reconstruct Human Pose from Sparse Inertial Measurements in Real Time
Deep Inertial Poser: Learning to Reconstruct Human Pose from Sparse Inertial Measurements in Real Time

Huang, Y., Kaufmann, M., Aksan, E., Black, M. J., Hilliges, O., Pons-Moll, G.

ACM Transactions on Graphics, (Proc. SIGGRAPH Asia), 37, pages: 185:1-185:15, ACM, November 2018, Two first authors contributed equally (article)

Abstract
We demonstrate a novel deep neural network capable of reconstructing human full body pose in real-time from 6 Inertial Measurement Units (IMUs) worn on the user's body. In doing so, we address several difficult challenges. First, the problem is severely under-constrained as multiple pose parameters produce the same IMU orientations. Second, capturing IMU data in conjunction with ground-truth poses is expensive and difficult to do in many target application scenarios (e.g., outdoors). Third, modeling temporal dependencies through non-linear optimization has proven effective in prior work but makes real-time prediction infeasible. To address this important limitation, we learn the temporal pose priors using deep learning. To learn from sufficient data, we synthesize IMU data from motion capture datasets. A bi-directional RNN architecture leverages past and future information that is available at training time. At test time, we deploy the network in a sliding window fashion, retaining real time capabilities. To evaluate our method, we recorded DIP-IMU, a dataset consisting of 10 subjects wearing 17 IMUs for validation in 64 sequences with 330,000 time instants; this constitutes the largest IMU dataset publicly available. We quantitatively evaluate our approach on multiple datasets and show results from a real-time implementation. DIP-IMU and the code are available for research purposes.

ps

data code pdf preprint errata video DOI Project Page [BibTex]

data code pdf preprint errata video DOI Project Page [BibTex]


Universal Custom Complex Magnetic Spring Design Methodology
Universal Custom Complex Magnetic Spring Design Methodology

Woodward, M. A., Sitti, M.

IEEE Transactions on Magnetics, 54(1):1-13, October 2018 (article)

Abstract
A design methodology is presented for creating custom complex magnetic springs through the design of force-displacement curves. This methodology results in a magnet configuration, which will produce a desired force-displacement relationship. Initially, the problem is formulated and solved as a system of linear equations. Then, given the limited likelihood of a single solution being feasibly manufactured, key parameters of the solution are extracted and varied to create a family of solutions. Finally, these solutions are refined using numerical optimization. Given the properties of magnets, this methodology can create any well-defined function of force versus displacement and is model-independent. To demonstrate this flexibility, a number of example magnetic springs are designed; one of which, designed for use in a jumping-gliding robot's shape memory alloy actuated clutch, is manufactured and experimentally characterized. Due to the scaling of magnetic forces, the displacement region which these magnetic springs are most applicable is that of millimeters and below. However, this region is well situated for miniature robots and smart material actuators, where a tailored magnetic spring, designed to compliment a component, can enhance its performance while adding new functionality. The methodology is also expendable to variable interactions and multi-dimensional magnetic field design.

pi

DOI [BibTex]

DOI [BibTex]


A Value-Driven Eldercare Robot: Virtual and Physical Instantiations of a Case-Supported Principle-Based Behavior Paradigm
A Value-Driven Eldercare Robot: Virtual and Physical Instantiations of a Case-Supported Principle-Based Behavior Paradigm

Anderson, M., Anderson, S., Berenz, V.

Proceedings of the IEEE, pages: 1,15, October 2018 (article)

Abstract
In this paper, a case-supported principle-based behavior paradigm is proposed to help ensure ethical behavior of autonomous machines. We argue that ethically significant behavior of autonomous systems should be guided by explicit ethical principles determined through a consensus of ethicists. Such a consensus is likely to emerge in many areas in which autonomous systems are apt to be deployed and for the actions they are liable to undertake. We believe that this is the case since we are more likely to agree on how machines ought to treat us than on how human beings ought to treat one another. Given such a consensus, particular cases of ethical dilemmas where ethicists agree on the ethically relevant features and the right course of action can be used to help discover principles that balance these features when they are in conflict. Such principles not only help ensure ethical behavior of complex and dynamic systems but also can serve as a basis for justification of this behavior. The requirements, methods, implementation, and evaluation components of the paradigm are detailed as well as its instantiation in both a simulated and real robot functioning in the domain of eldercare.

am

link (url) DOI [BibTex]


Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective
Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

pn

link (url) Project Page [BibTex]