Nonlinear state estimation for rigid-body motion with low-pass sensors

In this paper, we consider the state estimation problem for the nonlinear kinematic equations of a rigid body observed under low-pass sensors. The problem is motivated from a walking robot application where inclinometers and gyros are the sensors used. We show that a non-local high gain observer exists for the nonlinear rigid-body kinematic equations and that it under a small angle assumption is possible to use one inclinometer only to estimate two angles.     

tweezercalib 2.0: Faster version of MatLab package for precise calibration of optical tweezers

We present a vectorized version of the MatLab (MathWorks Inc.) package tweezercalib for calibration of optical tweezers with precision. The calibration is based on the power spectrum of the Brownian motion of a dielectric bead trapped in the tweezers. Precision is achieved by accounting for a number of factors that affect this power spectrum, as described in vs. 1 of the package [I.M. Toli?-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Matlab program for precision calibration of optical tweezers, Comput. Phys. Comm. 159 (2004) 225-240]. The graphical user interface allows the user to include or leave out each of these factors. Several “health tests” are applied to the experimental data during calibration, and test results are displayed graphically. Thus, the user can easily see whether the data comply with the theory used for their interpretation. Final calibration results are given with statistical errors and covariance matrix.

New version program summary

Title of program: tweezercalibCatalogue identifier: ADTV_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTV_v2_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandReference in CPC to previous version: I.M. Toli?-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Comput. Phys. Comm. 159 (2004) 225Catalogue identifier of previous version: ADTVDoes the new version supersede the original program: YesComputer for which the program is designed and others on which it has been tested: General computer running MatLab (Mathworks Inc.)Operating systems under with the program has been tested: Windows2000, Windows-XP, LinuxProgramming language used: MatLab (Mathworks Inc.), standard licenseMemory required to execute with typical data: Of order four times the size of the data fileHigh speed storage required: noneNo. of lines in distributed program, including test data, etc.: 135 989No. of bytes in distributed program, including test data, etc.: 1 527 611Distribution format: tar. gzNature of physical problem: Calibrate optical tweezers with precision by fitting theory to experimental power spectrum of position of bead doing Brownian motion in incompressible fluid, possibly near microscope cover slip, while trapped in optical tweezers. Thereby determine spring constant of optical trap and conversion factor for arbitrary-units-to-nanometers for detection system.Method of solution: Elimination of cross-talk between quadrant photo-diode's output channels for positions (optional). Check that distribution of recorded positions agrees with Boltzmann distribution of bead in harmonic trap. Data compression and noise reduction by blocking method applied to power spectrum. Full accounting for hydrodynamic effects: Frequency-dependent drag force and interaction with nearby cover slip (optional). Full accounting for electronic filters (optional), for “virtual filtering” caused by detection system (optional). Full accounting for aliasing caused by finite sampling rate (optional). Standard non-linear least-squares fitting. Statistical support for fit is given, with several plots facilitating inspection of consistency and quality of data and fit.Summary of revisions: A faster fitting routine, adapted from [J. Nocedal, Y.x. Yuan, Combining trust region and line search techniques, Technical Report OTC 98/04, Optimization Technology Center, 1998; W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986], is applied. It uses fewer function evaluations, and the remaining function evaluations have been vectorized. Calls to routines in Toolboxes not included with a standard MatLab license have been replaced by calls to routines that are included in the present package. Fitting parameters are rescaled to ensure that they are all of roughly the same size (of order 1) while being fitted. Generally, the program package has been updated to comply with MatLab, vs. 7.0, and optimized for speed.Restrictions on the complexity of the problem: Data should be positions of bead doing Brownian motion while held by optical tweezers. For high precision in final results, data should be time series measured over a long time, with sufficiently high experimental sampling rate: The sampling rate should be well above the characteristic frequency of the trap, the so-called corner frequency. Thus, the sampling frequency should typically be larger than 10 kHz. The Fast Fourier Transform used works optimally when the time series contain n² data points, and long measurement time is obtained with n>12-15. Finally, the optics should be set to ensure a harmonic trapping potential in the range of positions visited by the bead. The fitting procedure checks for harmonic potential.Typical running time: SecondsUnusual features of the program: NoneReferences: The theoretical underpinnings for the procedure are found in [K. Berg-Sørensen, H. Flyvbjerg, Power spectrum analysis for optical tweezers, Rev. Sci. Ins. 75 (2004) 594-612].     

Interesting Interest Points

Not all interest points are equally interesting. The most valuable interest points lead to optimal performance of the computer vision method in which they are employed. But a measure of this kind will be dependent on the chosen vision application. We propose a more general performance measure based on spatial invariance of interest points under changing acquisition parameters by measuring the spatial recall rate. The scope of this paper is to investigate the performance of a number of existing well-established interest point detection methods. Automatic performance evaluation of interest points is hard because the true correspondence is generally unknown. We overcome this by providing an extensive data set with known spatial correspondence. The data is acquired with a camera mounted on a 6-axis industrial robot providing very accurate camera positioning. Furthermore the scene is scanned with a structured light scanner resulting in precise 3D surface information. In total 60 scenes are depicted ranging from model houses, building material, fruit and vegetables, fabric, printed media and more. Each scene is depicted from 119 camera positions and 19 individual LED illuminations are used for each position. The LED illumination provides the option for artificially relighting the scene from a range of light directions. This data set has given us the ability to systematically evaluate the performance of a number of interest point detectors. The highlights of the conclusions are that the fixed scale Harris corner detector performs overall best followed by the Hessian based detectors and the difference of Gaussian (DoG). The methods based on scale space features have an overall better performance than other methods especially when varying the distance to the scene, where especially FAST corner detector, Edge Based Regions (EBR) and Intensity Based Regions (IBR) have a poor performance. The performance of Maximally Stable Extremal Regions (MSER) is moderate. We observe a relatively large decline in performance with both changes in viewpoint and light direction. Some of our observations support previous findings while others contradict these findings.     

Rendering Caustics on Non-Lambertian Surfaces

This paper presents a new technique for rendering caustics on non-Lambertian surfaces. The method is based on an extension of the photon map which removes previous restrictions limiting the usage to Lambertian surfaces. We add information about the incoming direction to the photons and this allows us to combine the photon map with arbitrary reflectance functions. By using a cone-filter we improve the quality of the radiance estimate in particular at discontinuities. Furthermore we introduce balancing of the photon map which not only reduces the memory requirements but also significantly reduces the rendering time. We have used the method to render caustics on surfaces with reflectance functions varying from Lambertian to glossy specular.     

Drift-free attitude estimation for accelerated rigid bodies

In this paper we study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and abrupt changes in accelerations that can be expected in such an environment. We propose a state estimation algorithm that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates. The algorithm does not use any local parameterization of the rigid body kinematics and can thus be used for a rigid body performing any kind of rotations. The algorithm is a combination of two non-standard, but in a sense linear, Kalman filters between which a trigger based switching takes place. The kinematics representation used makes it possible to construct a linear algorithm that can be shown to give convergent estimates for this nonlinear problem. The state estimator is evaluated in simulations demonstrating how the estimates are long-term stable even in the presence of gyro drift.     

Comparative study of the fluid viscosity in tarsal hairy attachment systems of flies and beetles

Wet adhesive systems of insects strongly rely for their function on the formation of capillary bridges with the substrate. Studies on the chemical composition and evaporation dynamics of tarsal secretions strongly suggest a difference in chemistry of secretion in beetles and flies, both possessing hairy attachment devices. This difference is assumed to influence the viscosity of the secretion. Here, we applied a microrheological technique, based on the immersion of nanometric beads in the collected tarsal footprints, to estimate secretion viscosity in a beetle (Coccinella septempunctata) and a fly (Calliphora vicina). Both species studied possess distinct differences in viscosity, the median of which was calculated as 21.8 and 10.9 mPa s, respectively. We further present an approximate theoretical model to calculate the contact formation time of spatula-like terminal contact elements using the viscosity data of the covering fluid. The estimated contact formation time is proportional to the tarsal secretion viscosity and to the square of the contact radius of the contact element.     

Cultivating the Herb Garden of Scandinavian Mathematics: The Congresses of Scandinavian Mathematicians, 1909–1925

As a reaction to the changed political landscape in Scandinavia following the dissolution of the union between Norway and Sweden in 1905, the prominent Swedish mathematician Gösta Mittag‐Leffler extended ‘a brotherly hand,’ calling for Scandinavian colleagues to meet for a congress of mathematicians in Stockholm in 1909. This event became the first in a series of biannual meetings which proved to be an important institution for Scandinavian mathematics. During the first decades after 1909, the congresses would form and consolidate themselves through the construction of a new Scandinavian identity for mathematicians which developed alongside and in relation to both international and national contexts and developments. In this paper, we shall demonstrate that these meetings served a complex set of agendas at the individual, national, and international level. In particular, they reflect a changing conception of cooperation in science for mutual cultural gain combined with a flexible institutionalisation that allowed the Scandinavian mathematicians to use the congresses for various diplomatic ambitions. We base our analyses of the Scandinavian Congresses of Mathematics on the notion of a shared ‘conational’ identity developed adjacent to national identities. We then analyse the formation, consolidation, delineation, and reflections of this institution in order to demonstrate how the efforts to unite Scandinavian mathematicians were contingent on and influenced by simultaneous currents of internationalisation and shared history, culture, and language in the Scandinavian region.