scholarly journals Metrological Characterization of a Vision-Based System for Relative Pose Measurements with Fiducial Marker Mapping for Spacecrafts

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 43 ◽  
Author(s):  
Marco Pertile ◽  
Sebastiano Chiodini ◽  
Riccardo Giubilato ◽  
Mattia Mazzucato ◽  
Andrea Valmorbida ◽  
...  
Keyword(s):  
Measurement Errors ◽  
Closed Form Solution ◽  
Measurement Procedure ◽  
Form Solution ◽  
Bundle Adjustment ◽  
Physical Parameters ◽  
Position Measurement ◽  
Position Errors ◽  
Relative Pose

An improved approach for the measurement of the relative pose between a target and a chaser spacecraft is presented. The selected method is based on a single camera, which can be mounted on the chaser, and a plurality of fiducial markers, which can be mounted on the external surface of the target. The measurement procedure comprises of a closed-form solution of the Perspective from n Points (PnP) problem, a RANdom SAmple Consensus (RANSAC) procedure, a non-linear local optimization and a global Bundle Adjustment refinement of the marker map and relative poses. A metrological characterization of the measurement system is performed using an experimental set-up that can impose rotations combined with a linear translation and can measure them. The rotation and position measurement errors are calculated with reference instrumentations and their uncertainties are evaluated by the Monte Carlo method. The experimental laboratory tests highlight the significant improvements provided by the Bundle Adjustment refinement. Moreover, a set of possible influencing physical parameters are defined and their correlations with the rotation and position errors and uncertainties are analyzed. Using both numerical quantitative correlation coefficients and qualitative graphical representations, the most significant parameters for the final measurement errors and uncertainties are determined. The obtained results give clear indications and advice for the design of future measurement systems and for the selection of the marker positioning on a satellite surface.

scholarly journals Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

2021 ◽  
Author(s):  
Yves Achdou ◽  
Jiequn Han ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions ◽  
Benjamin Moll
Keyword(s):  
Continuous Time ◽  
Wealth Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heterogeneous Agent ◽  
Saving Behavior ◽  
Income And Wealth Distribution ◽  
Heterogeneous Agent Models ◽  
Special Case

Abstract We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

scholarly journals The Sustainable Characteristic of Bio-Bi-Phase Flow of Peristaltic Transport of MHD Jeffrey Fluid in the Human Body

2018 ◽  
Vol 10 (8) ◽  
pp. 2671 ◽  
Author(s):  
Ahmed Zeeshan ◽  
Nouman Ijaz ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Volume Fraction ◽  
Closed Form Solution ◽  
Pressure Rise ◽  
Expansion Method ◽  
Form Solution ◽  
Peristaltic Transport ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Phase Flow ◽  
Special Cases

This study deals with the peristaltic transport of non-Newtonian Jeffrey fluid with uniformly distributed identical rigid particles in a rectangular duct. The effects of a magnetohydrodynamics bio-bi-phase flow are taken into account. The governing equations for mass and momentum are simplified using the fact that wavelength is much greater than the amplitude and small Reynolds number. A closed-form solution for velocity is obtained by means of the eigenfunction expansion method whereby pressure rise is numerically calculated. The results are graphically presented to observe the effects of different physical parameters and the suitability of the method. The results for hydrodynamic, Newtonian fluid, and single-phase problems can be respectively obtained by taking the Hartmann number (M = 0), relaxation time (λ1=0), and volume fraction (C = 0) as special cases of this problem.

scholarly journals A CLOSED-FORM SOLUTION TO A MODEL OF TWO-SIDED, PARTIAL ALTRUISM

2012 ◽  
Vol 16 (2) ◽  
pp. 230-239
Author(s):  
Ana Fernandes
Keyword(s):  
Closed Form ◽  
Overlapping Generations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Allocation Of Resources ◽  
Overlapping Generations Model ◽  
Parents And Children ◽  
Saving Rates ◽  
Markov Strategies

This paper presents a closed-form characterization of the allocation of resources in an overlapping generations model of two-sided, partial altruism. Three assumptions are made: (i) parents and children play Markov strategies, (ii) utility takes the CRRA form, and (iii) the income of children is stochastic but proportional to the saving of parents. In families where children are rich relative to their parents, saving rates—measured as a function of the family's total resources—are higher than when children are poor relative to their parents. Income redistribution from the old to the young, therefore, leads to an increase in aggregate saving.

scholarly journals Refining Inaccurate Transmitter and Receiver Positions Using Calibration Targets for Target Localization in Multi-Static Passive Radar

Sensors ◽  
2019 ◽  
Vol 19 (15) ◽  
pp. 3365 ◽  
Author(s):  
Yongsheng Zhao ◽  
Dexiu Hu ◽  
Yongjun Zhao ◽  
Zhixin Liu ◽  
Chuang Zhao
Keyword(s):  
Lower Bound ◽  
Closed Form Solution ◽  
Form Solution ◽  
Measurement Noise ◽  
Target Localization ◽  
Passive Radar ◽  
Localization Accuracy ◽  
Position Errors ◽  
Simulation Results ◽  
Calibration Step

Transmitter and receiver position errors have been known to significantly deteriorate target localization accuracy in a multi-static passive radar (MPR) system. This paper explores the use of calibration targets, whose positions are known to the MPR system, to counter the loss in target localization accuracy arising from transmitter/receiver position errors. This paper firstly evaluates the Cramér–Rao lower bound (CRLB) for bistatic range (BR)-based target localization with calibration targets, which analytically indicates the potential of calibration targets in enhancing localization accuracy. After that, this paper proposes a novel closed-form solution, which includes two steps: calibration step and localization step. Firstly, the calibration step is devoted to refine the inaccurate transmitter and receiver locations using the BR measurements from the calibration targets, and then in the calibration step, the target localization can be accurately achieved by using the refined transmitter/receiver positions and the BR measurements from the unknown target. Theoretical analysis and simulation results indicate that the proposed method can attain the CRLB at moderate measurement noise level, and exhibits the superiority of localization accuracy over existing algorithms.

The Sliding With Coulomb Friction of a Rigid Indentor Over a Power-Law Inhomogeneous Linearly Viscoelastic Half-Plane

1984 ◽  
Vol 51 (2) ◽  
pp. 289-293 ◽  
Author(s):  
J. R. Walton
Keyword(s):  
Shear Modulus ◽  
Half Plane ◽  
Power Law ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Plane Boundary ◽  
Physical Parameters ◽  
Title Problem ◽  
Rigid Indentor

In a previous paper, the title problem was solved for a homogeneous power-law linearly viscoelastic half-plane. Such material has a constant Poisson’s ratio and a shear modulus with a power-law dependence on time. In this paper, the shear modulus is assumed also to have a power-law dependence on depth from the half-plane boundary. As in the earlier paper, only a quasi-static analysis is presented, that is, the enertial terms in the equations of motion are not retained and the indentor is assumed to slide with constant speed. The resulting boundary value problem is reduced to a generalized Abel integral equation. A simple closed-form solution is obtained from which all relevant physical parameters are easily computed.

LIFETIME CONSUMPTION AND INVESTMENT FOR WORST-CASE CRASH SCENARIOS

2015 ◽  
Vol 18 (01) ◽  
pp. 1550004 ◽  
Author(s):  
SASCHA DESMETTRE ◽  
RALF KORN ◽  
FRANK THOMAS SEIFRIED
Keyword(s):  
Portfolio Choice ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimal Consumption ◽  
Worst Case ◽  
Portfolio Decisions ◽  
Portfolio Strategy ◽  
Crash Exposure ◽  
The Impact

We investigate worst-case optimal consumption and portfolio decisions under the threat of a market crash on an infinite time horizon. We provide a closed-form solution for constant relative risk aversion and establish a rigorous verification result. More specifically, using martingale arguments we demonstrate that the optimal consumption-portfolio strategy can be characterized as the indifference strategy that achieves the best performance in the no-crash scenario. In addition, we find a dual characterization of the optimal strategy as the indifference strategy that minimizes the crash exposure. Finally, we quantify the impact of the crash on consumption and portfolio choice and analyze it in terms of the investor's risk and time preferences and prudence.

scholarly journals Multiple Iterations of Bundle Adjustment for the Position Measurement of Fiber Tips on LAMOST

2014 ◽  
Vol 14 (4) ◽  
pp. 190-197 ◽  
Author(s):  
Mingchi Feng ◽  
Yonggang Gu ◽  
Yi Jin ◽  
Chao Zhai
Keyword(s):  
Measurement Theory ◽  
Real Data ◽  
Initial Position ◽  
Position Error ◽  
Bundle Adjustment ◽  
Astronomical Observation ◽  
Position Measurement ◽  
Movement Trajectories ◽  
Position Errors ◽  
Observation Process

Abstract In the astronomical observation process of multi-object fiber spectroscopic telescope, the position measurement of fiber tips on the focal plane is difficult and critical, and is directly related to subsequent observation and ultimate data quality. The fibers should precisely align with the celestial target. Hence, the precise coordinates of the fiber tips are obligatory for tracking the celestial target. The accurate movement trajectories of the fiber tips on the focal surface of the telescope are the critical problem for the control of the fiber positioning mechanism. According to the special structure of the LAMOST telescope and the composition of the initial position error, this paper aims at developing a high precision and robust measurement method based on multiple iterations of bundle adjustment with a few control points. The measurement theory of the proposed methodology has been analyzed, and the measurement accuracy has been evaluated. The experimental results indicate that the new method is more accurate and more reliable than the polynomial fitting method. The maximum position error of the novel measurement algorithm of fiber tips with simulated and real data is 65.3 μm, and most of the position errors conform to the accuracy requirement (40 μm).

Transient-free convective flow with heat generation/absorption in an annular porous medium: A semi-analytical approach

2017 ◽  
Vol 232 (5) ◽  
pp. 599-612 ◽  
Author(s):  
Basant K Jha ◽  
Taiwo S Yusuf
Keyword(s):  
Heat Generation ◽  
Convective Flow ◽  
Closed Form Solution ◽  
Form Solution ◽  
Physical Parameters ◽  
Free Convective Flow ◽  
Riemann Sum ◽  
Annular Gap ◽  
Laplace Transform Technique ◽  
The Impact

This article presents the impact of heat-generating/absorbing fluid on fully developed transient free convective flow of a viscous and an incompressible fluid bounded by two concentric vertical cylinders filled with isotropic porous materials and saturated with the same fluid. In the present model, the convective current is setup due to internally generated heat and either isothermal or isoflux heating of the outer surface of the inner cylinder. The transport equations concerned with the model under consideration are rendered nondimensional and transformed into ordinary diffferential equation using Laplace transform technique. The solution of the momentum and energy equation obtained separately in Laplace domain is transformed into time domain using the Riemann-sum approximation approach, this is later validated by numerical comparisons at large time with the closed form solution obtained for steady flow. The accuray of this approach has further been extablished by presenting a numerical solution using implicit finite difference method. The effect of the various physical parameters entering into the model is demostrated with the aid of tables and line graphs. During the course of numerical computations, it is found that the effect of heat generation/absorption can be controlled by increasing/decreasing the viscosity ratio. The system can also be maintained by varying the annular gap and applying approprate phenomenon of heating.

scholarly journals Ferro Fluid Based Rough Porous Tilted Pad Bearing with Slip Effect

10.29007/cns9 ◽  
2018 ◽  
Author(s):  
Snehal Shukla ◽  
Gunamani Deheri
Keyword(s):  
Load Capacity ◽  
Fluid Pressure ◽  
Closed Form Solution ◽  
Form Solution ◽  
Squeeze Film ◽  
Physical Parameters ◽  
Slip Effect ◽  
Transverse Roughness ◽  
Bearing Design ◽  
Effect Of Surface

The focus of this paper is to propose an innovative mathematical model, which describes the influence of slip and transverse roughness on a hydromagnetic squeeze film in porous tilted pad bearing. The stochastic model of Christensen and Tonder is, applied to evaluate the effect of surface roughness. Beavers and Joseph slip model takes the care of slip effect. Applying these models which governing the fluid pressure; is solved for the calculation of load support. The closed form solution is, obtained for the pressure and load capacity as a function of various physical parameters. The effect of such parameters is, discussed through graphical representations. The computations indicate that slip has to be at minimum for any upgrading in the bearing design. Besides, the absence of flow fails to keep away the bearing from supporting good amount of load, which does not happen in the case of traditional lubricant.

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