Analytical Inverse Solution Research Articles

Research on Visual Servo Grasping of Household Objects for Nonholonomic Mobile Manipulator

This paper focuses on the problem of visual servo grasping of household objects for nonholonomic mobile manipulator. Firstly, a new kind of artificial object mark based on QR (Quick Response) Code is designed, which can be affixed to the surface of household objects. Secondly, after summarizing the vision-based autonomous mobile manipulation system as a generalized manipulator, the generalized manipulator’s kinematic model is established, the analytical inverse kinematic solutions of the generalized manipulator are acquired, and a novel active vision based camera calibration method is proposed to determine the hand-eye relationship. Finally, a visual servo switching control law is designed to control the service robot to finish object grasping operation. Experimental results show that QR Code-based artificial object mark can overcome the difficulties brought by household objects’ variety and operation complexity, and the proposed visual servo scheme makes it possible for service robot to grasp and deliver objects efficiently.

Analytical inverse solution for coupled thermoelastic problem for the evaluation of contact stress during steel strip rolling

Knowledge of the contact stress between roll and strip is a critical factor in modern, high-speed rolling mills. Previously two inverse analytical methods have been developed to determine the elastic contact stress on the one hand and the heat flux or the temperature in the whole roll (and especially at the surface) on the other hand, by measuring the stress tensor inside the roll body with fibre optics and by measuring the temperature with a thermocouple fully embedded at only one point inside the roll. However measurements done by fibre optics take into account the elastic stress and the thermal stress. However the contact stress was determined under isothermal assumption, which is strongly incorrect for hot rolling conditions. In this paper, the coupled thermoelastic problem is solved analytically using the theorem of superposition and the expression of the temperature field exhibited previously. A significant improvement of the accuracy of the inverse method for reconstructing the contact stress is observed by taking into account thermal stress. Hot rolling simulation is given to demonstrate this result. The computation time is studied to rapidly optimise the industrial parameters during the rolling process, and considering that both inverse methods have been run, the computation of thermal stress does not cost significant additional CPU times.

Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations

Nonparaxial ray tracing through Risley prisms of four different configurations is performed to give the exact solution of the inverse problem arisen from applications of Risley prisms to free space communications. Predictions of the exact solution and the third-order theory [Appl. Opt. 50, 679 (2011)] are compared and results are shown by curves for systems using prisms of different materials. The exact solution for the problem of precision pointing is generalized to investigate the synthesis of the scan pattern, i.e., to create a desirable scan pattern on some plane perpendicular to the optical axis of the system by controlling the circular motion of the two prisms.

An inverse solution for torque-free axisymmetric rigid body dynamics, with a test for non-precessional motion

The rotational motion of a torque-free axisymmetric rigid body is precession. This motion has been expressed analytically in the literature given the body's initial orientation and rotational dynamics parameters, i.e. inertia ratio and initial angular velocities or precession parameters. The inverse problem of deriving these dynamics parameters given orientation in time has been implemented numerically but has not yet been solved analytically. If a rigid body is precessing, and its orientation with respect to an arbitrary inertial frame is provided at three equally spaced points in time such that the rotational motion is not undersampled, an analytical inverse solution is presented for the precession rate, relative spin rate, coning angle and angular velocities; if the precessional motion is due to inertial axisymmetry and torque-free motion, the inertia ratio is also derived. Additionally, an analytical methodology is presented to test for non-precessional motion. These techniques are applicable to various problems in space science and astronomy, where non-precessional motion or the rotational dynamics parameters of this type of rigid body must be accurately derived from its orientation or relative orientation in time.

Acoustical determination of the parameters governing thermal dissipation in porous media

In this paper, the question of the acoustical determination of macroscopic thermal parameters used to describe heat exchanges in rigid open-cell porous media subjected to acoustical excitations is addressed. The proposed method is based on the measurement of the dynamic bulk modulus of the material, and analytical inverse solutions derived from different semiphenomenological models governing the thermal dissipation of acoustic waves in the material. Three models are considered: (1) Champoux-Allard model [J. Appl. Phys. 20, 1975-1979 (1991)] requiring knowledge of the porosity and thermal characteristic length, (2) Lafarge et al. model [J. Acoust. Soc. Am. 102, 1995-2006 (1997)] using the same parameters and the thermal permeability, and (3) Wilson model [J. Acoust. Soc. Am. 94, 1136-1145 (1993)] that requires two adjusted parameters. Except for the porosity that is obtained from direct measurement, all the other thermal parameters are derived from the analytical inversion of the models. The method is applied to three porous materials-a foam, a glass wool, and a rock wool-with very different thermal properties. It is shown that the method can be used to assess the validity of the descriptive models for a given material.

Improvement of inverse heat conduction solution using Laplace transformation: Method of partial division of time

AbstractAny solution for an inverse heat conduction problem makes the estimation of surface temperature and surface heat flux worsen in the case where these values behave like a triangular shape change with time. In order to compensate for this defect, Monde and colleagues, who succeeded in obtaining analytical inverse solutions using the Laplace transform technique, introduce a new idea where these changes over the entire measurement time can be split into several parts depending on the behavior. Therefore, an approximate equation to trace the measured temperature change can be derived, resulting in good estimation of surface temperature and surface heat flux even in the case of the triangular shape change and sharp change. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 630–638, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10117

Inverse solutions to radiative-transfer problems based on the binomial or the Henyey–Greenstein scattering law

Analytical techniques are used to solve two inverse radiative-transfer problems, for a finite plane-parallel medium, that are (i) based on the binomial scattering law and (ii) based on the Henyey–Greenstein scattering law. In addition, previously reported analytical results (valid for isotropic scattering) that yield an analytical inverse solution for the unknown optical thickness of the medium are extended to the case of anisotropic scattering. The algorithms for the inversions are verified numerically, and some effects of noise on the simulated experimental data are observed.

A new estimation method of thermal diffusivity using analytical inverse solution for one-dimensional heat conduction

A new procedure to estimate thermal diffusivity has been developed by using a solution explicitly obtained from an inverse problem of one-dimensional unsteady heat conduction. This method has merit being independent of surface condition and is simpler than the existing methods, which commonly use a direct heat conduction solution and are strongly subject to a boundary condition. The thermal diffusivity can be estimated by using a change in the temperatures, which includes some errors at two different points as uncertainty in the measurement. The value estimated thereby is found to be in good agreement with that of the tested materials, while thermal conductivity needs a reference to give a known heat to the tested material. This method makes the simultaneous measurement of both thermal diffusivity and thermal conductivity possible by using a reference material.

Qualitative analysis of physical and mathematical approximations necessary for induced radioactivity calculations in fusion devices

When engineers and designers of fusion research and power reactors require information related to the induced radioactivity in the first wall, blanket and shield, they turn to one of many codes to generate a solution. Unfortunately, these codes all make physical and mathematical approximations in order to turn a functionally infinite and highly complicated problem into a more manageable, simple problem. This paper examines these approximations, namely, the handling of loops in the decay scheme, the truncation of the decay scheme, and the modeling of pulsed/intermittent operation histories, as physical approximations and the choice of a solution method as a mathematical approximation. The final recommendation is a code that uses an exact representation of the pulsing history, handles loops by unraveling, truncates the decay schemes with a relative sub-tree production rule modified by a stable truncation restriction and uses an adaptively chosen analytical or Laplace inverse mathematical solution method.

A model study of instability of the inverse problem in electrocardiography

The inverse problem in electrocardiography is studied analytically using a concentric spheres model with no symmetry assumptions on the potential distribution. The mathematical formulation is presented, and existence and uniqueness of the solution are briefly discussed. Solution to the inverse problem is inherently very unstable. The magnitude of this instability is demonstrated using the derived analytical inverse solution for the spherical model. Regularization methods used to date are based on a regularization parameter that does not relate to any measurable physiological parameters. This paper presents a regularization method that is based on a parameter in the form of an a priori bound on the L 2 norm of the inverse solution. Such a bound can be obtained from the theoretical estimates based on the measured values of the body surface potentials together with experimental knowledge about the magnitudes of the epicardial potentials. Based on the presented regularization, an exact form of the regularized solution and estimates of its accuracy are derived.