scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

scholarly journals A New Closed-Form Solution of the Side Abutment Pressure Distribution of Roadway

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liang Cheng ◽  
Yidong Zhang
Keyword(s):  
Plastic Zone ◽  
Pressure Distribution ◽  
Closed Form ◽  
Abutment Pressure ◽  
Closed Form Solution ◽  
Evaluation Process ◽  
Friction Angle ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Roadway Stability

Instability of coal wall is one of the hot-button and difficult issues in the study of coal mine ground control. The shallow side coal of roadway in the coal measures is usually weak and consequently easy to bring about failure. Hence, the side abutment pressure redistributes and dramatically influences the roadway stability. Since the previous closed-form solutions of the side abutment pressure do not take into account all the necessary parameters which include the properties of the coal and the interface between coal and roof/floor, the roadway height, and the support strength, a mechanical model is established based on the equilibrium of the plastic zone, and a new closed-form solution is derived in this paper. Moreover, a numerical investigation is conducted to validate the accuracy of the closed-form solution. The numerical results of the side abutment pressure distribution are in good agreement with the closed-form solution. Afterwards, a parametric analysis of the width of the plastic zone is carried out, and the results show that the width of the plastic zone is nearly negatively linearly correlated with the friction angle and the cohesion of the coal, the interfacial cohesion, and the support strength. By contrast, it is positively linearly correlated with the roadway height and negatively exponentially correlated with the interfacial friction angle. The results obtained in the present study could be useful for the evaluation process of roadway stability.

On Saint-Venant's Problem for Helicoidal Beams

2015 ◽  
Vol 83 (2) ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Fem Analysis ◽  
Original System ◽  
Form Solution ◽  
Hamiltonian Matrix ◽  
Jordan Structure ◽  
Rigid Body Motions

This paper proposes a novel solution strategy for Saint-Venant's problem based on Hamilton's formalism. Saint-Venant's problem focuses on helicoidal beams and its solution hinges upon the determination of the subspace of the system's Hamiltonian matrix associated with its null and pure imaginary eigenvalues. A projection approach is proposed that reduces the system Hamiltonian matrix to a matrix of size 12 × 12, whose eigenvalues are identical to the null and purely imaginary eigenvalues of the original system, with the same Jordan structure. A fundamental theoretical result is established: Saint-Venant's solutions exist because rigid-body motions create no strains. Indeed, the solvability conditions for the governing equations of the problem are satisfied because a matrix identity holds, which expresses the fact that rigid-body motions create no strains. Because it avoids the identification of the Jordan structure of the original system, the implementation of the proposed projection for large, realistic problems is straightforward. Closed-form solutions of the reduced problem are found and three-dimensional stress and strain fields can be recovered from the closed-form solution. Numerical examples are presented to demonstrate the capabilities of the analysis. Predictions are compared to exact solutions of three-dimensional elasticity and three-dimensional FEM analysis.

Three-dimensional stress state in inclined backfilled stopes obtained from numerical simulations and new closed-form solution

2018 ◽  
Vol 55 (6) ◽  
pp. 810-828 ◽  
Author(s):  
Abtin Jahanbakhshzadeh ◽  
Michel Aubertin ◽  
Li Li
Keyword(s):  
Stress State ◽  
Closed Form ◽  
Numerical Solutions ◽  
Hanging Wall ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Solid Waste Disposal ◽  
Inclination Angles ◽  
Backfilled Stopes

Backfill is commonly used world-wide in underground mines to improve ground stability and reduce solid waste disposal on the surface. Practical solutions are required to assess the stress state in the backfilled stopes, as the stress state is influenced by the fill settlement that produces a stress transfer to the adjacent rock walls. The majority of existing analytical and numerical solutions for the stresses in backfilled openings were developed for two-dimensional (plane strain) conditions. In reality, mine stopes have a limited extension in the horizontal plane so the stresses are influenced by the four walls. This paper presents recent three-dimensional (3D) simulations results and a new 3D closed-form solution for the vertical and horizontal stresses in inclined backfilled stopes with parallel walls. This solution takes into account the variation of the stresses along the opening width and height, for various inclination angles and fills properties. The numerical results are used to validate the analytical solution and illustrate how the stress state varies along the opening height, length, and width, for different opening sizes and inclination angles of the footwall and hanging wall. Experimental results are also used to assess the validity of the proposed solution.

Use of Resultants and the Bernshtein Formula in the Dimensional Synthesis of Linkage Components

1994 ◽  
Vol 116 (4) ◽  
pp. 1171-1172 ◽  
Author(s):  
Chuen-Sen Lin ◽  
Bao-Ping Jia
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Polynomial Equations ◽  
Dimensional Synthesis ◽  
Fourth Degree ◽  
Finite Precision ◽  
Closed Form Solutions ◽  
System Of Polynomial Equations ◽  
Resultant Theory

The applications of resultants and the Bernshtein formula for the dimensional synthesis of linkage components for finite precision positions are discussed. The closed-form solutions, which are derived from systems of polynomials in multiple unknowns by applying resultant theory, are in forms of polynomial equations of a single unknown. For the case of two compatibility equations, the closed form solution is a sixth degree solution polynomial. For the case of three compatibility equations, the solution is a fifty-fourth degree solution polynomial. For each case, the Bernshtein formula is applied to calculate the number of solutions of the system of polynomial equations. The calculated numbers of solutions match the degrees of the solution polynomials for both cases.

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