Robot calibration based on nonlinear formulation for modular reconfigurable robots (MRRs).

Developed in this thesis is a full pose kinematic calibration method for modular reconfigurable robots (MRRs). This method is based on a nonlinear formulation as opposed to the conventional linear method that has a number of critical limitations. By avoiding linearization of the nonlinear robot forward kinematic equations, these nonlinear equations are directly used to identify the robot calibration parameters. A hybrid search method is developed to solve the nonlinear error equations by combining genetic algorithms with Monte Carlo simulations to ensure a global search over the robot workspace with good accuracy. A number of comparisons are made between the proposed method and the conventional linear method, indicating the advantages of the former over the latter by eliminating two critical limitations. The first one is the orthogonality sacrifice that leads to ill-conditioning of the Jacobian used in the linear method. The second one is quadrant sensitivity during the determination of the (Tait) Bryan angles from inverting the rotation matrix.

Robot calibration based on nonlinear formulation for modular reconfigurable robots (MRRs).

Developed in this thesis is a full pose kinematic calibration method for modular reconfigurable robots (MRRs). This method is based on a nonlinear formulation as opposed to the conventional linear method that has a number of critical limitations. By avoiding linearization of the nonlinear robot forward kinematic equations, these nonlinear equations are directly used to identify the robot calibration parameters. A hybrid search method is developed to solve the nonlinear error equations by combining genetic algorithms with Monte Carlo simulations to ensure a global search over the robot workspace with good accuracy. A number of comparisons are made between the proposed method and the conventional linear method, indicating the advantages of the former over the latter by eliminating two critical limitations. The first one is the orthogonality sacrifice that leads to ill-conditioning of the Jacobian used in the linear method. The second one is quadrant sensitivity during the determination of the (Tait) Bryan angles from inverting the rotation matrix.

Robotic tooling calibration based on linear and nonlinear formulations.

Industrial robot calibration packages, such as ABB CalibWare, are developed only for robot calibration. As a result, the robotic tooling systems designed and fabricated by the user are often calibrated in an ad-hoc fashion. In this thesis, a systematic way for robotic tooling calibration is presented in order to overcome this problem. The idea is to include the tooling system as an extended body in the robot kinematic model, from which two error models are established. The first error model is associated with the robot, while the second error model is associated with the tooling. Once the robot is fully calibrated, the first error will be reduced to the required accuracy. Thus, the method is focused on the second error model. For the tool error calibration, two formulations were used. The first is a linear formulation based on conventional calibration as well as self-calibration methods while the second is a nonlinear formulation. The conventional linear formulation was extensively investigated and implemented while the self-calibration was proven to be inadequate for the tooling calibration. Moreover, the nonlinear formulation was demonstrated to be very effective and accurate through experimental result. The end-effector position estimation as well as the tool pose estimation were obtained using a 3D vision system as an off-line error measurement technique.

Robotic tooling calibration based on linear and nonlinear formulations.

Industrial robot calibration packages, such as ABB CalibWare, are developed only for robot calibration. As a result, the robotic tooling systems designed and fabricated by the user are often calibrated in an ad-hoc fashion. In this thesis, a systematic way for robotic tooling calibration is presented in order to overcome this problem. The idea is to include the tooling system as an extended body in the robot kinematic model, from which two error models are established. The first error model is associated with the robot, while the second error model is associated with the tooling. Once the robot is fully calibrated, the first error will be reduced to the required accuracy. Thus, the method is focused on the second error model. For the tool error calibration, two formulations were used. The first is a linear formulation based on conventional calibration as well as self-calibration methods while the second is a nonlinear formulation. The conventional linear formulation was extensively investigated and implemented while the self-calibration was proven to be inadequate for the tooling calibration. Moreover, the nonlinear formulation was demonstrated to be very effective and accurate through experimental result. The end-effector position estimation as well as the tool pose estimation were obtained using a 3D vision system as an off-line error measurement technique.

Numerical investigation of stability multi-storey buildings on weak ground based on their non-linearity

The problems of loss of stability and collapse of high-rise buildings located on weak soils are studied numerically. The problem is solved in a nonlinear formulation using a bilinear model of the soil base. From the point of view of construction mechanics, the critical state of the «ground base – structure» system is considered as an indifferent state. To solve this problem, the perturbation theory is used in combination with the method of successive loadings. Based on the results obtained, a variant of strengthening the foundation is proposed.

Estimation of Koopman Transfer Operators for the Equatorial Pacific SST

In the last years ensemble methods have been widely popular in atmospheric, climate and ocean dynamics investigations and forecasts as convenient methods to obtain statistical information on these systems. In many cases, ensembles have been used as an approximation to the probability distribution that has acquired more and more a central role, as the importance of a single trajectory, or member, was recognized as less informative. This paper shows that using results from the dynamical systems and more recent results from the machine learning and AI communities, we can arrive at a direct estimation of the probability distribution evolution and also at the formulation of predictor systems based on a nonlinear formulation. The paper introduces the theory and demonstrates its application to two examples. The first is a one-dimensional system based on the NINO3 index, the second is a multidimensional case based on time series of monthly mean SST in the Pacific. We show that we can construct the probability distribution and set up a system to forecast its evolution and derive various quantities from it. The objective of the paper is not strict realism, but the introduction of these methods and the demonstration that they can be used also in the complex, multidimensional environment typical of atmosphere and ocean applications.

Dynamic stability of anisotropic fiber-reinforced plate

The dynamic stability problem of an anisotropic fiber-reinforced plate under increasing compressing load is considered in a geometrically nonlinear formulation using the Kirchhoff-Love’s shell theory. The problem is solved using the Bubnov-Galerkin method based on a polynomial approximation of the deflections in combination with a numerical method based on quadrature formulas. For a wide range of variations of physical, mechanical, and geometrical parameters, the dynamic behavior of the plate is studied.

Modeling of a brick building of high storeys on a pile foundation

Relevance. This work is devoted to modeling the stress-strain state of a high-rise brick building on a pile foundation in engineering and geological conditions using the MicroFe design and computing complex, which allows you to create a design scheme in the “base – foundation – building” system using piles in the form of rod end. elements in the soil mass.Goal. Analyzed-deformed state of the system “base – foundation – building”, obtaining the calculated values of tension and reinforcement in the grillage.Materials and methods. The calculation was carried out both in a linear formulation and in a constructively nonlinear formulation with one-sided nonlinear connections between bulk soil elements and pile bar elements. Results. In a nonlinear formulation of the solution to the problem, with a limitation of the permissible design load on the piles, a redistribution of efforts between the piles through the grillage is obtained. Conclusions. Linear calculation is carried out in the case when the greatest forces in the piles do not exceed the specified design load. If this condition is not met, then in the design model, a limitation is introduced on the value of the ultimate load on the piles, equal to the design value, and the calculation is performed considering the constructive nonlinearity of one-sided connections between the pile bar elements and bulk soil elements. Solving the problem in a non-linear formulation allows us to consider the redistribution of efforts between the piles through the grillage, because of which, by changing the location of the piles, it is possible to obtain an optimal design solution for both the pile foundation and the overhead part of the building.

On modeling of airflow in human lungs: constitutive relations to describe deformation of porous medium

Within the framework of a multilevel mathematical model to describe the evolution of functional disorders of the human organism under the influence of environment factors, a mathematical model of the "meso-level" of the human respiratory system is developed. The article is deals with the development of the meso-level model - the formulation of a constitutive model to describe the airflow in a porous lung medium. Human lungs filled with small airways and alveoli, with air contained in them, are modeled by an elastically deformable saturated porous medium enclosed in an internal chamber with varying volume (movable walls). Conceptual and mathematical statements are presented. Air movement in the deformable porous medium of lungs is described by ratios of the mechanics of deformable solid body and filtration theory. As an element of this sub-model an analytical solution is obtained for an auxiliary geometrically linear problem of the all-round compression of an elastic thin-walled hollow sphere filled with air to determine the rate of mean stress of the two-phase medium of the lungs, taking into account the interaction between the lung tissue and the air contained in the lungs. To confirm the hypothesis on the acceptability of a linear solution of an auxiliary problem for large deformations, a similar problem was numerically solved in a geometrically nonlinear formulation. The results show that the obtained analytical solution is in satisfactory agreement with the solution of a similar problem in a nonlinear formulation both for calm and deep breathing, which indicates the possibility of using the former in the construction of the considered sub-model.

Accounting for geometric nonlinearity in finite element strength calculations of thin-walled shell-type structures

Relevance. Currently, in connection with the wider spread of large-span thinwalled structures such as shells, an urgent issue is the development of computational algorithms for the strength calculation of such objects in a geometrically nonlinear formulation. Despite a significant number of publications on this issue, a rather important aspect remains the need to improve finite element models of such shells that would combine the relative simplicity of the resolving equations, allowance for shear deformations, compactness of the stiffness matrix being formed, the facilitated possibility of modeling and changing boundary conditions and etc. The aim of the work is to develop a finite element algorithm for calculating a thin shell with allowance for shear deformations in a geometrically nonlinear formulation using a finite element with a limited number of variable nodal parameters. Methods. As research tools, the numerical finite element method was chosen. The basic geometric relations between the increment of deformations and the increment of the components of the displacement vector and the increment of the components of the normal vector angle are obtained in two versions of the normal angle of the reference. The stiffness matrix and the column of nodal forces of the quadrangular finite element at the loading step were obtained by minimizing the Lagrange functional. Results. On the example of calculating a cylindrical panel rigidly clamped at the edges under the action of a concentrated force, the efficiency of the developed algorithm was shown in a geometrically nonlinear setting, taking into account the transverse shear strain.