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Journal articles on the topic 'Pseudo inverse matrix'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Gao, Yuefeng, Jianlong Chen, Pedro Patrício, and Dingguo Wang. "The pseudo core inverse of a companion matrix." Studia Scientiarum Mathematicarum Hungarica 55, no. 3 (2018): 407–20. http://dx.doi.org/10.1556/012.2018.55.3.1398.

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The notion of core inverse was introduced by Baksalary and Trenkler for a complex matrix of index 1. Recently, the notion of pseudo core inverse extended the notion of core inverse to an element of an arbitrary index in *-rings; meanwhile, it characterized the core-EP inverse introduced by Manjunatha Prasad and Mohana for complex matrices, in terms of three equations. Many works have been done on classical generalized inverses of companion matrices and Toeplitz matrices. In this paper, we discuss existence criteria and formulae of the pseudo core inverse of a companion matrix over a *-ring. A {1,3}-inverse of a Toeplitz matrix plays an important role in that process.

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2

Zhang, Zhihua. "Pseudo-inverse multivariate/matrix-variate distributions." Journal of Multivariate Analysis 98, no. 8 (2007): 1684–92. http://dx.doi.org/10.1016/j.jmva.2006.04.002.

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3

Leonov, A. S. "The minimal pseudo-inverse matrix method." USSR Computational Mathematics and Mathematical Physics 27, no. 4 (1987): 107–17. http://dx.doi.org/10.1016/0041-5553(87)90019-x.

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4

Fang, Wang, Yang Zhen, Q. S. Kang, Shang Dong Xi, and Lin Yang Shang. "A Simulation Research on the Visual Servo Based on Pseudo-Inverse of Image Jacobian Matrix for Robot." Applied Mechanics and Materials 494-495 (February 2014): 1212–15. http://dx.doi.org/10.4028/www.scientific.net/amm.494-495.1212.

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The image Jacobian Matrix must obtain during the course of uncalibrated visual servo for classic algorithms firstly. Then the inverse of image Jacobian Matrix or pseudo-inverse of image Jacobian Matrix can be taken. But when the inverse of image Jacobian Matrix is not exist or pseudo-inverse of image Jacobian Matrix is not easy to get, the uncalibrated visual servo for robot can not realize. In this paper, a research is carried on by simulation between the classic method for uncalibrared visual servo and the strategy by computing pseudo-inverse of image Jacobian Matrix. It is conclusion that the latter not only has advantage of the performance for tracking, but also reduces computational complexity for control.

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5

Jusufi, Azir. "DRAZIN’S PSEUDO-INVERSE OF RIGHT ANGLE SINGULAR MATRIX." Математички билтен/BULLETIN MATHÉMATIQUE DE LA SOCIÉTÉ DES MATHÉMATICIENS DE LA RÉPUBLIQUE MACÉDOINE, no. 1 (2013): 49–60. http://dx.doi.org/10.37560/matbil13100049j.

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6

Olkin, Ingram. "The density of the inverse and pseudo-inverse of a random matrix." Statistics & Probability Letters 38, no. 2 (1998): 131–35. http://dx.doi.org/10.1016/s0167-7152(97)00163-6.

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7

Gao, Yuefeng, and Jianlong Chen. "The pseudo core inverse of a lower triangular matrix." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113, no. 2 (2017): 423–34. http://dx.doi.org/10.1007/s13398-017-0486-4.

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8

KOBAYASHI, MASAKI. "PSEUDO-RELAXATION LEARNING ALGORITHM FOR COMPLEX-VALUED ASSOCIATIVE MEMORY." International Journal of Neural Systems 18, no. 02 (2008): 147–56. http://dx.doi.org/10.1142/s0129065708001452.

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HAM (Hopfield Associative Memory) and BAM (Bidirectinal Associative Memory) are representative associative memories by neural networks. The storage capacity by the Hebb rule, which is often used, is extremely low. In order to improve it, some learning methods, for example, pseudo-inverse matrix learning and gradient descent learning, have been introduced. Oh introduced pseudo-relaxation learning algorithm to HAM and BAM. In order to accelerate it, Hattori proposed quick learning. Noest proposed CAM (Complex-valued Associative Memory), which is complex-valued HAM. The storage capacity of CAM by the Hebb rule is also extremely low. Pseudo-inverse matrix learning and gradient descent learning have already been generalized to CAM. In this paper, we apply pseudo-relaxation learning algorithm to CAM in order to improve the capacity.

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9

GÓMEZ, ALFREDO, and DAVID ROMEU. "O-LATTICES FOR RANK-DEFICIENT DISPLACEMENT FIELD MATRICES." International Journal of Modern Physics B 14, no. 10 (2000): 1129–37. http://dx.doi.org/10.1142/s0217979200001382.

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In this work the properties of O-lattices are investigated in the case where the rank of the displacement field matrix is less than three. The approaches due to Bollmann are reviewed and it is shown that one of them is equivalent to the use of the Moore–Penrose pseudo-inverse of the displacement field matrix instead of its (in this case inexistent) inverse.The geometry of the pseudo-inverse approach is discussed and a general solution in terms of the singular value decomposition is proposed.

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10

Nagarajan, Anand, S. Joseph Winston, and S. Venugopal. "Spatially Hyper-Redundant Robotic Inverse Kinematics by Discrete Link Characterization ." Applied Mechanics and Materials 592-594 (July 2014): 2204–9. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.2204.

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In this paper, a novel design of a multi-sectioned, remotely-actuated, continuum type manipulator is presented. Spatially Hyper-Redundant Robot (SHRR) is based on a continuous backbone model which is divided into four sections. In the area of hyper redundant robotics, kinematic redundant systems result in non square Jacobian matrix which requires a pseudo inverse method to inverse the matrix. A methodology has been devised to solve the Inverse Kinematics (IK) problem of SHRR by predicting the curvature values of each of the section. Redundant IK techniques like Pseudo-Inverse Method (PIM), Jacobian Transpose Method (JTM), Damped Least Squares Method (DLS) and Selectively Damped Least Squares Method (SDLS) are tested on the formulated kinematic model of SHRR using MATLAB and a comparative study has been made.

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11

Song, Jingyan, and Yeung Yam. "Complex recurrent neural network for computing the inverse and pseudo-inverse of the complex matrix." Applied Mathematics and Computation 93, no. 2-3 (1998): 195–205. http://dx.doi.org/10.1016/s0096-3003(97)10064-9.

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12

Hoyle, D. C. "Accuracy of Pseudo-Inverse Covariance Learning—A Random Matrix Theory Analysis." IEEE Transactions on Pattern Analysis and Machine Intelligence 33, no. 7 (2011): 1470–81. http://dx.doi.org/10.1109/tpami.2010.186.

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13

Ataei, Alireza. "Improved Qrginv Algorithm for Computing Moore-Penrose Inverse Matrices." ISRN Applied Mathematics 2014 (March 12, 2014): 1–5. http://dx.doi.org/10.1155/2014/641706.

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Katsikis et al. presented a computational method in order to calculate the Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) (2011). In this paper, an improved version of this method is presented for computing the pseudo inverse of an m×n real matrix A with rank r>0. Numerical experiments show that the resulting pseudoinverse matrix is reasonably accurate and its computation time is significantly less than that obtained by Katsikis et al.

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14

Thapa, Gyan Bahadur, P. Lam-Estrada, and J. López-Bonilla. "Singular Factorization of an Arbitrary Matrix." Journal of the Institute of Engineering 12, no. 1 (2017): 77–86. http://dx.doi.org/10.3126/jie.v12i1.16728.

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In this paper, we study the Singular Value Decomposition of an arbitrary matrix Anxm, especially its subspaces of activation, which leads in natural manner to the pseudo inverse of Moore -Bjenhammar - Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution and our approach gives the Lanczos classification for these systems.Journal of the Institute of Engineering, 2016, 12(1): 77-86

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15

Murty, K. N., and S. Sivasundaram. "Generalized two point boundary value problems. existence and uniqueness." Journal of Applied Mathematics and Stochastic Analysis 5, no. 2 (1992): 147–56. http://dx.doi.org/10.1155/s1048953392000121.

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An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.

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16

Kutovyi, Viktor, Oleksandr Kutovyi, and Oleg Shutovskyi. "On calculation of the pseudo-inverse econometric models matrix with a rank deficient observation matrix." TRANSFER OF INNOVATIVE TECHNOLOGIES 2, no. 1 (2019): 68–74. http://dx.doi.org/10.31493/tit1921.0302.

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17

Dulęba, Ignacy, and Michał Opałka. "A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators." International Journal of Applied Mathematics and Computer Science 23, no. 2 (2013): 373–82. http://dx.doi.org/10.2478/amcs-2013-0028.

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The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, while the third one is a slightly modified version of the Levenberg-Marquardt method (mLM). Their comparison is based on the evaluation of a short distance approaching the goal point and on their computational complexity. As the reference method, the Jacobian pseudo-inverse is utilized. Simulation results reveal that the modified Levenberg-Marquardt method is promising, while the first order approximation method is reliable and requires mild computational costs. Some hints are formulated concerning the application of Jacobian-based methods in practice.

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18

Farooq, Ahmad, and Khan Hamid. "An Efficient and Simple Algorithm for Matrix Inversion." International Journal of Technology Diffusion 1, no. 1 (2010): 20–27. http://dx.doi.org/10.4018/jtd.2010010102.

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In this paper, a new algorithm is proposed for finding inverse and determinant of a given matrix in one instance. The algorithm is straightforward in understanding and manual calculations. Computer implementation of the algorithm is extremely simple and is quite efficient in time and memory utilization. The algorithm is supported by an example. The number of multiplication/division performed by the algorithm is exactly; however, its efficiency lies in the simplicity of coding and minimal utilization of memory. Simple applicability and reduced execution time of the method is validated form the numerical experiments performed on test problems. The algorithm is applicable in the cases of pseudo inverses for non-square matrices and solution of system of linear equations with minor modification.

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19

Deb, Shomen, and Md Mokammel Haque. "Elliptic curve and pseudo-inverse matrix based cryptosystem for wireless sensor networks." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 5 (2019): 4479. http://dx.doi.org/10.11591/ijece.v9i5.pp4479-4492.

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Applying asymmetric key security to wireless sensor network (WSN) has been challenging task for the researcher of this field. One common trade-off is that asymmetric key architecture does provide good enough security than symmetric key but on the other hand, sensor network has some resource limitations to implement asymmetric key approach. Elliptic curve cryptography (ECC) has significant advantages than other asymmetric key system like RSA, D-H etc. The most important feature of ECC is that it has much less bit requirement and at the same time, ensures better security compared to others. Hence, ECC can be a better option for implementing asymmetric key approach for sensor network. We propose a new cryptosystem which is based on Pseudo-inverse matrix and Elliptic Curve Cryptography. We establish a relationship between these two different concepts and evaluate our proposed system on the basis of the results of similar works as well as our own simulation done in TinyOS environment.

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20

Tetsuno, Shota, Kyuki Shibuya, and Tetsuo Iwata. "Subpixel-shift cyclic-Hadamard microscopic imaging using a pseudo-inverse-matrix procedure." Optics Express 25, no. 4 (2017): 3420. http://dx.doi.org/10.1364/oe.25.003420.

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21

Oda, Naoki, Toshiyuki Murakami, and Kouhei Ohnishi. "A Robust Control Strategy of Redundant Manipulator by Workspace Observer." Journal of Robotics and Mechatronics 8, no. 3 (1996): 235–42. http://dx.doi.org/10.20965/jrm.1996.p0235.

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This paper describes a decoupling force control strategy of redundant manipulator by workspace observer. In general, the calculation process of the redundant manipulator becomes complex as the number of degree-offreedom motion increases because the controller includes the pseudo inverse Jacobian matrix. To alleviate this problem, we develop a simplification method of the inverse kinematics solution including null space calculation by using the transposed Jacobian matrix, and the workspace observer. Here the stable condition of the proposed controller is also presented. Its condition is an important index to construct the stable workspace observer.

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22

Raudys, Sarunas, and Robert P. W. Duin. "Expected classification error of the Fisher linear classifier with pseudo-inverse covariance matrix." Pattern Recognition Letters 19, no. 5-6 (1998): 385–92. http://dx.doi.org/10.1016/s0167-8655(98)00016-6.

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23

Wen, Guang, Haonan Chen, Guifu Zhang, and Jiming Sun. "An Inverse Model for Raindrop Size Distribution Retrieval with Polarimetric Variables." Remote Sensing 10, no. 8 (2018): 1179. http://dx.doi.org/10.3390/rs10081179.

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This paper proposes an inverse model for raindrop size distribution (DSD) retrieval with polarimetric radar variables. In this method, a forward operator is first developed based on the simulations of monodisperse raindrops using a T-matrix method, and then approximated with a polynomial function to generate a pseudo training dataset by considering the maximum drop diameter in a truncated Gamma model for DSD. With the pseudo training data, a nearest-neighborhood method is optimized in terms of mass-weighted diameter and liquid water content. Finally, the inverse model is evaluated with simulated and real radar data, both of which yield better agreement with disdrometer observations compared to the existing Bayesian approach. In addition, the rainfall rate derived from the DSD by the inverse model is also improved when compared to the methods using the power-law relations.

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24

JIANG, Li, Taiga OMORI, Hisaichi SHIBATA, Taro IMAMURA, and Kenichi RINOIE. "Configuration Estimation of Three Dimensional Transonic Wings using Modified PARSEC with Pseudo-Inverse Matrix." AEROSPACE TECHNOLOGY JAPAN, THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 14 (2015): 17–21. http://dx.doi.org/10.2322/astj.14.17.

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25

Rusakov, Victor A. "On the Moore-Penrose Pseudo Inverse of the Incidence Matrix for Weighted Undirected Graph." Procedia Computer Science 169 (2020): 147–51. http://dx.doi.org/10.1016/j.procs.2020.02.126.

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26

Zahariev, Evtim, and John Mcphee. "Stabilization of Multiple Constraints in Multibody Dynamics Using Optimization and a Pseudo-inverse Matrix." Mathematical and Computer Modelling of Dynamical Systems 9, no. 4 (2003): 417–35. http://dx.doi.org/10.1076/mcmd.9.4.417.27898.

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27

Erokhin, V. I., V. V. Kashmet, and N. V. Lisitsyn. "Modification of Greville's algorithm for removing columns (rows) when constructing a pseudo-inverse matrix." USSR Computational Mathematics and Mathematical Physics 29, no. 6 (1989): 111. http://dx.doi.org/10.1016/s0041-5553(89)80019-9.

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28

Fukada, Yoshiki. "Support-free robust topology optimization based on pseudo-inverse stiffness matrix and eigenvalue analysis." Structural and Multidisciplinary Optimization 61, no. 1 (2019): 59–76. http://dx.doi.org/10.1007/s00158-019-02345-0.

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29

Xia, Changfeng, Yuanwen Cai, and Yuan Ren. "Steering law design for a magnetically suspended control and sensitive gyro cluster considering rotor tilt saturation." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 11 (2018): 4066–76. http://dx.doi.org/10.1177/0954410018816593.

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To effectively reject the influence of rotor tilt saturation in a magnetically suspended control and sensitive gyro cluster, an adaptive nonlinear pseudo-inverse steering law is developed in this study. Based on the working principle of a Lorentz force magnetic bearing–rotor system in a single magnetically suspended control and sensitive gyro, the dynamical model of a rigid spacecraft equipped with a magnetically suspended control and sensitive gyro cluster is established. Because of the monotonicity and symmetric properties of the chosen nonlinear function, an adaptive nonlinear weighting matrix is incorporated with the pseudo-inverse steering law for the magnetically suspended control and sensitive gyro cluster. The steering law adjusts the weighting matrix elements according to saturation penalty functions so that the rotors generate control torques consistent with the limited rotor tilting domain. The effectiveness and superiority of this steering law are verified by numerical simulations. The simulation results demonstrate that the proposed steering law not only imposes control torques on the carrier spacecraft with three degrees of freedom but also avoids rotor tilt saturation, ensuring rapid attitude control of agile maneuvering spacecraft.

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30

Prasanna, Parvathy, Jeevamma Jacob, and Mattida Ponnadiyil Nandakumar. "Inverse optimal control of a class of affine nonlinear systems." Transactions of the Institute of Measurement and Control 41, no. 9 (2019): 2637–50. http://dx.doi.org/10.1177/0142331218806338.

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This paper proposes a systematic formulation of inverse optimal control (IOC) law based on a rather straightforward reduction of control Lyapunov function (CLF), applicable to a class of second-order nonlinear systems affine in the input. This method exploits the additional design degrees of freedom resulting from the non-uniqueness of the state dependent coefficient (SDC) formulation, which is widely used in pseudo-linear control techniques. The applicability of the proposed approach necessitates an apparently effortless SDC formulation satisfying an SDC matrix criterion in terms of the structure and characteristics of the state matrix, [Formula: see text]. Subsequently, a sufficient condition for the global asymptotic stability (g.a.s) of the closed-loop system is established. The SDC formulations conforming to the sufficient condition ensure the existence and determination of a smooth radially unbounded polynomial CLF of the form [Formula: see text], while offering a benevolent choice for the gain matrix [Formula: see text], in the CLF. The direct relationship between the gain matrix [Formula: see text] and state weighing matrix [Formula: see text] ensures optimization of an equivalent [Formula: see text]. This feature enables one to rightfully choose the gain matrix [Formula: see text] as per the performance requisites of the system. Finally, the application of the proposed methodology for the speed control of a permanent magnet synchronous motor validates the efficacy and design flexibility of the methodology.

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31

Wang, Yuwei, Liangguo Dong, Yuzhu Liu, and Jizhong Yang. "2D frequency-domain elastic full-waveform inversion using the block-diagonal pseudo-Hessian approximation." GEOPHYSICS 81, no. 5 (2016): R247—R259. http://dx.doi.org/10.1190/geo2015-0678.1.

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Elastic full-waveform inversion (EFWI) of multicomponent seismic data is a powerful tool for estimating the subsurface elastic parameters with high accuracy. However, the trade-offs between multiple parameters increase the nonlinearity of EFWI. Although the conventional diagonal-approximate Hessian matrix describes the illumination and limited bandwidth effects, it ignores the trade-off effects and decreases the convergence rate of EFWI. We have developed a block-diagonal pseudo-Hessian operator for 2D frequency-domain EFWI to take into account the approximate trade-offs among the P-wave (compressional-wave) velocity, S-wave (shear-wave) velocity, and density without extra computational costs on forward simulations. The Hessian matrix tends toward a block-diagonal matrix as the frequency grows to infinity; thus, the proposed block-diagonal pseudo-Hessian matrix is more accurate at higher frequencies. The inverse of the block-diagonal pseudo-Hessian matrix is used as a preconditioner for the nonlinear conjugate-gradient method to simultaneously reconstruct P- and S-wave velocities and density. This approach effectively mitigates the crosstalk artifacts by correcting the gradients from the trade-off effects and produces more rapid inversion convergence, which becomes more significant at higher frequencies. Synthetic experiments on an inclusion model and the elastic Marmousi2 model demonstrate its feasibility and validity in EFWI.

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32

Dyda, Alexander Aleksandrovich, Kseniya Chumakova, and Van Thanh Nguyen. "DESIGNING SHIP COURSE MOVEMENT USING PSEUDOINVERSE MATRICES FOR MEASURING STATE VECTOR OF CONTROLLED OBJECT." Vestnik of Astrakhan State Technical University. Series: Management, computer science and informatics 2021, no. 1 (2021): 61–69. http://dx.doi.org/10.24143/2072-9502-2021-1-61-69.

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To configure the control systems of the ship movement along the trajectory, it is necessary to be concerned with the parameters of its controllability. There has been proposed building  a matrix model based on measurements of the state vector of a controlled object. The construction of the model is considered on the example of the problem of ship course control. An algorithm for determining the matrix coefficients of the selected model is proposed. The operation of the considered algorithm has been checked for square matrices by finding their inverse matrices, as well as for rectangular matrices for which the pseudo inverse matrix was found. The illustration of the proposed approach is carried out using the example of a simple 1-order linear Nomoto model. The considered approach is quite universal and can be applied to higher order models, including nonlinear ones.

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33

IKEDA, Mitsuru. "Estimation of the Contact Force between Pantograph and Contact Wire Using an Inverse Problem of Vibration with Pseudo-inverse Matrix." Proceedings of the JSME annual meeting 2002.7 (2002): 181–82. http://dx.doi.org/10.1299/jsmemecjo.2002.7.0_181.

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34

Wu, Xiao Ming. "MIMO Non-Linear Mechanism Analysis Based Matlab." Applied Mechanics and Materials 152-154 (January 2012): 1865–68. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.1865.

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A new method based on matlab matrix algorithm is proposed for analyzing the mechanism of MIMO non-linear system. Firstly, the mechanism is regarded as a system and system model is established. Secondly, the transfer matrix is got by separating relations between input and output, the equivalents are acquired by pseudo-inverse, then the kinematic analysis of mechanism is realized, which provide theory basis for the design of mechanism in a sense. Finally an example is given for explaining the whole calculational process.

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35

Liu, Liang, Wen Chen, Tao Li, and Yuling Liu. "Pseudo-Random Encryption for Security Data Transmission in Wireless Sensor Networks." Sensors 19, no. 11 (2019): 2452. http://dx.doi.org/10.3390/s19112452.

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The security of wireless sensor networks (WSN) has become a great challenge due to the transmission of sensor data through an open and wireless network with limited resources. In the paper, we discussed a lightweight security scheme to protect the confidentiality of data transmission between sensors and an ally fusion center (AFC) over insecure links. For the typical security problem of WSN’s binary hypothesis testing of a target’s state, sensors were divided into flipping and non-flipping groups according to the outputs of a pseudo-random function which was held by sensors and the AFC. Then in order to prevent an enemy fusion center (EFC) from eavesdropping, the binary outputs from the flipping group were intentionally flipped to hinder the EFC’s data fusion. Accordingly, the AFC performed inverse flipping to recover the flipped data before data fusion. We extended the scheme to a more common scenario with multiple scales of sensor quantification and candidate states. The underlying idea was that the sensor measurements were randomly mapped to other quantification scales using a mapping matrix, which ensured that as long as the EFC was not aware of the matrix, it could not distract any useful information from the captured data, while the AFC could appropriately perform data fusion based on the inverse mapping of the sensor outputs.

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36

Lin, Chih Jer, Chii Ruey Lin, Shen Kai Yu, and Cheng Chin Han. "Singularity Avoidance for a Redundant Robot Using Fuzzy Motion Planning." Applied Mechanics and Materials 479-480 (December 2013): 729–36. http://dx.doi.org/10.4028/www.scientific.net/amm.479-480.729.

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The purpose of this study is to design a redundant robot meeting the specific task and tracking the specific trajectory. Although the Moore-Penrose pseudo-inverse kinematic is commonly using to solve the inverse kinematic problem, it cannot solve the singularity exists in some situations that the rank of Jacobian matrix is not full rank for the redundant robot. Thus, a fuzzy motion planning algorithm is proposed to solve the inverse kinematic with singularity. Finally, we can obtain the position of five axes robot manipulator using fuzzy motion planning mapping method, and the errors of the singular points are approximately to zero. The results prove the fuzzy inverse kinematic mapping method can robust singular point when the tracking path with singular points.

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37

Xu, Qinhuan, and Qiang Zhan. "A real-time inverse kinematics solution based on joint perturbation for redundant manipulators." Mechanical Sciences 12, no. 1 (2021): 221–35. http://dx.doi.org/10.5194/ms-12-221-2021.

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Abstract. Aiming at the problem that the calculation of the inverse kinematics solution of redundant manipulators is very time-consuming, this paper presents a real-time method based on joint perturbation and joint motion priority. The method first seeks the pose nearest to the target pose in the manipulator's pose set through fine-tuning all the joints with different angle deviations at the same time and then regards this pose as the starting one to perform iterative calculations until the error between the current pose and the target pose is less than the predetermined error, thus obtaining the inverse kinematics solution corresponding to the target pose. This method can avoid the pseudo-inverse calculations of the Jacobian matrix and significantly reduce the solving complexity. Two types of manipulators are taken as examples to validate the proposed method. Under the premise that the manipulator motion trajectory is satisfied, the Jacobian pseudo-inverse method and the proposed method are both adopted to solve the inverse kinematics. Simulations and comparisons show that the proposed method has better real-time performance, and the joint motions can be flexibly controlled by setting different joint motion priorities. This method can make the work cycle faster and improve the production efficiency of redundant manipulators in real applications.

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38

Olaru, Adrian, Serban Olaru, Niculae Mihai, and Doru Bardac. "Controlling of the 3D Space Trajectory of the Multi Robots Applications by Using the Proper Iterative Pseudo Inverse Jacobian Neural Network Matrix Method." Applied Mechanics and Materials 841 (June 2016): 227–33. http://dx.doi.org/10.4028/www.scientific.net/amm.841.227.

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In many applications we used the multi robots with the central coordination of the 3D space trajectory. In the controlling of the space movement of the end effecter of the all robots from this type of applications and the robot’s joints one of the most important problem is to solve the forward and inverse kinematics, that is different from the single robot application. It is important to know with the extreme precision the joints relative displacements of all robots. One of the most precise method to solve the inverse kinematics problem in the robots with redundant chain is the complex coupled method of the neural network with Iterative Jacobian Pseudo Inverse method. In this paper was proposed and used the proper coupled method Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) with Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL). The paper contents the mathematical matrix model of the forward kinematics of multiple robots applications, mathematical model of the proper iterative algorithm and all proper virtual LabVIEW instrumentation, to obtain the space conventional and unconventional curves in different Euller planes for one case study of three simultaneously robots movement with extreme precision of the end-effecter less than 0.001mm. The paper shown how can be changed the multi robots application in to one application with parallel robot structure with three independent robots. The presented method and the virtual instrumentations (VI) are generally and they can be used in all other robots application and for all other conventional and unconventional space curves.

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39

Duleba, I., and I. Karcz-Duleba. "Suboptimal approximations in repeatable inverse kinematics for robot manipulators." Bulletin of the Polish Academy of Sciences Technical Sciences 65, no. 2 (2017): 209–17. http://dx.doi.org/10.1515/bpasts-2017-0025.

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Abstract In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

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Mamirov, Uktam. "ALGORITHMS OF SYSTEM SYNTHESIS FOR STABILIZING UNCERTAIN DYNAMIC OBJECTS." Technical science and innovation 2021, no. 1 (2020): 75–80. http://dx.doi.org/10.51346/tstu-02.21.1-77-0011.

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The article deals with the formation of stable algorithms for the system synthesis for the stabilizing uncertain dynamic objects based on the method of local optimization in the presence of approximate mathematical models. The article analyzes the issues of building adaptive control systems using the concept of roughness, taking into account the assessment of the maximum allowable discrepancy between the object and its model. Some of the most constructive algorithms for determining pseudo-inverse matrices are given. When calculating the pseudo-inverse matrix of the control object, modified QR decomposition algorithms are used, obtained by deleting or assigning a column. The obtained algorithms allow us to conclude that the stabilization systems can be built on the basis of the local optimization method in the presence of approximate mathematical models. At the same time, it turns out that the asymptotic stability, i.e., the limited output with a limited input, can be achieved with sufficiently rough estimates of the object parameters and external perturbations using regular methods.

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Slabospitsky, A. "Recurrent algorithm for non-stationary parameter estimation by least squares method with least deviations from ‘attraction’ points for bilinear discrete dynamic systems." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2018): 71–74. http://dx.doi.org/10.17721/1812-5409.2018/3.10.

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The estimation problem of slowly time-varying parameter matrices is considered for bilinear discrete dynamic system in the presence of disturbances. The least squares estimate with variable forgetting factor is investigated for this object in non-classical situation when this estimate may be not unique and additionally ‘attraction’ points for unknown parameter matrices are given at any moment. The set of all above-mentioned estimates of these unknown matrices is defined through the Moore-Penrose pseudo-inverse operator. The least squares estimate with variable forgetting factor and least deviation norm from given ‘attraction’ point at any moment is proposed as unique estimate on this set of all estimates. The explicit form of representation is obtained for this unique estimate of the parameter matrices by the least squares method with variable forgetting factor and least deviation norm from given ‘attraction’ points under non-classical assumptions. The recurrent algorithm for this estimate is also derived which does not require the usage of the matrix pseudo-inverse operator.

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Jiang, Meiying, Beiyan Jiang, and Qi Wang. "Internal Model Control for Rank-Deficient System with Time Delays Based on Damped Pseudo-Inverse." Processes 7, no. 5 (2019): 264. http://dx.doi.org/10.3390/pr7050264.

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It is a challenge to design a satisfactory controller for a complex multivariable industrial system with minimal offsetting and a slow response. An internal model control method is proposed for rank-deficient systems with a time delay based on a damped pseudo-inverse. An internal model control was designed to obtain the desired dynamic characteristics of the system by transforming the time-delay system into a system without a time delay, following the Pade approximation approach. By introducing a damping factor, the internal model controller was designed based on a damped pseudo-inverse, since the inverse matrix of the rank-deficient system does not exist. Furthermore, a singular value decomposition was used to analyze the steady-state performance of the system. The selection of the damping factor was also presented, and a μ analysis was made to evaluate the stability of the system. To demonstrate the effectiveness of the proposed method, a crude distillation process with five inputs and four outputs was considered as an example. The simulation results illustrate that not only can the proposed strategy guarantee the system’s stability, but it also has a relatively good dynamic performance.

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Abdulkareem, Ademola, E. J. Okoroafor, Ayokunle Awelewa, and Aderibigbe Adekitan. "PSEUDO-INVERSE MATRIX MODEL FOR ESTIMATING LONG-TERM ANNUAL PEAK ELECTRICITY DEMAND: THE COVENANT UNIVERSITY’S EXPERIENCE." International Journal of Energy Economics and Policy 9, no. 4 (2019): 103–9. http://dx.doi.org/10.32479/ijeep.7566.

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Mishra, Swati, Santhakumar Mohan, and Santosh Kumar Vishvakarma. "Simplified Motion Control of a Vehicle manipulator for the Coordinated Mobile Manipulation." Defence Science Journal 70, no. 1 (2020): 72–81. http://dx.doi.org/10.14429/dsj.70.14119.

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This paper considers a resolved kinematic motion control approach for controlling a spatial serial manipulator arm that is mounted on a vehicle base. The end-effector’s motion of the manipulator is controlled by a novel kinematic control scheme, and the performance is compared with the well-known operational-space control scheme. The proposed control scheme aims to track the given operational-space (end-effector) motion trajectory with the help of resolved configuration-space motion without using the Jacobian matrix inverse or pseudo inverse. The experimental testing results show that the suggested control scheme is as close to the conventional operational-space kinematic control scheme.

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Fabunmi, J., P. Chang, and J. Vorwald. "Damping Matrix Identification Using the Spectral Basis Technique." Journal of Vibration and Acoustics 110, no. 3 (1988): 332–37. http://dx.doi.org/10.1115/1.3269521.

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This paper presents a method for estimating the damping matrix of a structural system when the stiffness matrix, mass matrix, and frequency response data are given. The method is based on the fact that the forced responses of a structure can be decomposed into linear combinations of sets of frequency-dependent function. A set of orthonormal basis vectors of the frequency response is first determined. The forced responses are then expressed as linear combinations of these basis vectors. The coefficients of the damping matrix are then solved using the pseudo inverse of these basis vectors. Because the vectors that span the space of the frequency response are required to be linearly independent, an orthogonalization process is used to identify the number of significant basis vectors. Several examples are presented to illustrate the use and advantages of the proposed method.

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Seljebotn, D. S., T. Bærland, H. K. Eriksen, K. A. Mardal, and I. K. Wehus. "Multi-resolution Bayesian CMB component separation through Wiener filtering with a pseudo-inverse preconditioner." Astronomy & Astrophysics 627 (July 2019): A98. http://dx.doi.org/10.1051/0004-6361/201732037.

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We present a Bayesian model for multi-resolution component separation for cosmic microwave background (CMB) applications based on Wiener filtering and/or computation of constrained realizations, extending a previously developed framework. We also develop an efficient solver for the corresponding linear system for the associated signal amplitudes. The core of this new solver is an efficient preconditioner based on the pseudo-inverse of the coefficient matrix of the linear system. In the full sky coverage case, the method gives an increased speed of the preconditioner, and it is easier to implement in terms of practical computer code. In the case where a mask is applied and prior-driven constrained realization is sought within the mask, this is the first time full convergence has been achieved at the full resolution of the Planck data set.

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Young, Phil D., Joshua D. Patrick, and Dean M. Young. "Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs." International Journal of Statistics and Probability 9, no. 6 (2020): 108. http://dx.doi.org/10.5539/ijsp.v9n6p108.

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We provide a new, concise derivation of necessary and sufficient conditions for the explicit characterization of the general nonnegative-definite covariance structure V of a general Gauss-Markov model with E(y) and Var(y) such that the best linear unbiased estimator, the weighted least squares estimator, and the least squares estimator of X&beta; are identical. In addition, we derive a representation of the general nonnegative-definite covariance structure V defined above in terms of its Moore-Penrose pseudo-inverse.

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Zheng, Yikang, Wei Zhang, Yibo Wang, Qingfeng Xue, and Xu Chang. "An application of full-waveform inversion to land data using the pseudo-Hessian matrix." Interpretation 4, no. 4 (2016): T627—T635. http://dx.doi.org/10.1190/int-2015-0214.1.

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Full-waveform inversion (FWI) is used to estimate the near-surface velocity field by minimizing the difference between synthetic and observed data iteratively. We apply this method to a data set collected on land. A multiscale strategy is used to overcome the local minima problem and the cycle-skipping phenomenon. Another obstacle in this application is the slow convergence rate. The inverse Hessian can enhance the poorly blurred gradient in FWI, but obtaining the full Hessian matrix needs intensive computation cost; thus, we have developed an efficient method aimed at the pseudo-Hessian in the time domain. The gradient in our FWI workflow is preconditioned with the obtained pseudo-Hessian and a synthetic example verifies its effectiveness in reducing computational cost. We then apply the workflow on the land data set, and the inverted velocity model is better resolved compared with traveltime tomography. The image and angle gathers we get from the inversion result indicate more detailed information of subsurface structures, which will contribute to the subsequent seismic interpretation.

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Ragala, Ramesh, and G. Bharadwaja Kumar. "Recursive Block LU Decomposition based ELM in Apache Spark." Journal of Intelligent & Fuzzy Systems 39, no. 6 (2020): 8205–15. http://dx.doi.org/10.3233/jifs-189141.

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Due to the massive memory and computational resources required to build complex machine learning models on large datasets, many researchers are employing distributed environments for training the models on large datasets. The parallel implementations of Extreme Learning Machine (ELM) with many variants have been developed using MapReduce and Spark frameworks in the recent years. However, these approaches have severe limitations in terms of Input-Output (I/O) cost, memory, etc. From the literature, it is known that the complexity of ELM is directly propositional to the computation of Moore-Penrose pseudo inverse of hidden layer matrix in ELM. Most of the ELM variants developed on Spark framework have employed Singular Value Decomposition (SVD) to compute the Moore-Penrose pseudo inverse. But, SVD has severe memory limitations when experimenting with large datasets. In this paper, a method that uses Recursive Block LU Decomposition to compute the Moore-Penrose generalized inverse over the Spark cluster has been proposed to reduce the computational complexity. This method enhances the ELM algorithm to be efficient in handling the scalability and also having faster execution of the model. The experimental results have shown that the proposed method is efficient than the existing algorithms available in the literature.

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He, Jianjun, and Bin Xu. "Quick and Highly Efficient Modal Analysis Method Based on the Reanalysis Technique for Large Complex Structure and Topology Optimization." International Journal of Computational Methods 17, no. 03 (2019): 1850134. http://dx.doi.org/10.1142/s0219876218501347.

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Modal analysis is widely used to investigate the dynamic characteristics of large and complex structures. For finite element models, iterative solvers are needed to precisely calculate eigenpairs or frequency and vibration mode. However, in cases such as large-scale analysis or reanalysis studies, or optimization design of a huge structure, computational cost may become too time consuming. This paper focuses on the quick structural modal analysis based on the reanalysis technique for large complex structures. Based on the stiffness and mass matrix of the analytical structures, a high precision and efficiency eigensolution is generated by the proposed modal analysis method (the Pseudo Random Independent and Coupling Inverse Iteration (PRICII) method), which combines the pseudo random number initialization, ICII (Independent and Coupling Inverse Iteration) strategy with the double Rayleigh–Ritz analysis. By comparing with the Subspace iteration method, Lanczos method, etc. the large-scale numerical examples show that the actual computational savings of the proposed method are usually higher than 75% with sufficient precision. Also, its applications in topology optimization are greatly effective.

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