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Trajectory planning for energy minimization of industry robotic manipulators using the lagrange interpolation method

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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING 2015年第5期16卷 911-917页

作者： Luo, Lu-Ping Yuan, Chao Yan, Rui-Jun Yuan, Quan Wu, Jing Shin, Kyoo-Sik Han, Chang-Soo Hanyang Univ Dept Mech Engn Ansan 426791 Gyeonggi Do South Korea Hanyang Univ Dept Mechatron Engn Ansan 426791 Gyeonggi Do South Korea Hanyang Univ Dept Robot Engn Ansan 426791 Gyeonggi Do South Korea

We propose to use lagrange interpolation method to express each joint trajectory function to realize trajectory planning for energy minimization of industrial robotic manipulators. We give the position constraints to the industrial robotic manipulators and the stability of the industrial robotic manipulators should be satisfied. In order to avoid Runge's phenomenon of lagrange interpolation method, we use the Chebyshev interpolation points for our approach. Through derivation, the angular velocity functions and angular acceleration functions can be obtained. lagrange interpolation method can satisfy position constraints, and ensure the smoothness of joint angular positions, velocities, accelerations, and joint torques. By taking these functions into the Performance Index (PI) of energy minimization, as well as the direct iteration method used for optimization of energy consumption, we can obtain the optimal trajectory for industrial robotic manipulators.

关键词： Energy minimization Trajectory planning Industrial robotic manipulators lagrange interpolation method Performance Index (PI) Iterative method

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A Novel Probability Weighting Function Model with Empirical Studies

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2021年第1期14卷 208-227页

作者： Wu, Sheng Huang, Hong-Wei Li, Yan-Lai Chen, Haodong Pan, Yong Henan Univ Econ & Law Sch E Commerce & Logist Management Zhengzhou Peoples R China Zhengzhou Aeronaut Ind Management Coll Sch Math Zhengzhou Peoples R China Liaoning Univ Business Sch Shenyang Peoples R China

Probability weighting is one of the key components of the modern risky decision-making theories, an effective probability weight function can more accurately describe the decision-makers' subjective response to the event probability. While the probability weighting functions (PWFs) with several different parametric forms and parameter-free elicitation methods have been proposed. This paper first introduces a lagrange interpolation method (LIM) for building a parameter-free PWF model, then proposes a novel PWF model with the use of the LIM based on Prelec's PWF model. Furthermore, an experiment was designed and carried out. The results not only demonstrate that the novel PWF model could reflect the empirical regularities for maximizing the satisfaction degree of the curve fitting for the preference points obtained from experiment or questionnaire survey and better predict the preferences of decision-makers, but also are found to be consistent with the properties of PWF. This paper makes a significant methodological contribution to developing a numerical method, such as LIM, for constructing the probability weighting model. The finial error analysis suggests that the novel PWF model is a more effective approach. (C) 2021 The Authors. Published by Atlantis Press B.V.

关键词： Probability weighting function Decision making under risk lagrange interpolation method Risk preference Preference points Empirical studies

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Anonymous multi-receiver ID-based signcryption scheme

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IET INFORMATION SECURITY 2015年第3期9卷 194-201页

作者： Pang, Liaojun Gao, Lu Li, Huixian Wang, Yumin Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Peoples R China Xidian Univ Sch Life Sci & Technol Xian 710071 Peoples R China Wayne State Univ Dept Comp Sci Detroit MI 48202 USA Northwestern Polytech Univ Sch Comp Sci & Engn Xian 710072 Peoples R China

In earlier multi-receiver signcryption schemes, in order to help the authorised receivers to find the corresponding information for decryption from the ciphertext, the list of identities of all authorised receivers should be included in the ciphertext as a necessary element. However, this method has directly led to the privacy leakage problem of receivers. Later, several anonymous multi-receiver signcryption schemes use the lagrange interpolation method to mix and hide the real identities of all receivers, so that the ciphertext does not expose identities of the receivers any longer. Therefore the lagrange interpolation method is considered to be a perfect solution to the receiver anonymity problem, and multiple anonymous multi-receiver signcryption schemes have been proposed based on it. However, recently, this method has been proven to be insecure because it cannot assure the anonymity of receivers either. In fact, in any of the existing anonymous schemes based on the lagrange interpolation method, it is easy for one authorised receiver to judge whether anyone is an authorised receiver or not, which badly violates the receiver anonymity. Motivated by these concerns, the authors propose a new multi-receiver signcryption scheme to solve this problem. Analyses show that the proposed scheme meets confidentiality, unforgeablity and the sender and receivers' anonymity.

关键词： cryptography authorisation data privacy interpolation anonymous multireceiver one-dimensional-based signcryption scheme authorised receivers decryption ciphertext privacy leakage problem lagrange interpolation method receiver anonymity problem sender anonymity receiver anonymity

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A GENERAL FRAMEWORK FOR DEVELOPING AND EVALUATING BAND-LIMITED FUNCTION EXTRAPOLATION methodS

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PROCEEDINGS OF THE IEEE 1988年第10期76卷 1381-1383页

作者： KONG, FN R. Norwegian Council for Sci. & Ind. Res. Kjeller

It is shown that the bandlimited function extrapolation can be considered as an approximation problem in operator space. Within this framework, the Papoulis-Gerchberg method and two other methods for extrapolation are analyzed. Particular attention is given to approximation using Taylor and Chebyschev series, and to approximation using the lagrange interpolation method

关键词： Chebyschev series lagrange interpolation method Papoulis-Gerchberg method Taylor series approximation problem band-limited function extrapolation methods extrapolation series (mathematics)

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The sharing method of computerized accounting information resources based on Data Fusion Technology 13

The sharing method of computerized accounting information re...

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13th International Conference on Measuring Technology and Mechatronics Automation (ICMTMA)

作者： Xue, Jie Xian Med Univ Xian 710021 Shaanxi Peoples R China

ISBN: (纸本)9781665438926

In order to overcome the problems of low security and efficiency existing in traditional computerized accounting information resource fusion methods, this paper proposes a new method of computerized accounting information resource sharing based on data fusion technology. According to the function of data fusion, the mapping relationship of knowledge elements of computerized accounting information resources is constructed by using data fusion technology, and the computerized accounting information resources are fully integrated. Based on the fused computerized accounting information resources, the lagrange interpolation method is used to calculate the secure sharing key of computerized accounting information resources, and the secure sharing of computerized accounting information resources is completed. The experimental results show that the proposed resource sharing method can effectively ensure the security of computerized accounting information resources, and effectively improve the transmission efficiency of computerized accounting information resources.

关键词： Data fusion technology computerized accounting information resource sharing lagrange interpolation method

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An efficient v-fairness (t, n) threshold secret sharing scheme

An efficient v-fairness (t, n) threshold secret sharing sche...

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5th International Conference on Genetic and Evolutionary Computing, ICGEC2011

作者： Yang, Jen-Ho Chang, Chin-Chen Wang, Chih-Hung Department of Information and Electronic Commerce Kainan University Taoyuan County Taiwan Department of Information Engineering and Computer Science Feng Chia University Taichung Taiwan Department of Computer Science and Information Engineering National Chiayi University Chiayi Taiwan

Lee and Laih proposed a v-fairness (t, n) secret sharing scheme such that the participants can recover a secret without providing their shadows simultaneously. Besides, the honest participants can obtain the secret ev... 详细信息

ISBN: (纸本)9780769544496

关键词： Computers Cryptography interpolation lagrange interpolation method Lee and Laih's scheme Polynomials Secret sharing cheater detectio computation cost cryptography honest participants secret shadow v-fairness multisecret sharing scheme

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Research on spur face gear by electrochemical machining based on the complex surface mesh

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CHAOS SOLITONS & FRACTALS 2020年 130卷 109443-109443页

作者： Huang, Liang Cao, Yan Jia, Feng Lei, Yan Xian Technol Univ Mechatron Engn Xian 710000 Peoples R China Xian KunLun Ind Grp Co Ltd Liabil Tool Struct Mfg Xian 710000 Peoples R China

The tooth surface of the spur face gear is a kind of complex space curved surface, in order to solve the technical defects in traditional NC milling manufacturing. This paper utilizes the complex tooth surface grid planning principle to establish the cathode surface firstly;Secondly, the orthogonal test, linear regression analysis and weighted comprehensive scoring system is adopted to obtain the optimal processing parameters;And finally, the lagrange interpolation method is used to realize the modification of the cathode surface. The verification test shows that this method compared with the traditional NC milling, reduces the cost by 70% and the cycle by 75%, can realizes the rapid high-precision batch manufacturing of complex structure products. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Spur face gear Electrolytic machining Tooth surface grid planning principle Cathode surface modification Comprehensive scoring system lagrange interpolation method

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Research on SMC-predictive DPC strategy for Vienna rectifier

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IEICE ELECTRONICS EXPRESS 2018年第19期15卷 20180600-20180600页

作者： Ma, Hui Wei, Wei Wang, Liangkai Shi, Zeyu China Three Gorges Univ Coll Elect Engn & New Energy Yichang 443002 Peoples R China South China Univ Technol Sch Elect Power 381 Wushan Rd Guangzhou 510641 Guangdong Peoples R China

Predictive direct power control (PDPC) and sliding mode control (SMC) have been proposed as effective schemes for three-phase rectifiers. However, the conventional PDPC still has sampling power errors caused by control delay. Furthermore, the existing SMC can not well work with PDPC to provide fast error convergence and strong robustness during both start-up and load step change periods. To solve the problems above, this paper proposes an improved hybrid SMC-PDPC control scheme for Vienna rectifier, which uses lagrangian liner interpolation to predict the next sampling power value with eliminating inner-loop power errors. Additionally, this paper presents a novel SMC based on squared voltage in the outer loop. Experimental results based on 10 kW prototype circuit are presented to confirm the effectiveness of the proposed scheme.

关键词： Vienna-type rectifier sliding mode control predictive direct power control lagrange interpolation method

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Research on Chaos of Nonlinear Singular Integral Equation

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Journal of Applied Mathematics and Physics 2023年第4期11卷 1152-1159页

作者： Yannan Liu Yu Wang School of Science Tianjin University of Technology and Education Tianjin China

In this paper, one class of nonlinear singular integral equation is discussed through lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of... 详细信息

关键词： lagrange interpolation method Nonlinear Singular Integral Equation Iterative method

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Time-splitting finite difference method with the wavelet-adaptive grids for semiclassical Gross–Pitaevskii equation in supercritical case

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Journal of Computational Physics 2014年 267卷 146-161页

作者： Xueyang Li Aiguo Xiao School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 PR China

The Gross–Pitaevskii equation is the model equation of the single-particle wave function in a Bose–Einstein condensation. A computation difficulty of the Gross–Pitaevskii equation comes from the semiclassical problem in supercritical case. In this paper, we apply a diffeomorphism to transform the original one-dimensional Gross–Pitaevskii equation into a modified equation. The adaptive grids are constructed through the interpolating wavelet method. Then, we use the time-splitting finite difference method with the wavelet-adaptive grids to solve the modified Gross–Pitaevskii equation, where the approximation to the second-order derivative is given by the lagrange interpolation method. At last, the numerical results are given. It is shown that the obtained time-splitting finite difference method with the wavelet-adaptive grids is very efficient for solving the one-dimensional semiclassical Gross–Pitaevskii equation in supercritical case and it is suitable to deal with the local high oscillation of the solution.

关键词： Gross–Pitaevskii equation Wavelet-adaptive grids Time-splitting finite difference method Interpolating wavelet lagrange interpolation method

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