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Ahybrid biogeography-based optimization method for the inverse kinematics problem of an 8-DOF redundant

Zi-wu REN,Zhen-hua WANG,Li-ning SUN

《信息与电子工程前沿（英文）》 2015年 第16卷 第7期   页码 607-616 doi: 10.1631/FITEE.14a0335

摘要： The redundant humanoid manipulator has characteristics of multiple degrees of freedom and complex joint structure, and it is not easy to obtain its inverse kinematics solution. The inverse kinematics problem of a humanoid manipulator can be formulated as an equivalent minimization problem, and thus it can be solved using some numerical optimization methods. Biogeography-based optimization (BBO) is a new biogeography inspired optimization algorithm, and it can be adopted to solve the inverse kinematics problem of a humanoid manipulator. The standard BBO algorithm that uses traditional migration and mutation operators suffers from slow convergence and prematurity. A hybrid biogeography-based optimization (HBBO) algorithm, which is based on BBO and differential evolution (DE), is presented. In this hybrid algorithm, new habitats in the ecosystem are produced through a hybrid migration operator, that is, the BBO migration strategy and DE/best/1/bin differential strategy, to alleviate slow convergence at the later evolution stage of the algorithm. In addition, a Gaussian mutation operator is adopted to enhance the exploration ability and improve the diversity of the population. Based on these, an 8-DOF (degree of freedom) redundant humanoid manipulator is employed as an example. The end-effector error (position and orientation) and the ‘away limitation level’ value of the 8-DOF humanoid manipulator constitute the fitness function of HBBO. The proposed HBBO algorithm has been used to solve the inverse kinematics problem of the 8-DOF redundant humanoid manipulator. Numerical simulation results demonstrate the effectiveness of this method.

关键词： Inverse kinematics problem     8-DOF humanoid manipulator     Biogeography-based optimization (BBO)     Differential evolution (DE)    

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General closed-form inverse kinematics for arbitrary three-joint subproblems based on the product of

《机械工程前沿（英文）》 2022年 第17卷 第2期 doi: 10.1007/s11465-022-0681-7

摘要： The inverse kinematics problems of robots are usually decomposed into several Paden–Kahan subproblems based on the product of exponential model. However, the simple combination of subproblems cannot solve all the inverse kinematics problems, and there is no common approach to solve arbitrary three-joint subproblems in an arbitrary postural relationship. The novel algebraic geometric (NAG) methods that obtain the general closed-form inverse kinematics for all types of three-joint subproblems are presented in this paper. The geometric and algebraic constraints are used as the conditions precedent to solve the inverse kinematics of three-joint subproblems. The NAG methods can be applied in the inverse kinematics of three-joint subproblems in an arbitrary postural relationship. The inverse kinematics simulations of all three-joint subproblems are implemented, and simulation results indicating that the inverse solutions are consistent with the given joint angles validate the general closed-form inverse kinematics. Huaque III minimally invasive surgical robot is used as the experimental platform for the simulation, and a master–slave tracking experiment is conducted to verify the NAG methods. The simulation result shows the inverse solutions and six sets given joint angles are consistent. Additionally, the mean and maximum of the master–slave tracking experiment for the closed-form solution are 0.1486 and 0.4777 mm, respectively, while the mean and maximum of the master–slave tracking experiment for the compensation method are 0.3188 and 0.6394 mm, respectively. The experiments results demonstrate that the closed-form solution is superior to the compensation method. The results verify the proposed general closed-form inverse kinematics based on the NAG methods.

关键词： inverse kinematics     Paden–Kahan subproblems     three-joint subproblems     product of exponential     closed-form solution    

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Generation of closed-form inverse kinematics for reconfigurable robots

ZHAO Jie, WANG Weizhong, GAO Yongsheng, CAI Hegao

《机械工程前沿（英文）》 2008年 第3卷 第1期   页码 91-96 doi: 10.1007/s11465-008-0013-6

摘要： For reconfigurable robots, the automatic generation of inverse kinematics is a key problem, because such robots may assume various configurations. In this paper, the screw and product-of-exponentials (POE) formula are used to model the kinematics of reconfigurable robots. The POE formula can be converted to canonical subproblems through decomposition and adjoint transformation. Three classes and 28 types of subproblems containing geometric or algebraic solutions are identified and solved, which can be reused in different configurations. A generalized, decomposable, and reusable approach for close-form inverse kinematics of reconfigurable robots is developed based on POE and subproblems. The effectiveness of this method is shown in an example.

关键词： different     effectiveness     generation     reconfigurable     algebraic    

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Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

WANG Yan, HANG Lu-bin, YANG Ting-li

《机械工程前沿（英文）》 2006年 第1卷 第1期   页码 115-124 doi: 10.1007/s11465-005-0022-7

摘要：

This study presents a solution for the inverse kinematics problem in serial 6R manipulator. Using only seven equations composed of Duffy s four kinematical equations containing three angles and three corresponding angles identical equations instead of the traditional 14 equations, the authors reduced the inverse kinematics problem in the general 6R manipulator to a univariate polynomial with a minimum degree based on the Groebner Base method. From that, they concluded that the maximum number of the solutions is 16, generally. Also, the mathematics mechanization method can be extended to solve other mechanism problems involving nonlinear equations symbolically.

关键词： identical     manipulator     univariate polynomial     mechanism     traditional    

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Method for solving the nonlinear inverse problem in gas face seal diagnosis based on surrogate models

《机械工程前沿（英文）》 2022年 第17卷 第3期 doi: 10.1007/s11465-022-0689-z

摘要： Physical models carry quantitative and explainable expert knowledge. However, they have not been introduced into gas face seal diagnosis tasks because of the unacceptable computational cost of inferring the input fault parameters for the observed output or solving the inverse problem of the physical model. The presented work develops a surrogate-model-assisted method for solving the nonlinear inverse problem in limited physical model evaluations. The method prepares a small initial database on sites generated with a Latin hypercube design and then performs an iterative routine that benefits from the rapidity of the surrogate models and the reliability of the physical model. The method is validated on simulated and experimental cases. Results demonstrate that the method can effectively identify the parameters that induce the abnormal signal output with limited physical model evaluations. The presented work provides a quantitative, explainable, and feasible approach for identifying the cause of gas face seal contact. It is also applicable to mechanical devices that face similar difficulties.

关键词： surrogate model     gas face seal     fault diagnosis     nonlinear dynamics     tribology    

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一种改进BP算法在机械手逆运动学中的应用

吴爱国,郝润生

《中国工程科学》 2005年 第7卷 第7期   页码 34-38

摘要：

通过对传统BP算法的分析，提出了一种改进激励函数的学习方法，并且在神经网络的每一层采用不同的学习速率，以提高训练速度；采用所提出的改进BP算法，训练多层前向神经网络，建立机械手逆运动学模型，仿真结果表明了该算法的有效性；与传统BP算法相比，大大提高了机械手逆运动学的精度。

关键词： 神经网络     BP算法     激励函数     机械手     逆运动学    

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Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

《机械工程前沿（英文）》 2021年 第16卷 第3期   页码 435-450 doi: 10.1007/s11465-021-0630-x

摘要： Seven-degree-of-freedom redundant manipulators with link offset have many advantages, including obvious geometric significance and suitability for configu-ration control. Their configuration is similar to that of the experimental module manipulator (EMM) in the Chinese Space Station Remote Manipulator System. However, finding the analytical solution of an EMM on the basis of arm angle parameterization is difficult. This study proposes a high-precision, semi-analytical inverse method for EMMs. Firstly, the analytical inverse kinematic solution is established based on joint angle parameterization. Secondly, the analytical inverse kinematic solution for a non-offset spherical–roll–spherical (SRS) redundant manipulator is derived based on arm angle parameterization. The approximate solution of the EMM is calculated in accordance with the relationship between the joint angles of the EMM and the SRS manipulator. Thirdly, the error is corrected using a numerical method through the analytical inverse solution based on joint angle parameterization. After selecting the stride and termination condition, the precise inverse solution is computed for the EMM based on arm angle parameterization. Lastly, case solutions confirm that this method has high precision, and the arm angle parameterization method is superior to the joint angle parameterization method in terms of parameter selection.

关键词： 7-DOF redundant manipulator     inverse kinematics     semi-analytical     arm angle     link offset    

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Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: Mobility, kinematics

Fugui XIE,Xin-Jun LIU

《机械工程前沿（英文）》 2016年 第11卷 第2期   页码 135-143 doi: 10.1007/s11465-016-0389-7

摘要：

This study introduces a high-speed parallel robot with Schönflies motion. This robot exhibits a promising prospect in realizing high-speed pick-and-place manipulation for packaging production lines. The robot has four identical limbs and a single platform. Its compact structure and single-platform concept provides this robot with good dynamic response potential. A line graph method based on Grassmann line geometry is used to investigate the mobility characteristics of the proposed robot. A generalized Blanding rule is also introduced into this procedure to realize mutual conversion between the line graphs for motions and constraints. Subsequently, the inverse kinematics is derived, and the singularity issue of the robot is investigated using both qualitative and quantitative approaches. Input and output transmission singularity indices are defined based on the reciprocal product in screw theory and the virtual coefficient by considering motion/force transmission performance. Thereafter, the singular loci of the proposed robot with specific geometric parameters are derived. The mobility analysis, inverse kinematics modeling, and singularity analysis conducted in this study are helpful in developing the robot.

关键词： parallel robot     mobility     inverse kinematics     singularity     transmission performance    

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Inverse kinematics analysis and numerical control experiment for PRS-XY style hybrid machining tool

JIA Dongyong, ZHANG Jianmin, SUN Hongchang, NIU Zhigang

《机械工程前沿（英文）》 2007年 第2卷 第2期   页码 235-238 doi: 10.1007/s11465-007-0041-7

摘要： This paper analyzed the inverse kinematics for the new Parallel rotate slider- axes (PRS-) style hybrid machining tool and educed the five axes linkage inverse kinematics transform formula on the basis of the coordinates of the and virtual axes. The program for the PRS-XY style hybrid machining tool in accordance with the program manner for the common numerical control (NC) machine tool was made. The results of the experiments prove that the inverse kinematics transform formula is correct.

关键词： numerical     accordance     transform formula     virtual     slider-    

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Shape reconstruction of parallelogram flaw

ZHENG Gangfeng, WU Bin, HE Cunfu

《机械工程前沿（英文）》 2008年 第3卷 第1期   页码 17-22 doi: 10.1007/s11465-008-0015-4

摘要： To reconstruct the shape of the scatterer in elastic media, the authors deduce the Born approximation solution of the two-dimensional scattering problem, which includes the shape factor that embodies all information about the shape of the scatterer. Accordingly, the change in the shape of the scatterer only necessitates the number of the corresponding new shape factors. For a parallelogram void in a long Al rod, its shape factor can be obtained. In view of the definition of a characteristic function, the shape factor has a corresponding integral representation. Obviously, the shape factor can be considered as a Fourier transform of the characteristic function, which is reconstructed from the inverse Fourier transform. The integral equation is considered as the basic equation to reconstruct the shape of the scatterer. The identification of the geometrical character of a flaw is then given by the two dimensional inverse Born approximation in a low-frequency range. For the parallelogram void, a theoretical calculating identification is performed. At the same time, the numerical results are obtained by the finite element method.

关键词： approximation     scatterer     scattering problem     information     inverse    

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Stiffness of a 3-degree of freedom translational parallel kinematic machine

null

《机械工程前沿（英文）》 2014年 第9卷 第3期   页码 233-241 doi: 10.1007/s11465-014-0312-z

摘要：

In this paper, a typical 3-degree of freedom (3-DOF) translational parallel kinematic machine (PKM) is studied and analyzed whose tool platform has only translations along X-, Y- and Z-axes. It consists of three limbs, each of which have arm and forearm with prismatic-revolute-revolute-revolute (PRRR) joints. Inverse kinematics analysis is carried out to find the slider coordinates and joint angles for a given position of tool platform. Stiffness modeling is done based on the compliance matrices of arm and forearm of each limb. Using the stiffness modeling the variations of minimum and maximum translational stiffness in the workspace are analyzed. For various architectural parameters of the 3-DOF PKM the tendency of variations on the minimum and maximum stiffness over the entire workspace is studied; and also the deflections of the tool platform along X, Y, and Z directions with respect to various forces are presented.

关键词： 3-DOF translational PKM     inverse kinematics     stiffness modeling     translational stiffness    

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Approximation of structural damping and input excitation force

Mohammad SALAVATI

《结构与土木工程前沿（英文）》 2017年 第11卷 第2期   页码 244-254 doi: 10.1007/s11709-016-0371-9

摘要： Structural dynamic characteristics are the most significant parameters that play a decisive role in structural damage assessment. The more sensitive parameter to the damage is the damping behavior of the structure. The complexity of structural damping mechanisms has made this parameter to be one of the ongoing research topics. Despite all the difficulties in the modeling of damping, there are some approaches like as linear and nonlinear models which are described as the energy dissipation throughout viscous, material or structural hysteretic and frictional damping mechanisms. In the presence of a mathematical model of the damping mechanisms, it is possible to estimate the damping ratio from the theoretical comparison of the damped and un-damped systems. On the other hand, solving the inverse problem of the input force estimation and its distribution to each SDOFs, from the measured structural responses plays an important role in structural identification process. In this paper model-based damping approximation method and a model-less structural input estimation are considered. The effectiveness of proposed methods has been carried out through analytical and numerical simulation of the lumped mass system and the results are compared with reference data. Consequently, high convergence of the comparison results illustrates the satisfactory of proposed approximation methods.

关键词： structural modal parameters     damping identification method     input excitation force identification     Inverse problem    

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Identification of structural parameters and boundary conditions using a minimum number of measurement points

Ali KARIMPOUR, Salam RAHMATALLA

《结构与土木工程前沿（英文）》 2020年 第14卷 第6期   页码 1331-1348 doi: 10.1007/s11709-020-0686-4

摘要： This article proposes a novel methodology that uses mathematical and numerical models of a structure to build a data set and determine crucial nodes that possess the highest sensitivity. Regression surfaces between the structural parameters and structural output features, represented by the natural frequencies of the structure and local transmissibility, are built using the numerical data set. A description of a possible experimental application is provided, where sensors are mounted at crucial nodes, and the natural frequencies and local transmissibility at each natural frequency are determined from the power spectral density and the power spectral density ratios of the sensor responses, respectively. An inverse iterative process is then applied to identify the structural parameters by matching the experimental features with the available parameters in the myriad numerical data set. Three examples are presented to demonstrate the feasibility and efficacy of the proposed methodology. The results reveal that the method was able to accurately identify the boundary coefficients and physical parameters of the Euler-Bernoulli beam as well as a highway bridge model with elastic foundations using only two measurement points. It is expected that the proposed method will have practical applications in the identification and analysis of restored structural systems with unknown parameters and boundary coefficients.

关键词： structural model validation     eigenvalue problem     response surface     inverse problems    

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Non-convex sparse optimization-based impact force identification with limited vibration measurements

《机械工程前沿（英文）》 2023年 第18卷 第3期 doi: 10.1007/s11465-023-0762-2

摘要： Impact force identification is important for structure health monitoring especially in applications involving composite structures. Different from the traditional direct measurement method, the impact force identification technique is more cost effective and feasible because it only requires a few sensors to capture the system response and infer the information about the applied forces. This technique enables the acquisition of impact locations and time histories of forces, aiding in the rapid assessment of potentially damaged areas and the extent of the damage. As a typical inverse problem, impact force reconstruction and localization is a challenging task, which has led to the development of numerous methods aimed at obtaining stable solutions. The classical ℓ2 regularization method often struggles to generate sparse solutions. When solving the under-determined problem, ℓ2 regularization often identifies false forces in non-loaded regions, interfering with the accurate identification of the true impact locations. The popular ℓ1 sparse regularization, while promoting sparsity, underestimates the amplitude of impact forces, resulting in biased estimations. To alleviate such limitations, a novel non-convex sparse regularization method that uses the non-convex ℓ1−2 penalty, which is the difference of the ℓ1 and ℓ2 norms, as a regularizer, is proposed in this paper. The principle of alternating direction method of multipliers (ADMM) is introduced to tackle the non-convex model by facilitating the decomposition of the complex original problem into easily solvable subproblems. The proposed method named ℓ1−2-ADMM is applied to solve the impact force identification problem with unknown force locations, which can realize simultaneous impact localization and time history reconstruction with an under-determined, sparse sensor configuration. Simulations and experiments are performed on a composite plate to verify the identification accuracy and robustness with respect to the noise of the ℓ1−2-ADMM method. Results indicate that compared with other existing regularization methods, the ℓ1−2-ADMM method can simultaneously reconstruct and localize impact forces more accurately, facilitating sparser solutions, and yielding more accurate results.

关键词： impact force identification     inverse problem     sparse regularization     under-determined condition     alternating direction method of multipliers    

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Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

《环境科学与工程前沿（英文）》 2023年 第17卷 第7期 doi: 10.1007/s11783-023-1685-1

摘要：

● A hydrodynamic-Bayesian inference model was developed for water pollution tracking.

关键词： Identification of pollution sources     Water quality restoration     Bayesian inference     Hydrodynamic model     Inverse problem    

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标题 作者 时间 类型 操作

Ahybrid biogeography-based optimization method for the inverse kinematics problem of an 8-DOF redundant

Zi-wu REN,Zhen-hua WANG,Li-ning SUN

期刊论文

General closed-form inverse kinematics for arbitrary three-joint subproblems based on the product of

期刊论文

Generation of closed-form inverse kinematics for reconfigurable robots

ZHAO Jie, WANG Weizhong, GAO Yongsheng, CAI Hegao

期刊论文

Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base

WANG Yan, HANG Lu-bin, YANG Ting-li

期刊论文

Method for solving the nonlinear inverse problem in gas face seal diagnosis based on surrogate models

期刊论文

一种改进BP算法在机械手逆运动学中的应用

吴爱国,郝润生

期刊论文

Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

期刊论文

Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: Mobility, kinematics

Fugui XIE,Xin-Jun LIU

期刊论文

Inverse kinematics analysis and numerical control experiment for PRS-XY style hybrid machining tool

JIA Dongyong, ZHANG Jianmin, SUN Hongchang, NIU Zhigang

期刊论文

Shape reconstruction of parallelogram flaw

ZHENG Gangfeng, WU Bin, HE Cunfu

期刊论文

Stiffness of a 3-degree of freedom translational parallel kinematic machine

null

期刊论文

Approximation of structural damping and input excitation force

Mohammad SALAVATI

期刊论文

Identification of structural parameters and boundary conditions using a minimum number of measurement points

Ali KARIMPOUR, Salam RAHMATALLA

期刊论文

Non-convex sparse optimization-based impact force identification with limited vibration measurements

期刊论文

Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

期刊论文