A Novel Numerical Method to Solve the Inverse Kinematics of 3R Manipulators

2011 ◽  
Author(s):  
E. A. Gonza´lez-Barbosa ◽  
M. A. Gonza´lez-Palacios ◽  
L. A. Aguilera-Corte´s ◽  
C. A. Bernal-Marti´nez
Keyword(s):  
Differential Evolution ◽  
Numerical Method ◽  
Computational Efficiency ◽  
Software Package ◽  
Inverse Kinematics ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Simulation Results ◽  
General Geometry ◽  
Solution Problem

A new numerical method to solve the inverse kinematics solution problem of serial manipulators is developed in this paper. The proposed method is known as Differential Evolution (DE), a novel and efficient numerical method which has been adapted to solve the inverse kinematics solution of 3R serial manipulator of general geometry. Besides, the paper contains the complete structuring for the implementation of this new case in SnAP, a comprehensive software package for synthesis, analysis and simulation of serial manipulators. The DE method is stable since it converges to the solution with any initial values, and it is not sensitive to the singular configurations of serial manipulators. Simulation results are presented to show the performance benefits of the proposed algorithm. Computational efficiency of the method is shown based on the results, as well as in comparison with traditional methods used in this problem.

scholarly journals Research on the inverse kinematics of manipulator using an improved self-adaptive mutation differential evolution algorithm

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110144
Author(s):  
Qianqian Zhang ◽  
Daqing Wang ◽  
Lifu Gao
Keyword(s):  
Differential Evolution ◽  
Objective Function ◽  
Inverse Kinematics ◽  
Differential Evolution Algorithm ◽  
Weight Coefficient ◽  
Adaptive Mutation ◽  
Feasible Region ◽  
Serial Manipulators ◽  
De Algorithm ◽  
Self Adaptive

To assess the inverse kinematics (IK) of multiple degree-of-freedom (DOF) serial manipulators, this article proposes a method for solving the IK of manipulators using an improved self-adaptive mutation differential evolution (DE) algorithm. First, based on the self-adaptive DE algorithm, a new adaptive mutation operator and adaptive scaling factor are proposed to change the control parameters and differential strategy of the DE algorithm. Then, an error-related weight coefficient of the objective function is proposed to balance the weight of the position error and orientation error in the objective function. Finally, the proposed method is verified by the benchmark function, the 6-DOF and 7-DOF serial manipulator model. Experimental results show that the improvement of the algorithm and improved objective function can significantly improve the accuracy of the IK. For the specified points and random points in the feasible region, the proportion of accuracy meeting the specified requirements is increased by 22.5% and 28.7%, respectively.

scholarly journals Inverse kinematics of mobile manipulators based on differential evolution

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141775273 ◽  
Author(s):  
Carlos López-Franco ◽  
Jesús Hernández-Barragán ◽  
Alma Y. Alanis ◽  
Nancy Arana-Daniel ◽  
Michel López-Franco
Keyword(s):  
Differential Evolution ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Inverse Kinematic ◽  
Mobile Manipulator ◽  
Robot Kinematics ◽  
Mobile Manipulators ◽  
Inverse Kinematic Problem ◽  
Simulation Results ◽  
Traditional Approaches

The solution of the inverse kinematics of mobile manipulators is a fundamental capability to solve problems such as path planning, visual-guided motion, object grasping, and so on. In this article, we present a metaheuristic approach to solve the inverse kinematic problem of mobile manipulators. In this approach, we represent the robot kinematics using the Denavit–Hartenberg model. The algorithm is able to solve the inverse kinematic problem taking into account the mobile platform. The proposed approach is able to avoid singularities configurations, since it does not require the inversion of a Jacobian matrix. Those are two of the main drawbacks to solve inverse kinematics through traditional approaches. Applicability of the proposed approach is illustrated using simulation results as well as experimental ones using an omnidirectional mobile manipulator.

Inverse Kinematics of General 4R2P, 3R3P, 4R1C, 2R2C, and 3C Serial Manipulators

1992 ◽  
Author(s):  
Dilip Kohli ◽  
Michael Osvatic
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Serial Manipulators ◽  
Linearly Independent ◽  
The Matrix ◽  
Half Angle ◽  
Inverse Kinematics Problem ◽  
Joint Variable ◽  
General Geometry ◽  
Solution Methodology

Abstract This paper presents a solution to the inverse kinematics problem for 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators of general geometry. The method used to solve these is based on a technique recently presented by the authors for solving the inverse kinematics of general 6R and 5R1P manipulators. In the 6R and 5R1P cases, the method initially starts using 14 linearly independent equations where as for the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulator only 3, 6, 7 or 10 linearly independent equations are required, depending on the case. Through the use of a linearization and dialytic elimination method all 4R2P, 3R3P, 4R1C, 2R2C and 3C cases are reduced to equating to zero the determinant of a matrix whose elements are linear in the tangent of a half angle of a joint variable. The size of this matrix is (8 × 8) for all 4R2P manipulators, (2 × 2) for all 3R3P and 3C manipulators, (16 × 16) for 4R1C manipulators, (4 × 4) for RCRC and CRCR manipulators and (8 × 8) for the remaining 2R2C manipulators providing 8th, 2nd, 16th, 4th and 8th degree inverse kinematic polynomial respectively. Thus, the determinant equated to zero gives us the characteristic equation of the degree expected. The unique form of the matrix allows us to obtain the solution by solving an eigenvalue problem. Many variations of the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators are presented and the solution methodology is illustrated by several numerical examples.

Inverse Kinematics of General 6R and 5R,P Serial Manipulators

1992 ◽  
Author(s):  
Dilip Kohli ◽  
Michael Osvatic
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Kinematics ◽  
Linear Equations ◽  
Computation Time ◽  
Solution Procedure ◽  
Linearization Method ◽  
Solution Technique ◽  
Serial Manipulators ◽  
General Geometry ◽  
Imaginary Roots

Abstract In this paper we present a solution to the inverse kinematics problem for serial manipulators of general geometry. The method is presented in detail as it applies to a 6R manipulator of general geometry. The equations used are derived using a linearization method and dialytic elimination. In doing this, all variables except one, a tangent half angle of a joint variable, can be eliminated. The result is a 16 by 16 matrix in which all terms are linear in the suppressed variable. The unique design of this matrix allows the suppressed variable to be solved as an eigenvalue problem. Substituting these values of the suppressed variable back into the equations, all other joint variables can be found using linear equations. The result is the 16 solutions expected for the 6R case. The same technique is also applicable to manipulators with prismatic joints. We present the solution technique for all six possible 5R,P manipulators through numerical examples. The primary distinction between the technique presented in this paper and recently published Raghavan and Roth (90a,b.c) solution is that they removed two known spurious imaginary roots of multiplicity four to obtain a 16th order polynomial for 6R and 5R,P cases. In our formulation, the 16th degree polynomial can be derived directly without having to remove any spurious imaginary roots. Another distinction is that the solution procedure presented in this paper can be reduced to an eigenvalue problem. This results in significant gains in computation time.

SnAP: A Comprehensive Software Package for the Simulation of Serial Manipulators

2008 ◽  
Author(s):  
E. A. Gonza´lez-Barbosa ◽  
M. A. Gonza´lez-Palacios ◽  
L. A. Aguilera-Corte´s
Keyword(s):  
Software Package ◽  
Inverse Kinematics ◽  
Closed Loop ◽  
Computer Control ◽  
Design Parameters ◽  
Graphical Interface ◽  
Matrix Formulation ◽  
Embedded Control ◽  
Serial Manipulators ◽  
Actual Configuration

The solution of kinematics problem for serial manipulators is fundamental for their analysis, simulation and computer control, for this reason, this paper introduces the software package called SnAP (Serial n-Axes Manipulators), which is developed under the ADEFID framework [1], where the manipulator is conceptualized as a derived class from CRobokin, CMachine and CIpiSModel, which are fundamental ADEFID classes. SnAP has been developed with efficient algorithms in a closed-loop solution to solve direct kinematics, whereas for the case of inverse kinematics, matrix formulation, elimination and numerical methods are implemented. Furthermore, for the architecture definition, the user is able to display a dialog box in which the design parameters are set while the solid model is updated simultaneously showing the actual configuration. Since ADEFID provides tools to graphical interface with embedded control components, SnAP adopted them to not only simulate virtually, but also with a parametric prototype designed for this purpose.

Inverse Kinematics of General 6R and 5R,P Serial Manipulators

1993 ◽  
Vol 115 (4) ◽  
pp. 922-931 ◽  
Author(s):  
D. Kohli ◽  
M. Osvatic
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Kinematics ◽  
Linear Equations ◽  
Computation Time ◽  
Solution Procedure ◽  
Solution Technique ◽  
Serial Manipulators ◽  
Order Polynomial ◽  
General Geometry ◽  
Imaginary Roots

In this paper we present a solution to the inverse kinematics problems for serial manipulators of general geometry. The method is presented in detail as it applies to a 6R manipulator of general geometry. The equations used are derived using power products and dialytic elimination. In doing this, all variables except one, a tangent half angle of a joint variable, can be eliminated. The result is a 16 by 16 matrix in which all terms are linear in the suppressed variable. The unique design of this matrix allows the suppressed variable to be solved as an eigenvalue problem. Substituting these values of the suppressed variable back into the equations, all other joint variables can be found using linear equations. The result is the 16 solutions expected for the 6R case. The same technique is also applicable to manipulators with prismatic joints. We present the solution technique for all six possible 5R,P manipulators through numerical examples. The primary distinction between the technique presented in this paper and the recently published Raghavan and Roth (1990) solution is that they removed two spurious imaginary roots of multiplicity four from a 24th order polynomial to obtain a 16th order polynomial for 6R and 5R,P cases. In our formulation, the 16th degree polynomial can be derived directly without having to remove any spurious imaginary roots. Another distinction is that the solution procedure can be reduced to an eigenvalue problem. This results in significant gains in computation time.

The Sensitivity Simulation of Different Geometric Pretreatment in Method of Characteristics

2017 ◽  
Author(s):  
Tian XiaoRui ◽  
Zhou Tao ◽  
Li Zichao ◽  
Yu Tao
Keyword(s):  
Computational Efficiency ◽  
Method Of Characteristics ◽  
Azimuthal Angle ◽  
Reactor Core ◽  
Characteristic Line ◽  
Simulation Results ◽  
And Storage

In reactor core physics analysis,the research about the pre-processing of Method of Characteristic (MOC) including the generation and storage of characteristic line,the progress of calculation and the choosing of different quadrature set.In addition,doing some simulations,which is based on OpenMOC code and C5G7-MOX benchmark,about different parameters (including the track spacing,azimuthal angles and polar angles) and calculated its impacts on the computational efficiency and accuracy.the simulation results are as following:setting the track spacing as 0.1 cm or the azimuthal angle number as 4,the simulation results have better accuracy. Whether choosing the Leonard’s optimum quadrature set or the Tabuchi-Yamamoto quadrature set,the number of polar angles have tiny impact on accuracy.

scholarly journals STRESSING ISSUE OF A PIEZOCERAMIC CANTILEVER WITH LONGITUDINAL POLARISATION AND ELECTRODE COATINGS

2020 ◽  
Vol 19 (2) ◽  
pp. 113
Author(s):  
Igor Jovanović ◽  
Ljubiša Perić ◽  
Uglješa Jovanović ◽  
Dragan Mančić
Keyword(s):  
General Solution ◽  
Free Vibration ◽  
Electric Potential ◽  
Software Package ◽  
Longitudinal Polarization ◽  
Main Subject ◽  
Piezoceramic Material ◽  
Coupled Equations ◽  
Specific Strain ◽  
Simulation Results

The main subject of this study is the investigation of the free vibration of a rectangular prismatic piezoceramic cantilever with longitudinal polarization and electrode coatings. Based on the general solution of coupled equations for piezoceramic material, applying the equations of electro-elasticity and satisfying electrical and mechanical conditions for the stress of a cantilever made from PZT4 piezoceramic material, componential displacements, electric potential, specific strain, electric field, and piezoelectric displacement, are determined and numerically obtained with Matlab software package. Based on the obtained equations and simulation results, it is possible to optimize the dimensions of the cantilever and determine the type of piezoceramic.

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