Inverse Kinematics Analysis of General 6R Manipulator Based on Groebner Basis-Sylvester Hybrid Method

2006 ◽  
Author(s):  
Lubing Hang ◽  
Tingli Yang
Keyword(s):  
Hybrid Method ◽  
Inverse Kinematics ◽  
Minimum Degree ◽  
The Other ◽  
Groebner Basis ◽  
Kinematics Analysis ◽  
Mathematics Mechanization ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomial ◽  
General Geometry

In this paper we present a solution to the inverse kinematics problem for serial manipulator of general geometry. Using only seven equations which are consisted of Duffy’s four kinematical equations containing only three angles and three corresponding angles’ sincos identical equations instead of traditional fourteen equations, we reduce the inverse kinematics problem of the general 6R manipulator to a univariate polynomial with minimum degree based on Groebner-Sylvester method. From that, a conclusion can be drawn that the maximum number of the solutions is sixteen, generally. Also the mathematics mechanization method used in this paper can be extended to solve the other mechanism problem involving nonlinear equations symbolically.

Inverse Kinematics of Serial-Chain Manipulators

1996 ◽  
Vol 118 (3) ◽  
pp. 396-404 ◽  
Author(s):  
Hong-You Lee ◽  
Charles F. Reinholtz
Keyword(s):  
Inverse Kinematics ◽  
Minimum Degree ◽  
Complete Solution ◽  
Linear Equations ◽  
End Effector ◽  
Serial Chain ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomials ◽  
General Geometry

This paper proposes a unified method for the complete solution of the inverse kinematics problem of serial-chain manipulators. This method reduces the inverse kinematics problem for any 6 degree-of-freedom serial-chain manipulator to a single univariate polynomial of minimum degree from the fewest possible closure equations. It is shown that the univariate polynomials of 16th degree for the 6R, 5R-P and 4R-C manipulators with general geometry can be derived from 14, 10 and 6 closure equations, respectively, while the 8th and 4th degree polynomials for all the 4R-2P, 3R-P-C, 2R-2C, 3R-E and 3R-S manipulators can be derived from only 2 closure equations. All the remaining joint variables follow from linear equations once the roots of the univariate polynomials are found. This method works equally well for manipulators with special geometry. The minimal properties may provide a basis for a deeper understanding of manipulator geometry, and at the same time, facilitate the determination of all possible configurations of a manipulator with respect to a given end-effector position, the determination of the workspace and its subspaces with the different number of configurations, and the identification of singularity positions of the end-effector. This paper also clarifies the relationship between the three known solutions of the general 6R manipulator as originating from a single set of 14 equations by the first author.

A Computational Algorithm for a Spatial Serial Robot

2011 ◽  
Vol 217-218 ◽  
pp. 233-237
Author(s):  
Xi Guang Huang
Keyword(s):  
Automatic Control ◽  
Inverse Kinematics ◽  
Computational Algorithm ◽  
Polynomial Equation ◽  
Central Problem ◽  
Serial Robots ◽  
Symbolic Calculations ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Univariate Polynomial

The inverse kinematics of serial robots is a central problem in the automatic control of robot manipulators. The aim of this paper is to obtain a computational algorithm to compute the inverse kinematics problem of a spatial serial robot. We use a series of algebraic and numeric transformations to reduce the problem to a univariate polynomial equation. The results can be directly applied to symbolic calculations and decreased considerably the calculation time.

Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators

1985 ◽  
Vol 107 (2) ◽  
pp. 201-208 ◽  
Author(s):  
G. R. Pennock ◽  
A. T. Yang
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Manipulators ◽  
Closed Form Solutions ◽  
Dual Number ◽  
Special Geometry ◽  
Inverse Kinematics Problem ◽  
Concise Representation ◽  
Joint Parameters ◽  
General Geometry

This paper presents the application of dual-number matrices to the formulation of displacement equations of robot manipulators with completely general geometry. Dual-number matrices make possible a concise representation of link proportions and joint parameters; together with the orthogonality properties of the matrices we are able to derive, in a systematic manner, closed-form solutions for the joint displacements of robot manipulators with special geometry as illustrated by three examples. It is hoped that the method presented here will provide a meaningful alternative to existing methods for formulating the inverse kinematics problem of robot manipulators.

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.

Kinematics Analysis of a Novel 5-DOF Hybrid Manipulator

2015 ◽  
Vol 9 (6) ◽  
pp. 765-774 ◽  
Author(s):  
Wanjin Guo ◽  
◽  
Ruifeng Li ◽  
Chuqing Cao ◽  
Yunfeng Gao ◽  
...  
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Structure And Motion ◽  
Reachable Workspace ◽  
Hybrid Manipulator ◽  
Inverse Kinematics Problem

Application of hybrid robotics is a continuously developing field, as hybrid manipulators have demonstrated that they can combine the benefits of serial structures and parallel mechanisms. In this paper, a novel 5-degree-of-freedom hybrid manipulator is designed. The structure of this manipulator and its kinematics analysis are presented. An innovative closed-form solution was proposed to address the inverse kinematics problem. Additionally, the validity of the closed-form solution was verified via co-simulation using MATLAB and ADAMS. Finally, the reachable workspace of this manipulator was obtained for further optimizing the structure and motion control.

scholarly journals Kinematic analysis of the 3-RPS-3-SPR series–parallel manipulator

Robotica ◽  
2018 ◽  
Vol 37 (7) ◽  
pp. 1240-1266 ◽  
Author(s):  
Abhilash Nayak ◽  
Stéphane Caro ◽  
Philippe Wenger
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
End Effector ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomial ◽  
Six Degree Of Freedom ◽  
Independent Parameters ◽  
Direct Kinematics

SUMMARYThis paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

Inverse Kinematics Analysis of 5-DOF Robot Manipulators Based on Virtual Joint Method

2011 ◽  
Vol 143-144 ◽  
pp. 265-268
Author(s):  
Zhi Zhong Liu ◽  
Hong Yi Liu ◽  
Zhong Luo
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Kinematics Analysis ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Joint Method

To solve the inverse kinematics problem of a robot manipulator without closed form solutions, one-dimensional iterative method is very useful. However, for a 5-DOF robot manipulator, because of the uncontrolable and uncertain orientation vectors, it's difficult to analytically express all joint variables by one of them, therefore one-dimensional iterative method can not be directedly used. By adding an appropriate virtual joint to it, a 5-DOF manipulator can be changed into a 6-DOF one so that the uncertain orientation vectors can be pre-given, and the difficulty is solved. To illustrate this virtual joint method a 5-DOF serial robot manipulator with prismatic arm joint and offset wrist is discussed in this paper as an example.

scholarly journals Study on the Inverse Kinematics Problem of Robot (2nd Report)

1997 ◽  
Vol 63 (5) ◽  
pp. 699-703
Author(s):  
Xiaohai JIN ◽  
Sachio SHIMIZU ◽  
Nobuyuki FURUYA
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematics Problem
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