Minimum Degree Solutions for the Inverse Kinematics Problem by Application of the Buchberger Algorithm

1991 ◽  
pp. 326-334 ◽  
Author(s):  
Peter Kovács
Keyword(s):  
Inverse Kinematics ◽  
Minimum Degree ◽  
Inverse Kinematics Problem ◽  
Buchberger Algorithm

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.

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.

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

scholarly journals Cerebellum-inspired neural network solution of the inverse kinematics problem

2015 ◽  
Vol 109 (6) ◽  
pp. 561-574 ◽  
Author(s):  
Mitra Asadi-Eydivand ◽  
Mohammad Mehdi Ebadzadeh ◽  
Mehran Solati-Hashjin ◽  
Christian Darlot ◽  
Noor Azuan Abu Osman
Keyword(s):  
Neural Network ◽  
Inverse Kinematics ◽  
Network Solution ◽  
Inverse Kinematics Problem

Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Vol 6 (2) ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Surgical Instruments ◽  
End Effector ◽  
Minimally Invasive Surgical ◽  
Inverse Kinematics Problem

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

scholarly journals A comparative study of soft computing methods to solve inverse kinematics problem

2018 ◽  
Vol 9 (4) ◽  
pp. 2535-2548 ◽  
Author(s):  
Ahmed El-Sherbiny ◽  
Mostafa A. Elhosseini ◽  
Amira Y. Haikal
Keyword(s):  
Comparative Study ◽  
Soft Computing ◽  
Inverse Kinematics ◽  
Computing Methods ◽  
Inverse Kinematics Problem ◽  
Soft Computing Methods

Improved Artificial Potential Field Method Manipulator Inverse Kinematics

2013 ◽  
Vol 273 ◽  
pp. 119-123
Author(s):  
Ding Jin Huang ◽  
Teng Liu
Keyword(s):  
Potential Field ◽  
Inverse Kinematics ◽  
Search Space ◽  
Field Method ◽  
Robotic Arm ◽  
Artificial Potential Field ◽  
Robot Arm ◽  
Potential Field Method ◽  
Inverse Kinematics Problem ◽  
Artificial Potential Field Method

The use of traditional analytical method for manipulator inverse kinematics is able to get a display solution with the limitations of the application, only when the robotic arm has a specific structure. In view of the insufficient, this paper presents an improved artificial potential field method to solve the inverse kinematics problem of the manipulator which does not have a special structure. Firstly, establish the standard DH model for the robot arm. Then the strategy that improves search space of artificial potential field method and motion control standard is presented by combining artificial potential field method with the manipulator. Finally, the simulation results show that the proposed method is effective.

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