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.

Determination of the inverse kinematics branches of solution based on joint coordinates for UR-like serial robot architecture

2021 ◽  
pp. 1-13
Author(s):  
Louis-Thomas Schreiber ◽  
Clement Gosselin
Keyword(s):  
Inverse Kinematics ◽  
Degree Of Freedom ◽  
Robot Architecture ◽  
Serial Robots ◽  
Joint Coordinates ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Six Degree Of Freedom

Abstract This paper introduces a classification of the inverse kinematics solutions (or robot postures) of six-degree-of-freedom serial robots with a geometry based on or similar to Universal Robots' arms. The solution of the inverse kinematics problem is first presented briefly and the equations required to classify the robot postures(branches) based on the joint coordinates are then introduced.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Author(s):  
Zhi Xin Shi ◽  
Yu Feng Luo ◽  
Lu Bing Hang ◽  
Ting Li Yang
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Algebraic Method ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Parallel Mechanisms ◽  
Simple Method ◽  
Inverse Kinematics Problem ◽  
Serial Robot

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Vol 129 (8) ◽  
pp. 793-798 ◽  
Author(s):  
Shi Zhi Xin ◽  
Luo Yu Feng ◽  
Hang Lu Bing ◽  
Yang Ting Li
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Forward Kinematics ◽  
The Real ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Inverse Kinematic Analysis

The inverse kinematic analysis of the general 6R serial robot has been a very significant and important problem in the theory of the spatial mechanisms. Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on a one-dimension searching algorithm. All the real solutions to inverse kinematics problems of the general 6R serial robot or forward kinematics problems of the general 7R single-loop mechanism can be obtained. The new method has the following features: (1) using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; and (2) compared with the algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

scholarly journals Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

2013 ◽  
Vol 5 (3) ◽  
Author(s):  
Zhongtao Fu ◽  
Wenyu Yang ◽  
Zhen Yang
Keyword(s):  
Real Time ◽  
Geometric Algebra ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Robot Manipulators ◽  
Kinematic Modeling ◽  
Highly Nonlinear ◽  
Inverse Kinematics Problem ◽  
Painting Robot ◽  
Serial Robot

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

A New Algorithm for a Spatial Serial Robot

2010 ◽  
Vol 29-32 ◽  
pp. 952-955
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Duan Ling Li
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Greatest Common Divisor ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Serial Robot ◽  
Univariate Polynomial

In this paper a new algorithm to compute all the closed-form inverse kinematics solutions of a spatial serial robot. Based on the method, A 16th degree univariate polynomial of the spatial serial robot is obtained without factoring out or deriving the greatest common divisor. We also obtain all the closed-form solutions for the inverse kinematics of the robot. Finally a numerical example is given to demonstrate the algorithm process.

A Genetic Algorithm as Support in the Movement Optimisation of a Redundant Serial Robot

2006 ◽  
Author(s):  
Massimo Antonini ◽  
Alberto Borboni ◽  
Roberto Bussola ◽  
Rodolfo Faglia
Keyword(s):  
Genetic Algorithm ◽  
Inverse Kinematics ◽  
Inverse Matrix ◽  
Working Environment ◽  
End Effector ◽  
Redundant Robot ◽  
Linear Motors ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Pseudo Inverse

The paper illustrates the application of a genetic algorithm as a methodology to choose and improve the motion law governing the movement of a redundant robot. The subject of this research is an innovative system developed to introduce the laser ray technology in the on-line tube cutting. This technique allows a quality improvement in the pipe-cutting sector, thanks to the various goals. Firstly we underline the improvement of the working environment due to the elimination of cutting noise taking off the tool changing and the steel shaving creation. Secondarily there is a drastic reduction of the cutting cycle time and an improvement of the productivity accomplished by the use of brushless drives and linear motors. In the robot design, particular attention was dedicated to the masses distributions allowing a good natural machine dynamics. The ability of the robot to avoid the cutting object, the demand to maintain the laser torch orthogonal to the cutting surfaces, as well the necessity to impose a velocity behaviour as constant as possible during the cutting operation, suggested the introduction of a redundant degree of freedom. This aspect gives a lot of opportunities in the choose of movements because there are thousands motion profiles for the joints whichever satisfying the conditions imposed to the end-effector path. In this context, we have proposed the idea to combine the procedure to solve the inverse kinematics problem with the contemporaneous optimization of the trajectory. Literature offers a series of algorithms to solve well-known inverse kinematics problem of redundant robot. These are based on the inversion of the matrix representing the link between the end-effector co-ordinates and the joints. The presence of redundancy makes this matrix rectangular and requires the use of the pseudo-inverse matrix to solve the problem in several points of the trajectory. The introduction of some weights, one for each joint co-ordinate, allows to obtain a different distribution of the joint movements computing the pseudo-inverse matrix. If we change these weights in a continuous way in time domain, we can supervise the dynamic behaviors of the machine. The new idea we propose here is the use of an adapted multi-objective genetic algorithm to define a several of particular motion laws reducing vibrations and realizing “special harmonies” in the robot motion. The procedure, that will be completely discussed in the full paper, is actually working on a laser pipe cutting machine. This robot awarded the first prize between two thousand competitor at the EMO MILANO 2003 exhibition.

Position Kinematics of the Generalized Lobster Arm and Its Series-Parallel Dual

1992 ◽  
Vol 114 (3) ◽  
pp. 406-413 ◽  
Author(s):  
V. Murthy ◽  
K. J. Waldron
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Specific Geometry ◽  
Univariate Polynomial ◽  
The One ◽  
Dual Mechanism ◽  
The Relationship ◽  
Direct Kinematics

The generalized lobster arm is a six revolute open kinematic chain with 3 consecutive intersecting pairs of axes. A new solution of the inverse position kinematics problem of this arm which takes advantage of its specific geometry is presented. A comparison is made with the direct position kinematics problem of the series-parallel dual mechanism. The equations governing the two problems show strong similarity and can each be reduced to a sixteenth degree univariate polynomial equation. The dual series-parallel mechanism is the one that exhibits, with the lobster arm, the symmetry that exists between the wrench and the velocity motor. Although the results presented here have intrinsic interest, a more generally important feature is the relationship between the solutions to the inverse kinematics of the serial mechanism and the direct kinematics of the parallel mechanism. Although the series-parallel duality has not been shown to hold in the position domain, except in terms of very general characteristics, it is shown here that the two solutions are of the same degree and have other features in common.

Inverse Kinematic Analysis of General 5R Serial Robot Based on Linear Transformation

2000 ◽  
Author(s):  
Lubin Hang ◽  
Qiong Jin ◽  
Tingli Yang
Keyword(s):  
Linear Transformation ◽  
Kinematic Analysis ◽  
Traditional Method ◽  
Polynomial Equation ◽  
Inverse Kinematic ◽  
Transformation Theory ◽  
Serial Robots ◽  
Serial Robot ◽  
Inverse Kinematic Analysis ◽  
General Method

Abstract Based on the linear transformation theory, a general method for inverse kinematic analysis of 5R serial robots is proposed in this paper. Using this method, a polynomial equation, which contains only one variable and no extraneous roots, can be derived from 3 original kinematic equations, whereas the traditional method needs 4 equations. The assembly condition of 5R manipulator (5R loop) and its application in kinematic analysis are discussed. This assembly condition is very useful for finding 6R manipulator’s real configuration.

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.

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