scholarly journals Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

2020 ◽  
Vol 10 (8) ◽  
pp. 2781
Author(s):  
José Guzmán-Giménez ◽  
Ángel Valera Fernández ◽  
Vicente Mata Amela ◽  
Miguel Ángel Díaz-Rodríguez
Keyword(s):  
Control System ◽  
Kinematic Model ◽  
Lexicographic Order ◽  
Inverse Kinematic ◽  
Robotic Systems ◽  
Walking Robots ◽  
Groebner Basis ◽  
Open Chain ◽  
Monomial Order ◽  
Kinematic Models

One of the most important elements of a robot’s control system is its Inverse Kinematic Model (IKM), which calculates the position and velocity references required by the robot’s actuators to follow a trajectory. The methods that are commonly used to synthesize the IKM of open-chain robotic systems strongly depend on the geometry of the analyzed robot. Those methods are not systematic procedures that could be applied equally in all possible cases. This project presents the development of a systematic procedure to synthesize the IKM of non-redundant open-chain robotic systems using Groebner Basis theory, which does not depend on the geometry of the robot’s structure. The inputs to the developed procedure are the robot’s Denavit–Hartenberg parameters, while the output is the IKM, ready to be used in the robot’s control system or in a simulation of its behavior. The Groebner Basis calculation is done in a two-step process, first computing a basis with Faugère’s F4 algorithm and a grevlex monomial order, and later changing the basis with the FGLM algorithm to the desired lexicographic order. This procedure’s performance was proved calculating the IKM of a PUMA manipulator and a walking hexapod robot. The errors in the computed references of both IKMs were absolutely negligible in their corresponding workspaces, and their computation times were comparable to those required by the kinematic models calculated by traditional methods. The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots.

scholarly journals Analysis of Open Architecture 6R Robot Forward and Inverse Kinematics Adaptive to Structural Variations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Chong Wang ◽  
Dongxue Liu ◽  
Qun Sun ◽  
Tong Wang
Keyword(s):  
Inverse Kinematics ◽  
Industrial Robot ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Open Architecture ◽  
Model Parameters ◽  
Structural Variations ◽  
Robot Controller ◽  
Kinematic Models ◽  
Kinematic Studies

This paper presents a kinematic analysis for an open architecture 6R robot controller, which is designed to control robots made by domestic manufactures with structural variations. Usually, robot kinematic studies are often introduced for specific robot types, and therefore, difficult to apply the kinematic model from one to another robot. This study incorporates most of the robot structural variations in one model so that it is convenient to switch robot types by modifying model parameters. By combining an adequate set of parameters, the kinematic models, especially the inverse kinematics, are derived. The kinematic models are proved to be suitable for many classic industrial robot types, such as Puma560, ABB IRB120/1600, KAWASAKI RS003N/RS010N, FANUC M6iB/M10iA, and therefore be applicable to those with similar structures. The analysis and derivation of the forward and inverse kinematic models are presented, and the results are proven to be accurate.

scholarly journals Kinematics of Serial Manipulators

2020 ◽  
Author(s):  
Ivan Virgala ◽  
Michal Kelemen ◽  
Erik Prada
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Body Motion ◽  
Robot Kinematics ◽  
Kinematic Modeling ◽  
Open Chain ◽  
Serial Manipulators ◽  
Serial Robot

This book chapter deals with kinematic modeling of serial robot manipulators (open-chain multibody systems) with focus on forward as well as inverse kinematic model. At first, the chapter describes basic important definitions in the area of manipulators kinematics. Subsequently, the rigid body motion is presented and basic mathematical apparatus is introduced. Based on rigid body conventions, the forward kinematic model is established including one of the most used approaches in robot kinematics, namely the Denavit-Hartenberg convention. The last section of the chapter analyzes inverse kinematic modeling including analytical, geometrical, and numerical solutions. The chapter offers several examples of serial manipulators with its mathematical solution.

Geometric and Kinematic Modelling of a New Parallel Kinematic Machine Tool: The Tripteor X7 Designed by PCI

2010 ◽  
Vol 112 ◽  
pp. 159-169 ◽  
Author(s):  
Sylvain Pateloup ◽  
Helene Chanal ◽  
Emmanuel Duc
Keyword(s):  
Machine Tools ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Parallel Kinematic Machine ◽  
Joint Coordinates ◽  
Kinematic Behaviour ◽  
Kinematic Modelling ◽  
Kinematic Models ◽  
Automotive Part ◽  
Parallel Kinematic

Today, Parallel Kinematic Machine tools (PKMs) appear in automotive and aeronautic industry. These machines propose high kinematic performances allowing a higher productivity than Serial Kinematic Machine tools (SKMs). However, this kinematic behaviour is anisotropic and a particular study is then necessary to locate the part in a workspace where the kinematic performances are well exploited. The study presented in this article deals with the determination of geometric and kinematic models of a new PKM : the Tripteor X7 designed by PCI. The inverse kinematic model expresses the joint coordinates with regard to the cartesian coordinates. The kinematic model which takes into account velocity, acceleration and jerk limits axis, allows computing the displacement time between two tool positions. Finally, this model can be used to determine the workspace where Non Effective cutting Times (TNE) are minimum. The method is applied for an automotive part machining

scholarly journals Kinematic Modeling of a Combined System of Multiple Mecanum-Wheeled Robots with Velocity Compensation

Sensors ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 75
Author(s):  
Yunwang Li ◽  
Shirong Ge ◽  
Sumei Dai ◽  
Lala Zhao ◽  
Xucong Yan ◽  
...  
Keyword(s):  
Large Scale ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Kinematic Modeling ◽  
Combined System ◽  
Wheeled Mobile Robots ◽  
Physical Prototype ◽  
Kinematic Models ◽  
Simulated Motion ◽  
Multiple Robot

In industry, combination configurations composed of multiple Mecanum-wheeled mobile robots are adopted to transport large-scale objects. In this paper, a kinematic model with velocity compensation of the combined mobile system is created, aimed to provide a theoretical kinematic basis for accurate motion control. Motion simulations of a single four-Mecanum-wheeled virtual robot prototype on RecurDyn and motion tests of a robot physical prototype are carried out, and the motions of a variety of combined mobile configurations are also simulated. Motion simulation and test results prove that the kinematic models of single- and multiple-robot combination systems are correct, and the inverse kinematic correction model with velocity compensation matrix is feasible. Through simulations or experiments, the velocity compensation coefficients of the robots can be measured and the velocity compensation matrix can be created. This modified inverse kinematic model can effectively reduce the errors of robot motion caused by wheel slippage and improve the motion accuracy of the mobile robot system.

GENERALIZED RECONFIGURABLE 6 - JOINT ROBOT MODELING

2006 ◽  
Vol 30 (4) ◽  
pp. 533-565 ◽  
Author(s):  
A. M. Djuric ◽  
W. H. ElMaraghy
Keyword(s):  
Manufacturing Systems ◽  
Kinematic Model ◽  
Geometric Approach ◽  
Inverse Kinematic ◽  
Robotic Systems ◽  
Reconfigurable Manufacturing ◽  
Unified Approach ◽  
Inverse Kinematic Problem ◽  
Computer Controlled ◽  
Robot Modeling

Automated model generation and solution for motion planning and re-planning of robotic systems will play an important role in the future reconfigurable manufacturing systems. Solving the inverse kinematic problem has always been the key issue for computer-controlled robots. Considering the large amount of similarities that exist among the industrial 6R robotic systems, this work classifies them into two main types (Puma-type and Fanuc-type) and then provides a unified geometric solution based on a unified kinematic structure called Generic Puma-Fanuc (GPF) model. A widespread study of different kinematic groups originating from eleven robot manufacturers made it possible to develop the GPF model that can be reconfigured according to the D-H rules (Denavit, and Hartenberg1). A graphical interface by which the robot kinematic model is represented and the D-H parameters are auto-generated for use in solving the inverse kinematic problem. A generic solution module called Unified Kinematic Modeler and Solver (UKMS) implements the geometric approach for solving the inverse kinematic problem. The outcomes are then employed for robot control. Numerical examples are presented for exploring the solution capabilities of our unified approach.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

A Novel Vertical Lift Machine and its Precise Pose Control

2014 ◽  
Vol 989-994 ◽  
pp. 3105-3109
Author(s):  
Xiao Bo Liu ◽  
Xiao Feng Wei ◽  
Xiao Dong Yuan ◽  
Wei Ni
Keyword(s):  
Control System ◽  
Theoretical Analysis ◽  
Control Method ◽  
High Accuracy ◽  
Inverse Kinematic ◽  
Design Model ◽  
Pose Control ◽  
Vertical Lift ◽  
Position And Orientation ◽  
Control Principle

This paper deals with the design and theoretical analysis on a novel vertical lift machine which can vertically lift above 700 kg load up to 3.2 meters above the floor and located the load with high accuracy of position and orientation. Firstly the design model based on the installment demands of line-replaceable units (LRUs) is constructed. Then theoretical analysis including the number of degree of freedom of the lift machine, the inverse kinematic, the control principle, the lift platform pose error and the precise pose control method are conducted in the article. The validity of the design model and the effectiveness of the precise pose control system are confirmed by experiments using a prototype lift machine.

A Sensitivity Analysis Based Method for Robot Calibration

1992 ◽  
Author(s):  
S. Kaizerman ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
G. Zak
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

Abstract A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two degree of freedom revolute-joint planar manipulator.

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