An Analytical Inverse Kinematics Solution Method for Robotic Manipulators

2000 ◽  
Author(s):  
Tuna Balkan ◽  
M. Kemal Özgören ◽  
M. A. Sahir Arikan ◽  
H. Murat Baykurt
Keyword(s):  
Inverse Kinematics ◽  
Industrial Robot ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Industrial Robots ◽  
Solution Approach ◽  
Joint Variable ◽  
Forward Kinematic ◽  
Six Degree Of Freedom ◽  
Kinematic Solution

Abstract In this study, an inverse kinematic solution approach applicable to six degree-of-freedom industrial robotic manipulators is introduced. The approach is based on a previously introduced kinematic classification of industrial robotic manipulators by Balkan et al. (1999), and depending on the kinematic structure, either an analytical or a semi-analytical inverse kinematic solution is obtained. The semi-analytical method is named as the parametrized joint variable (PJV) method. Compact forward kinematic equations obtained by utilizing the properties of exponential rotation matrices. In the inverse kinematic solutions of the industrial robots surveyed in the previous study, most of the simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a numerical solution of a single univariate equation. In these solutions, the singularities and the multiple configurations of the manipulators can be determined easily. By the method employed in this study, the kinematic and inverse kinematic analysis of any manipulator or designed-to-be manipulator can be performed and using the solutions obtained, the inverse kinematics can also be computerized by means of short and fast algorithms. As an example for the demonstration of the applicability of the presented method to manipulators with closed-chains, ABB IRB2000 industrial robot is selected which has a four-bar mechanism for the actuation of the third link, and its compact forward kinematic equations are given as well as the inverse kinematic solution.

A Method of Inverse Kinematics Solution for a Class of Robotic Manipulators

1997 ◽  
Author(s):  
Tuna Balkan ◽  
M. Kemal Özgören ◽  
M. A. Sahir Arikan ◽  
H. Murat Baykurt
Keyword(s):  
Nonlinear Equation ◽  
Analytical Method ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Industrial Robot ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Singular Configurations ◽  
Inverse Kinematics Problem ◽  
Joint Variable

Abstract A semi-analytical method and a computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in wrist point equations. For this case, it becomes possible to express all the joint variables in terms of a joint variable, and this reduces the inverse kinematics problem to solving a nonlinear equation in terms of that joint variable. The solution can be obtained by iterative methods and the remaining joint variables can easily be computed by using the solved joint variable. Since the method is manipulator dependent, the equations will be different for kinematically different classes of manipulators, and should be derived analytically. A significant benefit of the method is that, the singular configurations and the multiple solutions indicated by sign ambiguities can be determined while deriving the inverse kinematic expressions. The developed method is applied to a six-revolute-joint industrial robot, FANUC Arc Mate Sr.

Inverse kinematic solutions of 6-D.O.F. biopolymer segments

Robotica ◽  
2016 ◽  
Vol 34 (8) ◽  
pp. 1734-1753 ◽  
Author(s):  
Jin Seob Kim ◽  
Gregory S. Chirikjian
Keyword(s):  
Jacobian Matrix ◽  
Heuristic Method ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Robot Kinematics ◽  
Joint Angles ◽  
Elimination Method ◽  
Six Degree Of Freedom ◽  
Theoretic Description ◽  
Kinematic Solution

SUMMARYWe present two methods to find all the possible conformations of short six degree-of-freedom segments of biopolymers which satisfy end constraints in position and orientation. One of our methods is motivated by inverse kinematic solution techniques which have been developed for “general” 6R serial robotic manipulators. However, conventional robot kinematics methods are not directly applicable to the geometry of polymers, which can be treated as a degenerate case where all the “link lengths” are zero. Here, we propose a method which extends the elimination method of Kohli and Osvatic. This method can be applied directly to the geometry of biopolymers. We also propose a heuristic method based on a Lie-group-theoretic description. In this method, we utilize inverse iterations of the Jacobian matrix to obtain all conformations which satisfy end constraints. This can be easily implemented for both the general 6R manipulator and polymers. Although the extended elimination method is computationally faster than the Jacobian method, in cases where some of the joint angles are 180° (i.e., where the elimination method fails), we combine these two methods effectively to obtain the full set of inverse kinematic solutions. We demonstrate our approach with several numerical examples.

Inverse Kinematic Solution of Robot Manipulators Using Interval Analysis

1998 ◽  
Vol 120 (1) ◽  
pp. 147-150 ◽  
Author(s):  
R. S. Rao ◽  
A. Asaithambi ◽  
S. K. Agrawal
Keyword(s):  
Computational Complexity ◽  
Numerical Algorithm ◽  
Interval Analysis ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Real Numbers ◽  
Computational Mathematics ◽  
All Solutions ◽  
Inverse Kinematics Problem ◽  
Kinematic Solution

Interval analysis is a growing branch of computational mathematics where operations are carried out on intervals instead of real numbers. This paper presents the first application of this method to robotic mechanisms for the solution of inverse kinematics. As shown in this paper, it is possible to potentially compute all solutions of the inverse kinematics problem using this method. This paper describes the preliminaries of interval analysis, the numerical algorithm, the computational complexity, and illustrations with examples.

scholarly journals Inverse kinematic solution of 6R robot manipulators based on screw theory and the Paden–Kahan subproblem

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881829 ◽  
Author(s):  
Rongbo Zhao ◽  
Zhiping Shi ◽  
Yong Guan ◽  
Zhenzhou Shao ◽  
Qianying Zhang ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Matrix Theory ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Kinematics Modeling ◽  
High Level ◽  
Kinematic Solution

The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.

Inverse Kinematic Simulation of Industrial Robotic Manipulators Using RecurDyn and Matlab with Experiment Verification

2020 ◽  
Vol 900 ◽  
pp. 35-43
Author(s):  
Yunn Lin Hwang ◽  
Jung Kuang Cheng ◽  
Thanh Dat Pham
Keyword(s):  
Computer Science ◽  
Dynamic Simulation ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Industrial Robots ◽  
Dynamic Study ◽  
Kinematic Parameters ◽  
Kinematic Simulation ◽  
Experiment Verification ◽  
Cae Simulation

The simulation and application of industrial robots has developed very quickly in recent decades. Along with the development of computer science, a lot of softwares to perform dynamic simulation have been created. The results of simulation can be used for layout evaluation, kinematic, dynamic study, off-line programming to avoid obstacle and for design mechanical structure of robots. A co-simulation of 2R industrial robots have been performed by Recurdyn and Matlab. The input parameters are executed under Matlab, and then exported to Recurdyn environment. Kinematic parameters will be executed by RecurDyn then exported to Matlab. The main tasks of this paper are performing 2R robotic manipulator kinematic simulation in two postures with the same trajectory and the same time. Thus, the result of simulation can be compared with theories. Finally, a real 2R robot model was used to verify the trajectory with CAE simulation.

Automated inverse-kinematics for robot off-line programming

Robotica ◽  
1994 ◽  
Vol 12 (1) ◽  
pp. 45-53 ◽  
Author(s):  
W.Edward Red ◽  
Shao-Wei Gongt
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Broad Class ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Lower Degree ◽  
Serial Robots ◽  
Automated Methods ◽  
Kinematic Solution

Automated methods are developed to classify a robot's kinematic type and select an appropriate library inverse-kinematic solution based on this classification. These methods automatically generate DenavitHartenberg joint frame parameters, given any frame representation that can mathematically be represented as a homogeneous transformation.To reduce the number of closed-form inverse-kinematics solutions required for a broad class of serial robots, additional methods account for differences in robot zero state, base frame location, and joint polarity. Further generalization results from using joint frame decoupling to map lower degree-of-freedom robots into the inverse-kinematics solutions of higher degree-offreedom 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 Solving Approach of Inverse Kinematics for Manipulators Based on Improved Adaptive Niche Genetic Algorithm

2019 ◽  
Vol 37 (3) ◽  
pp. 488-495
Author(s):  
Huizhen Yang ◽  
Xiyang Liu
Keyword(s):  
Genetic Algorithm ◽  
Inverse Kinematics ◽  
Fitness Function ◽  
Optimal Solution ◽  
Solution Approach ◽  
The Poor ◽  
Pose Control ◽  
Simulation Results ◽  
Six Degree Of Freedom ◽  
Speed And Accuracy

Solving the inverse kinematics for a manipulator is of great importance to the manipulator's pose control and trajectory planning. Aiming at the poor generality and difficulty of finding an optimal solution from the multiple inverse kinematics solutions, a novel solution approach based on the modified adaptive niche genetic algorithm is proposed in this study. The principle of 'most suppleness' is integrated into the fitness function such that the only optimal solution can be found; The clustering is introduced into the approach for enhancing the generality and the genetic algorithm is improved for increasing the convergence speed and accuracy. Simulation results based on a six degree of freedom manipulator show that the proposed approach is effective and high precision, and can find the optimal solution.

A Semiparametric Model-Based Friction Compensation Method for Multi-Joint Industrial Robot

2021 ◽  
Author(s):  
Miao He ◽  
Xiaomin Wu ◽  
Guifang Shao ◽  
Yuhua Wen ◽  
Tundong Liu
Keyword(s):  
Industrial Robot ◽  
Lyapunov Theory ◽  
Industrial Robots ◽  
Learning Ability ◽  
Robot System ◽  
Joint Friction ◽  
Tracking Tasks ◽  
Physical Information ◽  
The Stability ◽  
Six Degree Of Freedom

Abstract Industrial robots have received enormous attention due to their widespread uses in modern manufacturing. However, due to the frictional discontinuous and other unknown dynamics in robotic system, existing researches are limited to simulation and single- or double-joint robot. In this paper, we introduce a semiparametric controller combined by a radial basis function neural network (RBFNN) and complete physical model considering joint friction. First, to extend the NN controller to real-world problems, the continuously differentiable friction (CDF) model is adopted to bring physical information into the learning process. Then, RBFNN is employed to approximate the model error and other unmolded dynamics, and the parameters of CDF model are updated online according to its learning ability. The stability of the robot system can be guaranteed by the Lyapunov theory. The primary parameters of CDF model are determined by the identification experiment and subsequently iteratively updated by the NN. Real-time tracking tasks are performed on a six degree of freedom (DoF) manipulator to follow the desired trajectory. Experimental results demonstrate the effectiveness and superiority of the proposed controller, especially at low speed.

Kinematic analysis of an augmented 3-RPSP tripod mechanism with six degrees of freedom for bone reduction surgery

2021 ◽  
pp. 095440622110480
Author(s):  
Sinh Nguyen Phu ◽  
Terence Essomba
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Femoral Shaft ◽  
Polynomial Equation ◽  
Velocity Model ◽  
Inverse Kinematic ◽  
Reachable Workspace ◽  
Bone Fragments ◽  
Forward Kinematic ◽  
Six Degree Of Freedom

Robotic-assisted bone reduction surgery consists in using robots to reconnect patients’ bone fragments prior to fracture healing. The goal of this study is to propose a novel augmented 3-RPSP tripod mechanism with six degree of freedom for longitudinal bone reduction surgery. Its inverse kinematic model is studied and its forward kinematic model is solved by establishing the constraint equations, applying Sylvester’s dialytic method and finding the solutions of the resulting polynomial equation. The velocity model is calculated and its Jacobian matrix is used to identify its singular configurations. In comparison to the Stewart–Gough platform that is a typical mechanism used in this application, the proposed mechanism offers larger reachable workspace which is an important aspect in the femoral shaft bone reduction. A Physiguide and Msc Adams software are used to carry out a simulation of a real femur fracture reduction using the proposed mechanism to validate its suitability. A robotic prototype has been designed and manufactured in order to test its capability of performing diaphyseal femur reduction surgery.

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