Optimal conditions for inverse kinematics of a robot manipulator with redundancy

Robotica ◽  
1995 ◽  
Vol 13 (1) ◽  
pp. 95-101 ◽  
Author(s):  
Dong Kwon Cho ◽  
Byoung Wook Choi ◽  
Myung Jin Chung
Keyword(s):  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Inverse Kinematic ◽  
Performance Measure ◽  
Configuration Change ◽  
Necessary Conditions For Optimality ◽  
Kinematic Solution

SummaryThe algorithms of inverse kinematics based on optimality constraints have some problems because those are based only on necessary conditions for optimality. One of the problems is a switching problem, i.e., an undesirable configuration change from a maximum value of a performance measure to a minimum value may occur and cause an inverse kinematic solution to be unstable. In this paper, we derive sufficient conditions for the optimal solution of the kinematic control of a redundant manipulator. In particular, we obtain the explicit forms of the switching condition for the optimality constraintsbased methods. We also show that the configuration at which switching occurs is equivalent to an algorithmic singularity in the extended Jacobian method. Through a numerical example of a cyclic task, we show the problems of the optimality constraints-based methods. To obtain good configurations without switching and kinematical singularities, we propose a simple algorithm of inverse kinematics.

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 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.

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.

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 unified approach to the inverse kinematic solution for a redundant manipulator

Robotica ◽  
1993 ◽  
Vol 11 (2) ◽  
pp. 159-165 ◽  
Author(s):  
J. H. Won ◽  
B. W. Choi ◽  
M. J. Chung
Keyword(s):  
Differential Equations ◽  
Optimal Solution ◽  
Inverse Kinematic ◽  
Necessary Condition ◽  
Redundant Manipulator ◽  
Performance Indices ◽  
Unified Approach ◽  
Joint Velocity ◽  
Velocity Level ◽  
Kinematic Solution

SUMMARYFor a kinematically redundant manipulator, some performance indices can be optimized while carrying out a given task. So far, the redundancy resolution has been solved at the joint angle level, the joint velocity level, or joint acceleration level depending on the performance indices. According to the resolution level, the solution is represented by high-order differential equations or superfluous number of equations. We propose a unified approach to the inverse kinematic solution which optimizes it at the joint velocity level regardless of the types of the performance indices. A unified approach to obtain an optimal joint velocity is derived by using the necessary condition for optimality so that the proposed method provides an optimal solution for any performance indices and tasks. The optimal solution becomes a set of the minimum number of first-order differential equations which requires a minimum search dimension.To show the validity of the approach, it is applied to a three-link planar manipulator for various types of performance indices.

scholarly journals Inverse kinematic analysis of 4 DOF pick and place arm robot manipulator using fuzzy logic controller

2020 ◽  
Vol 10 (2) ◽  
pp. 1376
Author(s):  
Tresna Dewi ◽  
Siti Nurmaini ◽  
Pola Risma ◽  
Yurni Oktarina ◽  
Muhammad Roriz
Keyword(s):  
Fuzzy Logic ◽  
Inverse Kinematics ◽  
Fuzzy Logic Controller ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Experimental Results ◽  
Position Errors ◽  
Motion System ◽  
Pick And Place ◽  
The Right

The arm robot manipulator is suitable for substituting humans working in tomato plantation to ensure tomatoes are handled efficiently. The best design for this robot is four links with robust flexibility in x, y, and z-coordinates axis. Inverse kinematics and fuzzy logic controller (FLC) application are for precise and smooth motion. Inverse kinematics designs the most efficient position and motion of the arm robot by adjusting mechanical parameters. The FLC utilizes data input from the sensors to set the right position and motion of the end-effector. The predicted parameters are compared with experimental results to show the effectiveness of the proposed design and method. The position errors (in x, y, and z-axis) are 0.1%, 0.1%, and 0.04%. The rotation errors of each robot links (θ1, θ2, and θ3) are 0%, 0.7% and 0.3%. The FLC provides the suitable angle of the servo motor (θ4) responsible in gripper motion, and the experimental results correspond to FLC’s rules-based as the input to the gripper motion system. This setup is essential to avoid excessive force or miss-placed position that can damage tomatoes. The arm robot manipulator discussed in this study is a pick and place robot to move the harvested tomatoes to a packing system.

Inverse Kinematics Solution for a 6R Special Configuration Manipulators Based on Screw Theory

2011 ◽  
Vol 216 ◽  
pp. 250-253
Author(s):  
Yue Sheng Tan ◽  
Peng Le Cheng ◽  
Ai Ping Xiao
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Screw Theory ◽  
Inverse Kinematic ◽  
Special Configuration ◽  
Kinematic Solution

Three basic sub-problems of screw theory are acceptable for some particular configuration manipulators’ inverse kinematics, which can not solve the inverse kinematics of all configuration manipulators. This paper introduces two extra extended sub-problems, through which all inverse kinematic solutions for 6-R manipulators having closed-form inverse kinematics can be gained. The inverse kinematic solution for a new particular configuration manipulator is presented.

Forward and Inverse Kinematic Solution of the Variable Geometry Truss Robot Based on an N-Celled Tetrahedron-Tetrahedron Truss

1990 ◽  
Vol 112 (1) ◽  
pp. 16-22 ◽  
Author(s):  
S. Jain ◽  
S. N. Kramer
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Variable Geometry ◽  
Load Carrying ◽  
Forward And Inverse Kinematics ◽  
Actuation Scheme ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss ◽  
Exceptional Stability ◽  
Kinematic Solution

The Tetrahedron-Tetrahedron truss (or TT truss for short) has exceptional stability, stiffness, and load-carrying capabilities. Because of this fact, the TT truss is well suited for use as a variable geometry truss manipulator (VGTM) by appropriately choosing certain links whose variable lengths can be controlled. Since the TT truss is composed of n-cells, its applications include the retrieval of equipment, bridges over and around obstacles, and applications which utilize collapsible programmable structures capable of relatively large displacements. In this paper an actuation scheme and the general solution to the forward and inverse kinematics problems for an n-celled TT truss are presented. Numerical examples are also presented.

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