Complex Robotic Inverse Kinematic Solutions

1993 ◽  
Vol 115 (3) ◽  
pp. 509-514 ◽  
Author(s):  
E. D. Pohl ◽  
H. Lipkin
Keyword(s):  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Complex Numbers ◽  
Error Minimization ◽  
Important Criterion ◽  
Real Numbers ◽  
End Effector ◽  
Industrial Manipulators ◽  
Complex Joint ◽  
Kinematic Solution

A new method exploiting complex numbers in the inverse kinematic solution of serial robotic manipulators is presented. If a prescribed end effector location is outside of the manipulator workspace, complex joint values result. While they cannot be implemented physically, they may be mapped to real numbers. The result approximates the prescribed location. For many industrial manipulators, mapped solutions may be explained using spherical and planar dyads. An important criterion characterizes error minimization properties, and is illustrated for a 3R regional robot.

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.

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.

Polynomial Inverse Kinematic Solution of the Jaco Robot

2014 ◽  
Author(s):  
Clément Gosselin ◽  
Hanwei Liu
Keyword(s):  
Polynomial Solution ◽  
Solution Process ◽  
Inverse Kinematic ◽  
Degree Polynomial ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Numerical Examples ◽  
Position And Orientation ◽  
Kinematic Solution

This article presents a polynomial solution to the inverse kinematic problem of the 6R serial Jaco robot. The solution is specifically tailored to the Jaco robot, which is not wrist-partitioned. The derivation of the univariate 16-degree polynomial is presented, starting from the direct kinematic equations providing the position and orientation of the end-effector as a function of the joint variables. Upon calculation of the roots of the polynomial, all joint variables are obtained by backsubstitution, leading to a unique set of joint variables for each of the roots. Also, it is shown that for certain configurations, the 16-degree polynomial contains only terms of even powers while all terms are not zero in general. Two numerical examples are given to demonstrate the effectiveness of the solution process.

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.

The Characteristic Point and the Characteristic Length of Robotic Manipulators

1992 ◽  
Author(s):  
Murat Tandirci ◽  
Jorge Angeles ◽  
Farzam Ranjbaran
Keyword(s):  
Condition Number ◽  
Jacobian Matrix ◽  
Characteristic Length ◽  
Characteristic Point ◽  
Robotic Manipulators ◽  
End Effector ◽  
Industrial Manipulators

Abstract The characteristic point of a serial manipulator is defined here as a point on the end-effector, at which the condition number of the Jacobian matrix is minimized. However, when evaluating the condition number of the Jacobian matrix, dimensional inhomogeneities arise, that render the condition number physically meaningless. As a means to cope with this problem, the entries of the Jacobian that have units of length are divided by a characteristic length L that is chosen so as to minimize the condition number of the dimensionless Jacobian matrix thus resulting. Finally, the values of the joint variables minimizing the condition number of the dimensionless Jacobian lead to a naturally defined home configuration of the manipulator. The concepts introduced here are illustrated with a few examples involving industrial manipulators.

Inverse Kinematic Control Algorithms With a Reduced Coriolis Component for Use in Motion Simulators

1995 ◽  
Vol 117 (4) ◽  
pp. 570-577 ◽  
Author(s):  
D. W. Repperger
Keyword(s):  
Human Subjects ◽  
Inverse Kinematic ◽  
Moving Frame ◽  
Coordinate Frame ◽  
Linear Quadratic ◽  
End Effector ◽  
Quadratic Optimization Problem ◽  
Motion Simulator ◽  
Simple Feedback ◽  
Kinematic Solution

A motion simulator is studied within the framework of a multilink robotic manipulator and a class of inverse kinematic algorithms are investigated. Human subjects, for this motion simulator, sit at the end effector and are subjected to all relative motions of the respective links. From the perspective of the subject, one undesired artifact of this simulation occurs when Coriolis accelerations are induced at the end effector as a consequence of a coordinate frame moving relative to another moving frame. This paper adapts the inverse kinematic solution to those which have a minimum Coriolis component and can be used to control the motion simulator. A simple feedback control law is derived which, it turns out, has an additional interpretation as the solution of a related linear quadratic optimization problem.

Inverse Kinematic Solution and Dynamic Model to 3PTT Parallel Mechanism

2014 ◽  
Vol 945-949 ◽  
pp. 1421-1425
Author(s):  
Xiu Qing Hao
Keyword(s):  
Dynamic Model ◽  
Dynamic Simulation ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Euler Method ◽  
Research Subject ◽  
Adams Software ◽  
Inverse Kinematic Analysis ◽  
Simulation Results ◽  
Kinematic Solution

Take typical parallel mechanism 3PTT as research subject, its inverse kinematic analysis solution was gotten. Dynamic model of the mechanism was established by Newton-Euler method, and the force and torque equations were derived. Dynamic simulation of 3PTT parallel mechanism was done by using ADAMS software, and simulation results have verified the correctness of the theoretical conclusions.

Time suboptimal control of industrial manipulators along specified paths while keeping an end-effector orientation unchanged

Robotica ◽  
2003 ◽  
Vol 21 (2) ◽  
pp. 153-161 ◽  
Author(s):  
S. Kilicaslan ◽  
Y. Ercan
Keyword(s):  
Suboptimal Control ◽  
Time Step ◽  
End Effector ◽  
Industrial Manipulator ◽  
Industrial Manipulators ◽  
Angular Velocities ◽  
System Equations ◽  
Six Degree Of Freedom ◽  
Time Suboptimal Control

A method for the time suboptimal control of an industrial manipulator that moves along a specified path while keeping its end-effector orientation unchanged is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in a case study to verify the method developed.

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