scholarly journals Regularization of the Spatial Inverse Positioning Problem of Revolute Joint Manipulators

2017 ◽  
Vol 61 (3) ◽  
pp. 279
Author(s):  
Dániel András Drexler
Keyword(s):  
Inverse Kinematics ◽  
Closed Loop ◽  
Singular Values ◽  
Singular Configurations ◽  
Revolute Joints ◽  
Singular Direction ◽  
Inverse Kinematics Problem ◽  
Singular Configuration ◽  
Damped Least Squares ◽  
Kinematic Singularities

Inverse kinematics is a central problem in robotics, and its solution is burdened with kinematic singularities, i.e. the task Jacobian of the problem is singular. A subproblem of the general inverse kinematics problem, the inverse positioning problem is considered for spatial manipulators consisting of revolute joints, and a regularization method is proposed that results in a regular task Jacobian in singular configurations as well, provided that the manipulator’s geometry makes movement in singular directions possible. The conditions of regularizability are investigated, and bounds on the singular values of the regularized task Jacobian are given that can be used to create stable closed-loop inverse kinematics algorithms. The proposed method is demonstrated on the inverse positioning problem of an elbow manipulator and compared to the Damped Least Squares and the Levenberg-Marquardt methods, and it is shown that only the proposed method can leave the singular configuration in the singular direction.

Dynamics of redundant robots – inverse solutions

Robotica ◽  
1986 ◽  
Vol 4 (4) ◽  
pp. 263-267 ◽  
Author(s):  
Ronald L. Huston ◽  
Timothy P. King
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Solution Algorithm ◽  
Redundant Robot ◽  
Redundant Robots ◽  
Revolute Joints ◽  
Inverse Kinematics Problem ◽  
Inverse Solutions ◽  
Natural Dynamics ◽  
Least Energy

SUMMARYThe dynamics of “simple, redundant robots” are developed. A “redundant” robot is a robot whose degrees of freedom are greater than those needed to perform a given kinetmatic task. A “simple” robot is a robot with all joints being revolute joints with axes perpendicular or parallel to the arm segments. A general formulation, and a solution algorithm, for the “inverse kinematics problem” for such systems, is presented. The solution is obtained using orthogonal complement arrays which in turn are obtained from a “zero-eigenvalues” algorithm. The paper concludes with an assertion that this solution, called the “natural dynamics solution,” is optimal in that it requires the least energy to drive the robot.

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.

Kinematic Singularities of Free-Floating Open-Chain Planar Manipulators

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
J. Rambhaskar
Keyword(s):  
Polynomial Equations ◽  
Joint Angles ◽  
Systematic Method ◽  
Open Chain ◽  
Singular Configurations ◽  
Revolute Joints ◽  
Planar Manipulators ◽  
Fixed Base ◽  
External Forces ◽  
Kinematic Singularities

Abstract This paper deals with Jacobian singularities of free-floating open-chain planar manipulators. The problem, in essence, is to find the joint angles where the Jacobian mapping between the end-effector rates and the joint rates is singular. In the absence of external forces and couples, for free-floating manipulators, the linear and angular momentum are conserved. This makes the singular configurations of free-floating manipulators different from structurally similar fixed-base manipulators. In order to illustrate this idea, we present a systematic method to obtain the singular solutions of a free-floating series-chain planar manipulator with revolute joints. We show that the singular configurations are solutions of simultaneous polynomial equations in the half-tangent of the joint variables. From the structure of these polynomial equations, we estimate the upper bound on the number of singularities of free-floating planar manipulators and compare these with analogous results for structurally similar fixed-base manipulators.

Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

2003 ◽  
Author(s):  
Hee-Byoung Choi ◽  
Atsushi Konno ◽  
Masaru Uchiyama
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Loop Structure ◽  
Singular Configurations ◽  
Planning And Control ◽  
Kinematic Singularities ◽  
And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

scholarly journals A Parallel Manipulator With Only Translational Degrees of Freedom

1996 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Richard Stamper
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Translational Motion ◽  
Forward Kinematics ◽  
Closed Form Solutions ◽  
Real Solutions ◽  
Revolute Joints ◽  
Inverse Kinematics Problem ◽  
Three Degree Of Freedom

Abstract This paper presents a novel three degree of freedom parallel manipulator that employs only revolute joints and constrains the manipulator output to translational motion. Closed-form solutions are developed for both the inverse and forward kinematics. It is shown that the inverse kinematics problem has up to four real solutions, and the forward kinematics problem has up to 16 real solutions.

Singularity-Robust Inverse Kinematics Using Lagrange Multiplier for Redundant Manipulators

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Youngjin Choi
Keyword(s):  
Lagrange Multiplier ◽  
Inverse Kinematics ◽  
Equality Constraint ◽  
Primary Task ◽  
Redundant Manipulator ◽  
Natural Choice ◽  
Inverse Kinematics Problem ◽  
Ill Conditioning ◽  
Singular Configuration ◽  
Dual Arm

In this paper, a singularity-robust inverse kinematics is newly suggested by using a Lagrange multiplier for redundant manipulator systems. Two tasks are considered with priority orders under the assumption that a primary task has no singularity. First, an inverse kinematics problem is formulated to be an optimization one subject to an equality constraint, in other words, to be a minimization problem of secondary task error subject to an equality constraint for primary task execution. Second, in the procedure of minimization for a given objective function, a new inverse kinematics algorithm is derived. Third, since nonzero Lagrange multiplier values appear in the neighborhood of a singular configuration of a robotic manipulator, we choose them as a natural choice of the dampening factor to alleviate the ill-conditioning of matrix inversion, ultimately for singularity-robust inverse kinematics. Finally, the effectiveness of the suggested singularity-robust inverse kinematics is shown through a numerical simulation about deburring and conveyance tasks of a dual arm manipulator system.

Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory

2003 ◽  
Vol 125 (3) ◽  
pp. 573-581 ◽  
Author(s):  
Ilian A. Bonev ◽  
Dimiter Zlatanov ◽  
Cle´ment M. Gosselin
Keyword(s):  
Screw Theory ◽  
Singularity Analysis ◽  
Point Of View ◽  
Mobile Platform ◽  
Parallel Mechanisms ◽  
Singular Configurations ◽  
Revolute Joints ◽  
Singular Configuration

This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified.

Singularity analysis and avoidance of a planar parallel mechanism with kinematic redundancy under a fixed orientation

2020 ◽  
pp. 095440622097671
Author(s):  
Haibo Qu ◽  
Lanqing Hu ◽  
Sheng Guo
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Singularity Analysis ◽  
Kinematic Redundancy ◽  
Comparison Analysis ◽  
Singularity Avoidance ◽  
Singular Configurations ◽  
Fixed Orientation ◽  
Free Transition ◽  
Singular Configuration

In this paper, the singularity of a planar mechanism with kinematic redundancy is studied. First, the architecture of the mechanism and the concept schematic diagram for singularity avoidance are stated. Next, inverse kinematics model of the planar parallel mechanism with kinematic redundancy is established. For determining the unique inverse solution of the mechanism under certain initial installation configuration, a comparison analysis based on the strategy tree and the virtual prototype is performed. Then, based on the obtained Jacobian matrices and the singular condition, the workspace-singularity map and two singular configurations of the mechanism are drawn. Finally, with the obtained workspace-singularity map, a singularity-free transition layer and an aisle can be found to perform to singularity avoidance, even if the initial designed trajectory passing through the second kind of singularity. Three tasks are carried out to illustrate that the workspace boundary and singular configuration can be changed by adjusting the kinematic redundant actuated parameter.

Inverse kinematics of six-degree of freedom “general” and “special” manipulators using symbolic computation

Robotica ◽  
1994 ◽  
Vol 12 (5) ◽  
pp. 421-430 ◽  
Author(s):  
C. Mavroidis ◽  
F. B. Ouezdou ◽  
P. Bidaud
Keyword(s):  
Trivial Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Six Degrees Of Freedom ◽  
Industrial Manipulator ◽  
Revolute Joints ◽  
Closure Equation ◽  
Inverse Kinematics Problem ◽  
A Chain ◽  
Six Degree Of Freedom

SUMMARYThis paper presents an algorithm that solves the inverse kinematics problem of all six degrees of freedom manipulators, “general” or “special”. A manipulator is represented by a chain of characters that symbolizes the position of prismatic and revolute joints in the manipulator and the special geometry that may exist between its joint axes. One form of the loop closure equation is chosen and the Raghavan and Roth method is used to obtain symbolically a square matrix. The determinant of this matrix yields the characteristic polynomial of the manipulator in one of the kinematic variables. As an example of the use of this algorithm we present the solution to the inverse kinematics problem of the GMF Arc Mate welding manipulator. In spite of its geometry, this industrial manipulator has a non-trivial solution to its inverse kinematics problem.

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