Pose Optimization of Serial Manipulators Using Knowledge of Their Velocity-Degenerate (Singular) Configurations

2003 ◽  
Vol 20 (5) ◽  
pp. 239-249 ◽  
Author(s):  
Scott B. Nokleby ◽  
Ron P. Podhorodeski
Keyword(s):  
Serial Manipulators ◽  
Singular Configurations ◽  
Pose Optimization

Feasible Motion Solutions for Serial Manipulators at Singular Configurations

2003 ◽  
Vol 125 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Yuefa Fang ◽  
Lung-Wen Tsai
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Full Rank ◽  
Joint Space ◽  
Serial Manipulators ◽  
First Order ◽  
Singular Configurations ◽  
Cartesian Space ◽  
Novel Approach ◽  
Singular Configuration

When a serial manipulator is at a singular configuration, the Jacobian matrix will lose its full rank causing the manipulator to lose one or more degrees of freedom. This paper presents a novel approach to model the manipulator kinematics and solve for feasible motions of a manipulator at singular configurations such that the precise path tracking of a manipulator at such configurations is possible. The joint screw linear dependency is determined by using known line varieties so that not only the singular configurations of a manipulator can be identified but also the dependent joint screws can be determined. Feasible motions in Cartesian space are identified by using the theory of reciprocal screws and the resulting equations of constraint. The manipulator first-order kinematics is then modeled by isolating the linearly dependent columns and rows of the Jacobian matrix such that the mapping between the feasible motions in Cartesian space and the joint space motions can be uniquely determined. Finally, a numerical example is used to demonstrate the feasibility of the approach. The simulation results show that a PUMA-type robot can successfully track a path that is singular at all times.

scholarly journals Internal redundancy: an approach to improve the dynamic parameters around sharp corners

2013 ◽  
Vol 4 (1) ◽  
pp. 233-242 ◽  
Author(s):  
S. S. Parsa ◽  
J. A. Carretero ◽  
R. Boudreau
Keyword(s):  
Parallel Manipulator ◽  
Dynamic Properties ◽  
Dynamic Performance ◽  
Parallel Manipulators ◽  
Variable Geometry ◽  
Centre Of Mass ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Planar Parallel Manipulator ◽  
Sharp Corners

Abstract. In recent years, redundancy in parallel manipulators has been studied broadly due to its capability of overcoming some of the drawbacks of parallel manipulators including small workspaces and singular configurations. Internal redundancy, first introduced for serial manipulators, refers to the concept of adding movable masses to some links so as to allow to control the location of the centre of mass and other dynamic properties of some links. This concept has also been referred to as variable geometry. This paper investigates the effects of internal redundancy on the dynamic properties of a planar parallel manipulator while performing a family of trajectories. More specifically, the 3-RRR planar manipulator, where a movable mass has been added to the distal link, is allowed to trace trajectories with rounded corners and different radii. The proposed method uses the manipulator's dynamic model to actively optimise the location of the redundant masses at every point along the trajectory to improve the dynamic performance of the manipulator. Numerical examples are shown to support the idea.

A Study of the Singular Configurations of Serial Manipulators

1987 ◽  
Vol 109 (1) ◽  
pp. 14-20 ◽  
Author(s):  
Shih-Liang Wang ◽  
Kenneth J. Waldron
Keyword(s):  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Singular Configuration ◽  
Six Degree Of Freedom ◽  
Joint Motions ◽  
Robotic Applications

A manipulator is at a singular configuration when the screws representing the instantaneous joint motions of the manipulator are linearly dependent, and the manipulator cannot be moved along an exact path with specified orientation in world coordinates. There are ∞3 singular configurations for a six-degree-of-freedom manipulator, and all these configurations constitute the singularity field. An algorithm is derived to trace the singularity field. Another algorithm presented in this paper finds all the joint screws reciprocal to a given wrench screw. Some new robotic applications are then possible using the principle of aligning a power tool with the screw of the reciprocal wrench.

Instantaneous Kinematics and Singularity Analysis of a Novel Three-Legged Mobile Robot With Active S-R-R-R Legs

2008 ◽  
Author(s):  
Ping Ren ◽  
Dennis Hong
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
The Body ◽  
Jacobian Matrices ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Grassmann Line Geometry ◽  
Actuation Scheme ◽  
Complete Investigation

STriDER (Self-excited Tripedal Dynamic Experimental Robot) is a unique three-legged walking robot that utilizes its innovative tripedal gait to walk. Previous work on the kinematic analysis of STriDER mainly focused on solving the forward and inverse displacement problems. As a continuation, this paper addresses the instantaneous kinematics and singularity analysis. The kinematic configuration of STriDER is modeled as a three-legged in-parallel manipulator when all three feet of the robot are in contact with the ground without slipping. The results obtained from this study can be implemented to the velocity control and the resistance of disturbance forces, thus improving the motion accuracy and stability of the robot. By using screw theory, the screw-based Jacobian matrices of the manipulator can be derived since the forward displacement problems have already been solved. Based on these Jacobian matrices, the transformation equations from the active joint rates to the velocities of the body and vice versa are derived. Then, a complete investigation on the identification and elimination of singularities is presented. Unlike serial manipulators, in-parallel manipulators have two types of singularities, i.e., forward and inverse singularities. The inverse singularities are identified by checking the singular configurations of individual legs and the determinant of the inverse Jacobian matrix. By using Grassmann line geometry, the analytical conditions under which the forward singularities occur are obtained. A study on each case of these singular configurations shows that the redundant-actuation scheme of the active joints can effectively eliminate forward singularities.

A Novel Numerical Method to Solve the Inverse Kinematics of 3R Manipulators

2011 ◽  
Author(s):  
E. A. Gonza´lez-Barbosa ◽  
M. A. Gonza´lez-Palacios ◽  
L. A. Aguilera-Corte´s ◽  
C. A. Bernal-Marti´nez
Keyword(s):  
Differential Evolution ◽  
Numerical Method ◽  
Computational Efficiency ◽  
Software Package ◽  
Inverse Kinematics ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Simulation Results ◽  
General Geometry ◽  
Solution Problem

A new numerical method to solve the inverse kinematics solution problem of serial manipulators is developed in this paper. The proposed method is known as Differential Evolution (DE), a novel and efficient numerical method which has been adapted to solve the inverse kinematics solution of 3R serial manipulator of general geometry. Besides, the paper contains the complete structuring for the implementation of this new case in SnAP, a comprehensive software package for synthesis, analysis and simulation of serial manipulators. The DE method is stable since it converges to the solution with any initial values, and it is not sensitive to the singular configurations of serial manipulators. Simulation results are presented to show the performance benefits of the proposed algorithm. Computational efficiency of the method is shown based on the results, as well as in comparison with traditional methods used in this problem.

scholarly journals Analysis of Singular Configuration of Robotic Manipulators

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2189
Author(s):  
Xinglei Zhang ◽  
Binghui Fan ◽  
Chuanjiang Wang ◽  
Xiaolin Cheng
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Joint Angle ◽  
Robotic Manipulators ◽  
Jacobian Determinant ◽  
End Effector ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Manipulability Measure ◽  
Singular Configuration

Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

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