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.

Singularity Analysis of Serial Robot-Manipulators

1996 ◽  
Vol 118 (4) ◽  
pp. 520-525 ◽  
Author(s):  
A. Karger
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Singularity Analysis ◽  
Singular Set ◽  
Singular Configurations ◽  
Special Cases ◽  
Serial Robot ◽  
Singular Configuration ◽  
Actual Configuration

This paper is devoted to the description of the set of all singular configurations of serial robot-manipulators. For 6 degrees of freedom serial robot-manipulators we have developed a theory which allows to describe higher order singularities. By using Lie algebra properties of the screw space we give an algorithm, which determines the degree of a singularity from the knowledge of the actual configuration of axes of the robot-manipulator only. The local shape of the singular set in a neighbourhood of a singular configuration can be determined as well. We also solve the problem of escapement from a singular configuration. For serial robot-manipulators with the number of degrees of freedom different from six we show that up to certain exceptions singular configurations can be avoided by a small change of the motion of the end-effector. We also give an algorithm which allows to determine equations of the singular set for any serial robot-manipulator. We discuss some special cases and give examples of singular sets including PUMA 560.

A New Approach for Environmental Contour and Multivariate De-Clustering

2019 ◽  
Author(s):  
Quentin Derbanne ◽  
Guillaume de Hauteclocque
Keyword(s):  
Joint Distribution ◽  
Degrees Of Freedom ◽  
Accurate Estimate ◽  
Direct Computation ◽  
New Approach ◽  
Clustering Techniques ◽  
First Order ◽  
Novel Approach ◽  
Reliability Method

Abstract When the long term behaviour of a floating unit is assessed, the environmental contour concept is often applied together with IFORM (Inverse First Order Reliability Method). This approach avoids direct computation on all sea-states, which is computationally very demanding, and most often simply not feasible. Instead, only a few conditions (the contour) are assessed and results in an accurate estimate of the long term extreme. However, most of available methods to derive the contour require the knowledge of the joint distribution of the different random variables (waves, wind, current...), which is often difficult to derive accurately. In fact, some complex dependences exist and are attempted to be simplified in too few coefficients. Another limitation of current environmental contour is its difficulty to deal with the dependence issue. Indeed, extreme sea-states arise by groups (storms, hurricanes...) and are not independent. While de-clustering techniques exist and are quite straightforward in univariate problems, this becomes difficult when the number of dimension increases. In an attempt to tackle those challenges, this paper presents a novel approach to derive IFORM contours. The method does not require any joint distribution and makes use of much more degrees of freedom to capture the dependence between variables. It also allows for an easy de-clustering. The approach is illustrated on two locations, using actual hindcast data of significant wave height and period; the resulting contours are compared to the ones obtained with more traditional methods.

Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot

Robotica ◽  
2012 ◽  
Vol 31 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Yongjie Zhao
Keyword(s):  
Performance Evaluation ◽  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
End Effector ◽  
Transmission Index ◽  
Delta Robot ◽  
Singular Configuration ◽  
Velocity Transmission

SUMMARYPerformance evaluation of a parallel robot is a multicriteria problem. By taking Delta robot as an object of study, this paper presents the kinematic performance evaluation of a three translational degrees-of-freedom parallel robot from the viewpoint of singularity, isotropy, and velocity transmission. It is shown that the determinant of a Jacobian matrix cannot measure the distance from the singular configuration due to the existing inverse kinematic singularity of a Delta robot. The determinants of inverse and direct kinematic Jacobian matrices are adopted for the measurement of distance from the singular configuration based on the theory of numerical linear dependence. The denominator of the Jacobian matrix will be lost in the computation of the condition number when the end-effector is on the centerline of the workspace, so the Delta robot may also be nearly at a singular configuration when the condition number of the Jacobian matrix is equal to 1. The velocity transmission index whose physical meaning is the maximum input angular velocity when the end-effector translates in the unit velocity is presented. The evaluation of singularity, isotropy, and velocity transmission of a Delta robot is investigated by simulation. The velocity transmission index can also be used for the velocity transmission evaluation of a parallel robot with pure rotational degrees-of-freedom based on the principle of similarity. The physical meaning is modified to be the maximum input velocity when the end-effector rotates in the unit angular velocity.

Singularity Elimination of Stewart Parallel Manipulator Based on Redundant Actuation

2010 ◽  
Vol 143-144 ◽  
pp. 308-312 ◽  
Author(s):  
Yi Cao ◽  
Hui Zhou ◽  
Bao Kun Li ◽  
Shen Long ◽  
Meng Si Liu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Singular Value ◽  
Kinematics And Dynamics ◽  
Redundant Actuation ◽  
Numerical Examples ◽  
Singular Configurations ◽  
Parallel Platform ◽  
Singular Configuration

This paper mainly addresses the principle of the singularity elimination of the Stewart parallel platform. By adding appropriate redundant actuation, the rank of the Jacobian matrix of the parallel platform is always full, accordingly the singular value of the Jacobian matrix of the parallel platform is nonzero. Then the singular configuration of the parallel platform can be eliminated by adding one redundant actuation. Numerical examples are taken to illuminate the principle’s effectiveness. It is shown that not only singular configurations of the Stewart parallel platform can be eliminated, but also performances of kinematics and dynamics of the parallel platform can be greatly perfected by adding appropriate redundant actuation.

scholarly journals An Algebraic Method to Check the Singularity-Free Paths for Parallel Robots

2015 ◽  
Author(s):  
R. Jha ◽  
D. Chablat ◽  
F. Rouillier ◽  
G. Moroz
Keyword(s):  
Degrees Of Freedom ◽  
Complex Shape ◽  
Algebraic Method ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Joint Space ◽  
Parallel Robots ◽  
Singular Configuration ◽  
End Effectors ◽  
Three Degrees Of Freedom

Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the trajectories are projected in the joint space using Gröbner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manipulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.

A new method of applying differential kinematics through dual quaternions

Robotica ◽  
2015 ◽  
Vol 35 (4) ◽  
pp. 907-921 ◽  
Author(s):  
Andre Schneider de Oliveira ◽  
Edson Roberto De Pieri ◽  
Ubirajara Franco Moreno
Keyword(s):  
Jacobian Matrix ◽  
Traditional Approach ◽  
Joint Space ◽  
Robotic System ◽  
New Method ◽  
Dual Quaternions ◽  
Novel Approach ◽  
Kinematic Singularities ◽  
Redundant Systems

SUMMARYDifferential kinematics is a traditional approach to linearize the mapping between the workspace and joint space. However, a Jacobian matrix cannot be inverted directly in redundant systems or in configurations where kinematic singularities occur. This work presents a novel approach to the solution of differential kinematics through the use of dual quaternions. The main advantage of this approach is to reduce “drift” error in differential kinematics and to ignore the kinematic singularities. An analytical dual-quaternionic Jacobian is defined, which allows for the application of this approach in any robotic system.

Cartesian workspace optimization of Tricept parallel manipulator with machining application

Robotica ◽  
2014 ◽  
Vol 33 (9) ◽  
pp. 1948-1957 ◽  
Author(s):  
M. A. Hosseini ◽  
H. M. Daniali
Keyword(s):  
Velocity Vector ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Research Work ◽  
Singular Values ◽  
Maximum Size ◽  
Space Velocity ◽  
Parallel Robot ◽  
Joint Space ◽  
Work Piece

SUMMARYIn this research work, the maximum Cartesian workspace of a Tricept parallel robot with two rotational and one translational degrees of freedom was investigated. Generally, the Cartesian workspace identifies the maximum size of a work-piece, specifying its cubicx,yandzdimensions, on which the milling machine could perform operations. However, the workspace of a robot can be considered in its task space, such as ψ × θ ×zfor the Tricept Parallel Kinematic Mechanism (PKM). A novel homogeneous Jacobian matrix which transforms joint space velocity vector into end-effector Cartesian velocity vector has been generated named as a Cartesian Jacobian matrix. Using the indices derived from the homogeneous Cartesian Jacobian matrix, i.e. the maximum singular values and local conditioning indices, the manipulator is designed to reach the Cartesian workspace with rapid positioning rates as well as with singularity avoidance.

Singularity and Controllability Analysis of Parallel Manipulators

1998 ◽  
Author(s):  
Prasun Choudhury ◽  
Ashitava Ghosal
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Transformation Matrix ◽  
Constraint Forces ◽  
Numerical Examples ◽  
Cartesian Space ◽  
Force Transformation

Abstract This paper presents a study of kinematic and force singularities and their relationship to the controllability of planar and spatial parallel manipulators. Parallel manipulators are classified according to their degrees of freedom, number of output Cartesian variables used to describe their motion and the number of actuated joint inputs. The singularities in the workspace of a parallel manipulator are studied by considering the force transformation matrix which maps the forces and torques in joint space to output forces and torques in Cartesian space. The uncontrollable regions in the workspace of the parallel manipulator are obtained by deriving the equations of motion in terms of Cartesian variables and by using techniques from Lie Algebra. We show that when the number of actuated joint inputs is equal to the number of output Cartesian variables, and the force transformation matrix loses rank, the parallel manipulator is uncontrollable. For the case of manipulators where the number of joint inputs is less than the number of output Cartesian variables, if the constraint forces and torques (represented by the Lagrange multipliers) become infinite, the force transformation matrix loses rank. Finally, we show that the singular and uncontrollable regions in the workspace of a parallel manipulator can be reduced by adding redundant joint actuators and links. The results are illustrated with the help of numerical examples where we plot the singular and uncontrollable regions of parallel manipulators belonging to the above mentioned classes.

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.

Research on Painting Robot Manipulator for Irregular Components in Reproducing Cartridge

2011 ◽  
Vol 121-126 ◽  
pp. 1358-1362
Author(s):  
Qian Qian Chen ◽  
Xiu Ting Wei ◽  
Jiang Hai Lin ◽  
Gang Li
Keyword(s):  
Inverse Problem ◽  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Joint Space ◽  
Forward Problem ◽  
Cartesian Space ◽  
Painting Robot

In order to implement the surface painting automation of irregular components of reproducing cartridge, a painting robot manipulator with four degrees of freedom is carried out in this paper. Kinematics forward problem and inverse problem of the manipulator are firstly formulated and then painting trajectory is described by adopting the structure of endpoints and line-style. Furthermore, painting trajectory is generated in both joint space and Cartesian space according to robot’s trajectory planning principle.

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