A Global Performance Index for the Kinematic Optimization of Robotic Manipulators

1991 ◽  
Vol 113 (3) ◽  
pp. 220-226 ◽  
Author(s):  
C. Gosselin ◽  
J. Angeles
Keyword(s):  
Condition Number ◽  
Performance Index ◽  
Jacobian Matrix ◽  
Robotic Manipulators ◽  
Degree Of Freedom ◽  
Global Index ◽  
Global Performance ◽  
Three Degree Of Freedom ◽  
Kinematic Optimization

In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.

Global Performance Index System for Kinematic Optimization of Robotic Mechanism

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Pu Zhang ◽  
Zhenqiang Yao ◽  
Zhengchun Du
Keyword(s):  
Performance Index ◽  
Index System ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Linear Mapping ◽  
Distribution Characteristics ◽  
Global Performance ◽  
Kinematic Performance ◽  
Performance Distribution ◽  
Kinematic Optimization

Correct evaluation of robot performance has been a problem in the field of robotics. Many scholars have proposed a variety of performance indices, such as manipulability, condition number, and minimum singular value, to describe quantitatively the kinematic performance of a robotic mechanism. However, two questions remain: (1) how to describe the kinematic performance completely for the design of a robotic mechanism, and (2) how to comprehensively describe the global performance distribution characteristics in the workspace. This paper presents a global performance index system for kinematic optimization of a robotic mechanism based on Jacobian matrix, manipulability ellipsoid, and descriptive statistics theory that can comprehensively describe the kinematic performance and the performance distribution characteristics in a robot's workspace. First, the Jacobian matrix, a linear mapping from the joint space to the task space of a robotic mechanism, is analyzed, and the kinematic transmission ability indices and the kinematic transmission accuracy index are determined. Second, four indices, including global average value, global volatility, global skewness, and global kurtosis, are presented to describe the global performance index's distribution in the workspace. Third, the global performance index system is established to evaluate a robot's global kinematic performance based on the above analysis. Finally, a two-degrees of freedom (DOF) robotic mechanism is designed based on the global performance index system as a case, analysis of which shows that the final mechanism has good kinematic performance in the workspace. This demonstrates that the global performance index system proposed in this paper can be useful for the evaluation of the kinematic performance and kinematic optimization of a robotic mechanism.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Novel Design and Analysis of a Fully Decoupled 3-DOF Spherical Parallel Robot

2009 ◽  
Author(s):  
Dan Zhang ◽  
Fan Zhang
Keyword(s):  
Physical Meaning ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Redundant Constraints ◽  
Rotational Motions ◽  
Three Degree Of Freedom ◽  
Novel Design

In this paper, we propose a unique, decoupled Three Degree-of-Freedom (DOF) parallel wrist. The condition required for synthesizing a fully isotropic parallel mechanism is obtained based on the physical meaning of the row vector in the Jacobian Matrix. Specifically, an over-constrained spherical 3-DOF parallel mechanism is presented and the modified structure, which avoids the redundant constraints, is also introduced. The proposed manipulator is capable of decoupled rotational motions around the x, y and z axes and contains an output angle that is equal to the input angle. Since this device is analyzed with the Jacobian Matrix, which is constant, the mechanism is free of singularity and maintains homogenous stiffness over the entire workspace.

Inertial Vibration Damping Control for a Flexible Base Manipulator

2002 ◽  
Author(s):  
Lynnane E. George ◽  
Wayne J. Book
Keyword(s):  
Performance Index ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Joint Space ◽  
Vibration Damping ◽  
Degree Of Freedom ◽  
Inertia Effects ◽  
Inertial Interaction ◽  
Flexible Base ◽  
Three Degree Of Freedom

A rigid (micro) robot mounted serially to the tip of a long, flexible (macro) manipulator is often used to increase reach capability, but flexibility in the macromanipulator can interfere with positioning accuracy. A rigid manipulator attached to a flexible but unactuated base was used to study a scheme to achieve positioning of the micromanipulator combined with enhanced vibration damping of the base. Inertial interaction forces and torques acting between the robot and its base were modeled and studied to determine how to use them to damp the vibration. One issue is that there are locations in the workspace where the rigid robot loses its ability to create interactions in one or more degrees of freedom. These “inertial singularities” are functions of the rigid robot’s joint variables. A performance index was developed to predict the ability of the rigid robot to damp vibration and will help ensure the robot is operating in joint space configurations favorable for inertial damping. When the performance index is used along with the appropriate choice of feedback gains, the inertia effects, or those directly due to accelerating the robot’s links, have the greatest influence on the interactions. By commanding the robot link’s accelerations out of phase with the base velocity, vibration energy will be removed from the system. This signal is then added to the rigid robot’s position control signal. Simulations of a rigid three degree of freedom anthropomorphic robot mounted on a flexible base were developed and show the effectiveness of the control scheme. In addition, experimental results demonstrating two degree of freedom vibration damping are included.

Kinematic Inversion of Parallel Manipulators in the Presence of Incompletely Specified Tasks

1990 ◽  
Vol 112 (4) ◽  
pp. 494-500 ◽  
Author(s):  
C. Gosselin ◽  
J. Angeles
Keyword(s):  
Continuous Function ◽  
Condition Number ◽  
Performance Index ◽  
Free Parameter ◽  
Optimization Problem ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Cartesian Coordinates ◽  
Kinematic Inversion ◽  
On Line

In this paper, the kinematic inversion of redundant parallel manipulators in the presence of incompletely specified tasks is formulated as an optimization problem. The performance index used is the condition number of the Jacobian matrix of the manipulator which is a measure of Jacobian invertibility. In order to optimize this index along a partially prescribed Cartesian trajectory, the concept of trajectory map is introduced. It is also shown that the optimum value of the free parameter that minimizes the condition number is not a continuous function of the prescribed Cartesian coordinates. An on-line algorithm producing continuous joint histories is then discussed. This method has been implemented and tested, as illustrated with the results presented here.

Dimensional Synthesis of a 2UPS-UPR Parallel Machine Tool

2009 ◽  
Vol 16-19 ◽  
pp. 554-558
Author(s):  
Liang Zhao ◽  
Ya Dong Gong ◽  
Jian Ye Guo ◽  
Guang Qi Cai
Keyword(s):  
Condition Number ◽  
Performance Index ◽  
Machine Tools ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Structural Parameters ◽  
Parallel Machine ◽  
Dimensional Synthesis ◽  
Parallel Machine Tools ◽  
Parallel Machine Tool

This paper deals with the dimensional synthesis of a 2UPS-UPR parallel mechanism tool newly designed by Northeastern University. On the basis of establishing kinematics equations and obtaining Jacobian matrix, the performance index of dimensional synthesis is given which is the average of 729 values of the condition number of Jacobian matrix corresponding to 729 positions in the workspace. With MATLAB software, the effects are simulated which the structural parameters of parallel machine tools have on dimensional synthesis, their change laws are gained, and then dimensional synthesis of parallel machine tools is conducted based on these laws.

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.

Design of a Redundantly Actuated Asymmetric Linear DELTA Parallel Mechanism for Singularity-Free Mode Changes

2014 ◽  
Vol 575 ◽  
pp. 711-715 ◽  
Author(s):  
Takashi Harada
Keyword(s):  
Numerical Simulations ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Moving Plate ◽  
Mode Change ◽  
Redundantly Actuated ◽  
Free Mode ◽  
Linear Actuators ◽  
Three Degree Of Freedom

A novel parallel mechanism which enlarges the workspace by singularity-free mode change is proposed. The proposed mechanism is inherited the design of Linear DELTA which has three degree-of-freedom translational moving plate driven by three linear actuators, in addition, extended it by redundantly actuation by four linear actuators and asymmetric design. New criterions about redundancy and singularity of redundantly actuated parallel mechanism using summation and product of determinants of minor matrices of the transposed Jacobian matrix are proposed. Redundantly actuation and asymmetric design enables singularity-free mode changes with loss redundancy but maintain non-singularity, that are evaluated by the proposed criterions. Numerical simulations demonstrate the singularity-free mode changes of the proposed mechanism.

Cylinder-Slider Parallel Manipulators for Singularity-Free Path Generation

2011 ◽  
Author(s):  
Hong Zhou ◽  
Phani Kumar Mallampati ◽  
Venkata Krishna Perivilli
Keyword(s):  
Free Path ◽  
Condition Number ◽  
Performance Index ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Path Generation ◽  
Point Position

A challenge for cylinder-slider parallel manipulators is their limited workspace and singularity-free path generation. In this paper, the linkage feasibility conditions are derived based on the elimination of dead point position within the workspace. The workspace is generated using the curve-enveloping theory. The singularity-free path generation capability is analyzed. The performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. This paper shows that five-bar cylinder-slider parallel manipulators can be used as effective singularity-free path generators if properly designed. The results of this paper provide a useful map for designing this type of parallel manipulator.

Five-Bar Cylinder-Crank Two-DOF Parallel Manipulators for Singularity-Free Path Generation

2009 ◽  
Author(s):  
Hong Zhou ◽  
Swetha Minupuri ◽  
Shilpa Indroju ◽  
Vasuda Gorti
Keyword(s):  
Free Path ◽  
Condition Number ◽  
Performance Index ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Path Generation ◽  
Operation Speed ◽  
Proper Design

Parallel manipulators have the merits of high stiffness, load-bearing, operation speed and precision positioning capabilities that are required in many industrial applications. The main challenges for parallel manipulators are their limited workspace and singularity-free path generation capability. This paper is focused on the singularity-free path generation of five-bar cylinder-crank two-DOF parallel manipulators. The linkage feasibility conditions are derived based on the elimination of dead point position within the workspace. The workspace is generated using the curve-enveloping theory. The singularity characteristics and linkage configurations are presented. The singularity-free path generation capability is analyzed. The performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. This paper shows that five-bar cylinder-crank two-DOF parallel manipulators can be used as effective singularity-free path generators if properly designed. The results of this paper provide a useful map for the proper design of this type of parallel manipulator.

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