Robust H∞ kinematic control of manipulator robots using dual quaternion algebra

Purpose The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions. Design/methodology/approach The dual quaternions are the combination of dual-number theory and quaternion algebra, which means that they can represent spatial transformation. The dual quaternions can represent the screw displacement in a compact and efficient way, so that they are used for the kinematic analysis of serial robot. The error model proposed in this paper is derived from the forward kinematic equations via using dual quaternion algebra. The full pose measurements are considered to apply the error model to the serial robot by using Leica Geosystems Absolute Tracker (AT960) and tracker machine control (T-MAC) probe. Findings Two kinematic-parameter identification algorithms are derived from the proposed error model based on dual quaternions, and they can be used for serial robot calibration. The error model uses Denavit–Hartenberg (DH) notation in the kinematic analysis, so that it gives the intuitive geometrical meaning of the kinematic parameters. The absolute tracker system can measure the position and orientation of the end-effector (EE) simultaneously via using T-MAC. Originality/value The error model formulated by dual quaternion algebra contains all the basic geometrical parameters of serial robot during the kinematic calibration process. The vector of dual quaternion error can be used as an indicator to represent the trend of error change of robot’s EE between the nominal value and the actual value. The accuracy of the EE is improved after nearly 20 measurements in the experiment conduct on robot SDA5F. The simulation and experiment verify the effectiveness of the error model and the calibration algorithms.

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Spatial Distance of Point-Lines

Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2004-57450 ◽

2004 ◽

Author(s):

Yi Zhang ◽

Kwun-Lon Ting

Keyword(s):

Reference Point ◽

Quaternion Algebra ◽

The Other ◽

Spatial Distance ◽

Dual Quaternion ◽

Directed Line ◽

Shortest Distance ◽

The Common ◽

Point Line ◽

Displacement Model

A point-line is the combination of a directed line with a reference point on it. In this article, the spatial distance between two point-lines in space is defined based on a point-line displacement model. The displacement of a point-line from one position to the other is uniquely described as the composition of a pure translation along the point-line and a screw displacement about the common normal of the two positions. It is shown that such a displacement model leads to a simpler configuration of the underlying screw triangle and defines the shortest distance between two point-lines. The dual quaternion algebra is used to describe the idea with mathematic expressions.

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Error propagation and formation structure design using dual quaternion algebra

2011 9th IEEE International Conference on Control and Automation (ICCA) ◽

10.1109/icca.2011.6137966 ◽

2011 ◽

Author(s):

Xiangke Wang ◽

Changbin Yu ◽

Zhiyun Lin

Keyword(s):

Error Propagation ◽

Quaternion Algebra ◽

Structure Design ◽

Dual Quaternion

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Joint Stiffness Identification and Deformation Compensation of Serial Robots Based on Dual Quaternion Algebra

Applied Sciences ◽

10.3390/app9010065 ◽

2018 ◽

Vol 9 (1) ◽

pp. 65 ◽

Cited By ~ 2

Author(s):

Guozhi Li ◽

Fuhai Zhang ◽

Yili Fu ◽

Shuguo Wang

Keyword(s):

Quaternion Algebra ◽

Industrial Robot ◽

Joint Stiffness ◽

Industrial Robots ◽

Identification Algorithm ◽

Dual Quaternion ◽

Compensation Algorithm ◽

Serial Robots ◽

Stiffness Identification ◽

Deformation Compensation

As the application of industrial robots is limited by low stiffness that causes low precision, a joint stiffness identification algorithm for serial robots is presented. In addition, a deformation compensation algorithm is proposed for the accuracy improvement. Both of these algorithms are formulated by dual quaternion algebra, which offers a compact, efficient, and singularity-free way in robot analysis. The joint stiffness identification algorithm is derived from stiffness modeling, which is the combination of the principle of virtual work and dual quaternion algebra. To validate the effectiveness of the proposed identification algorithm and deformation compensation algorithm, an experiment was conducted on a dual arm industrial robot SDA5F. The robot performed a drilling operation during the experiment, and the forces and torques that acted on the end-effector (EE) of both arms were measured in order to apply the deformation compensation algorithm. The results of the experiment show that the proposed identification algorithm is able to identify the joint stiffness parameters of serial industrial robots, and the deformation compensation algorithm can improve the accuracy of the position and orientation of the EE. Furthermore, the performance of the forces and torques that acted on the EE during the operation were improved as well.

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