C2-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion
Joint Authors
Yaoyao, Shi
Pu, Yasong
Lin, Xiaojun
Hu, Yuan
Li, Zhishan
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-22
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
Smooth orientation planning is beneficial for the working performance and service life of industrial robots, keeping robots from violent impacts and shocks caused by discontinuous orientation planning.
Nevertheless, the popular used quaternion interpolations can hardly guarantee C2 continuity for multiorientation interpolation.
Aiming at the problem, an efficient quaternion interpolation methodology based on logarithmic quaternion was proposed.
Quaternions of more than two key orientations were expressed in the exponential forms of quaternion.
These four-dimensional quaternions in space S3, when logarithms were taken for them, could be converted to three-dimensional points in space R3 so that B-spline interpolation could be applied freely to interpolate.
The core formulas that B-spline interpolated points were mapped to quaternion were founded since B-spline interpolated point vectors were decomposed to the product of unitized forms and exponents were taken for them.
The proposed methodology made B-spline curve applicable to quaternion interpolation through dimension reduction and the high-order continuity of the B-spline curve remained when B-spline interpolated points were mapped to quaternions.
The function for reversely finding control points of B-spline curve with zero curvature at endpoints was derived, which helped interpolation curve become smoother and sleeker.
The validity and rationality of the principle were verified by the study case.
For comparison, the study case was also analyzed by the popular quaternion interpolations, Spherical Linear Interpolation (SLERP) and Spherical and Quadrangle (SQUAD).
The comparison results demonstrated the proposed methodology had higher smoothness than SLERP and SQUAD and thus would provide better protection for robot end-effector from violent impacts led by unreasonable multiorientation interpolation.
It should be noted that the proposed methodology can be extended to multiorientation quaternion interpolation with higher continuity than the second order.
American Psychological Association (APA)
Pu, Yasong& Yaoyao, Shi& Lin, Xiaojun& Hu, Yuan& Li, Zhishan. 2020. C2-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1193923
Modern Language Association (MLA)
Pu, Yasong…[et al.]. C2-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion. Mathematical Problems in Engineering No. 2020 (2020), pp.1-16.
https://search.emarefa.net/detail/BIM-1193923
American Medical Association (AMA)
Pu, Yasong& Yaoyao, Shi& Lin, Xiaojun& Hu, Yuan& Li, Zhishan. C2-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1193923
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193923