This paper proposes a novel computing method for higher-order accelerations vector field in the case of rigid body motion and multibody systems, using the property of the hyper-multidual algebra. The equations that allow the determination of higher-order accelerations for the spatial serial kinematic chains are the main subject of this paper. The results are closed-form and coordinate-free. Furthermore, the velocities, accelerations, jerks, and jounces fields are offered for an mC general manipulator.
Hyper-multidual Algebra and Higher-Order Kinematics
Springer Proceedings in Advanced Robotics
International Symposium on Advances in Robot Kinematics ; 2022 ; Bilbao, Spain June 26, 2022 - June 30, 2022
2022-06-18
8 pages
Article/Chapter (Book)
Electronic Resource
English
Hyper-multidual algebra , Lie group <inline-formula><alternatives><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>S</mi><mi>E</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math><tex-math>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SE(3)$$\end{document}</tex-math><inline-graphic></inline-graphic></alternatives></inline-formula> , Higher-order kinematics , Lie algebra <inline-formula><alternatives><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>s</mi><mi>e</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math><tex-math>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$se(3)$$\end{document}</tex-math><inline-graphic></inline-graphic></alternatives></inline-formula> Computational Intelligence , Engineering , Robotics , Control, Robotics, Mechatronics , Computational Science and Engineering
Hyper-multidual Algebra and Higher-Order Kinematics
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