Computation without Singularity for Logarithms of Homogeneous Matrices and Orthogonal Dual Tensors
By: Daniel Condurache and Ionuț Popa
References
- Angeles J., Fundamentals of Robotic Mechanical Systems, Springer: Berlin/Heidelberg, Germany, 2014.
- Angeles J., Rational Kinematics, Springer-Verlag, New-York, 1988.
- Bottema O., Roth B., Theoretical Kinematics, Dover, New York, 1990.
- Condurache D., Ciureanu I.-A., Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements, Mathematics, 2020, 8(7):1185, https://doi.org/10.3390/math8071185.
- Gallier J., Xu D., Computing Exponential of Skew-Symmetric Matrices and Logarithms of Orthogonal Matrices, International Journal of Robotics and Automation, Vol. 17, no. 4, (2002).
- Marsden J.E., Ratiu T.S., Introduction to Mechanics and Symmetry, New-York, Springer-Verlag, 1994.
- McCarthy M., An Introduction to Theoretical Kinematics, MIT Press, Cambridge, MA, 1990.
- Angeles J., The Application of Dual Algebra to Kinematic Analysis, Comput. Methods Mech. Syst. 1998, 161, 3-32.
- Condurache D., Burlacu A., Dual tensors based solutions for rigid body motion parameterization, Mech. Mach. Theory 2014, 74, 390-412.
- Condurache D., Burlacu A., Orthogonal dual tensor method for solving the AX= XB sensor calibration problem, Mech. Mach. Theory 2016, 104, 382–404.
- Muller A., Group theoretical approaches to vector parameterization of rotations, J. Geom. Symmetry Phys. 2010, 19, 43-72.
- Pennestrì E., Valentini P.P., Dual Quaternions as a Tool for Rigid Body Motion Analysis: A Tutorial with an Application to Biomechanics, Arch. Mech. Eng. 2010, LVII, 187-205.
- Leclercq G., Lefèvre P., Blohm G., 3D kinematics using dual quaternions: Theory and applications in neuroscience, Front. Behav. Neuroscience, 2013, 7, 7.
- Condurache D., Burlacu A., Recovering Dual Euler Parameters from Feature-Based Representation of Motion, In Advances in Robot Kinematics, Lenarčič J., Khatib O. (Eds.) Springer: Cham, Switzerland, 2014, pp. 295-305._31.
DOI: https://doi.org/10.2478/bipmf-2025-0004 | Journal eISSN: 2537-4990
Language: English
Page range: 39 - 56
Submitted on: Jun 1, 2025
Accepted on: Jun 26, 2025
Published on: May 29, 2026
Published by: Gheorghe Asachi Technical University of Iasi
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
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© 2026 Daniel Condurache, Ionuț Popa, published by Gheorghe Asachi Technical University of Iasi
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.