Efficient kinematics using quaternions for serial and antiparallel link robot arms
DOI:
https://doi.org/10.51094/jxiv.874Keywords:
kinematics, parallel linkAbstract
Dual quaternions have been proposed as an alternative to homogeneous transformation matrices in robotic kinematics. To perform inverse kinematics calculations using quaternions, logarithmic mapping of quaternions is required, however two challenges remain. In states with large errors, the analytical gradient becomes significantly large and stable convergence cannot be obtained. Additionally, there is a tendency to fall into local solutions during the convergence process. Furthermore, efficient modeling methods for parallel-link mechanisms have not yet been discussed. This study proposes a new method for stably obtaining the analytical gradient of quaternions. The proposed method was applied to a robot arm that combined serial and antiparallel link mechanisms, and a new kinematics modeling method for the antiparallel link mechanisms was proposed. The proposed method provides a more stable solution than conventional methods, and an improvement of approximately 10% in solution accuracy was confirmed.
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References
W. R. Hamilton, Elements of quaternions. Longmans, Green, & Company, 1866.
X. Wang and H. Zhu, “On the comparisons of unit dual quaternion and homogeneous transformation matrix,” Advances in Applied Clifford Algebras, vol. 24, pp. 213–229, 2014.
N. A. Aspragathos and J. K. Dimitros, “A comparative study of three methods for robot kinematics,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 28, no. 2, pp. 135–145, 1998.
J. Funda, R. H. Taylor, and R. P. Paul, “On homogeneous transforms, quaternions, and computational efficiency,” IEEE transactions on Robotics and Automation, vol. 6, no. 3, pp. 382–388, 1990.
A. T. Yang and F. Freudenstein, “Application of dual-number quaternion algebra to the analysis of spatial mechanisms,” Journal of Applied Mechanics, vol. 31, no. 2, pp. 300–308, 1964.
H.-L. Pham, V. Perdereau, B. V. Adorno, and P. Fraisse, “Position and orientation control of robot manipulators using dual quaternion feedback,” in 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 658–663, IEEE, 2010.
M. d. P. A. Fonseca, B. V. Adorno, and P. Fraisse, “Coupled task-space admittance controller using dual quaternion logarithmic mapping,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6057–6064, 2020.
R. N. Colomba, R. Laha, L. F. Figueredo, and S. Haddadin, “Adaptive admittance control for cooperative manipulation using dual quaternion representation and logarithmic mapping,” in 2022 IEEE 61st Conference on Decision and Control (CDC), pp. 107–144, IEEE, 2022.
H. Abaunza, R. Chandra, E. Özgür, J. A. C. Ramón, and Y. Mezouar, “Kinematic screws and dual quaternion based motion controllers,” Control Engineering Practice, vol. 128, p. 105325, 2022.
L. Figueredo, B. V. Adorno, J. Y. Ishihara, and G. A. Borges, “Robust kinematic control of manipulator robots using dual quaternion representation,” in 2013 IEEE International Conference on Robotics and Automation, pp. 1949–1955, IEEE, 2013.
B. V. Adorno, P. Fraisse, and S. Druon, “Dual position control strategies using the cooperative dual task-space framework,” in 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3955–3960, IEEE, 2010.
F. F. Afonso Silva, J. José Quiroz-Omaña, and B. Vilhena Adorno, “Dynamics of mobile manipulators using dual quaternion algebra,” Journal of Mechanisms and Robotics, vol. 14, no. 6, p. 061005, 2022.
J. Cheng, J. Kim, Z. Jiang, and W. Che, “Dual quaternion-based graphical slam,” Robotics and Autonomous Systems, vol. 77, pp. 15– 24, 2016.
X. Wang, C. Yu, and Z. Lin, “A dual quaternion solution to attitude and position control for rigid-body coordination,” IEEE Transactions on Robotics, vol. 28, no. 5, pp. 1162–1170, 2012.
H. J. Savino, L. C. Pimenta, J. A. Shah, and B. V. Adorno, “Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators,” Journal of the Franklin Institute, vol. 357, no. 1, pp. 142–178, 2020.
B. V. Adorno, Two-arm manipulation: From manipulators to enhanced human-robot collaboration. PhD thesis, Université Montpellier IISciences et Techniques du Languedoc, 2011.
X. Yang, H. Wu, Y. Li, and B. Chen, “A dual quaternion solution to the forward kinematics of a class of six-dof parallel robots with full or reductant actuation,” Mechanism and Machine Theory, vol. 107, pp. 27–36, 2017.
V. Noppeney, T. Boaventura, and A. Siqueira, “Task-space impedance control of a parallel delta robot using dual quaternions and a neural network,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 43, no. 9, p. 440, 2021.
D. Chevallier, “Lie algebras, modules, dual quaternions and algebraic methods in kinematics,” Mechanism and Machine Theory, vol. 26, no. 6, pp. 613–627, 1991.
M. Gouasmi, “Robot kinematics, using dual quaternions,” IAES International Journal of Robotics and Automation, vol. 1, no. 1, p. 13, 2012.
D.-P. Han, Q. Wei, and Z.-X. Li, “Kinematic control of free rigid bodies using dual quaternions,” International Journal of Automation and Computing, vol. 5, pp. 319–324, 2008.
X. Wang, D. Han, C. Yu, and Z. Zheng, “The geometric structure of unit dual quaternion with application in kinematic control,” Journal of Mathematical Analysis and Applications, vol. 389, no. 2, pp. 1352– 1364, 2012.
E. Özgür and Y. Mezouar, “Kinematic modeling and control of a robot arm using unit dual quaternions,” Robotics and Autonomous Systems, vol. 77, pp. 66–73, 2016.
N. T. Dantam, “Robust and efficient forward, differential, and inverse kinematics using dual quaternions,” The International Journal of Robotics Research, vol. 40, no. 10-11, pp. 1087–1105, 2021.
K. Nishii, A. Hatano, and Y. Okumatsu, “Ultra-low inertia 6-dof manipulator arm for touching the world,” in 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 432–438, IEEE, 2023.
J.-P. Merlet, Parallel robots, vol. 128. Springer Science & Business Media, 2006.
G. S. Chirikjian, Stochastic models, information theory, and Lie groups, volume 2: Analytic methods and modern applications, vol. 2. Springer Science & Business Media, 2011.
P. Beeson and B. Ames, “Trac-ik: An open-source library for improved solving of generic inverse kinematics,” in 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pp. 928–935, IEEE, 2015.
S. Kumar, N. Sukavanam, and R. Balasubramanian, “An optimization approach to solve the inverse kinematics of redundant manipulator,” International Journal of Information and System Sciences (Institute for Scientific Computing and Information), vol. 6, no. 4, pp. 414–423, 2010.
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Submitted: 2024-09-03 00:14:21 UTC
Published: 2024-09-05 04:40:54 UTC
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Kazutoshi Nishii
Yoshihiro Okumatsu
Akira Hatano
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