ISSN 2466-4677; e-ISSN 2466-4847
SCImago Journal Rank
2023: SJR=0.19
CWTS Journal Indicators
2023: SNIP=0.57
FORWARD KINEMATICS ALGORITHM IN DUAL QUATERNION SPACE BASED ON DENAVIT-HARTENBERG CONVENTION
Authors:
Nikola LJ. Zivkovic1
,
,
1Lola Institute Ltd., Kneza Viseslava 70a, 11030 Belgrade, Serbia
2Faculty of Mechanical Engineering, Kraljice Marije 16, 11060 Belgrade, Serbia
Received: 31 March 2023
Revised: 26 May 2023
Accepted: 5 June 2023
Published: 30 June 2023
Abstract:
Forward kinematics is fundamental to robot design, control, and simulation. Different forward kinematics algorithms have been developed to deal with the complex geometry of a robot. This paper presents a robot forward kinematics algorithm in dual quaternion space. The presented method uses Denavit-Hartenberg (DH) convention for uniform definition of successive rotational and translational transformations in joints along the robot’s kinematic chain. This research aims to utilize the advantages of dual quaternions and DH convection for forward kinematics computation and make the algorithm, which is compact, intuitive, numerically robust, and computationally efficient as it uses the minimal number of parameters required for the computation, suitable for implementation in ROS and similar software. The algorithm is verified on the 6DoF industrial robot RL15, with the symbolic equations and numerical simulation presented.
Keywords:
Forward kinematics, kinematic modelling, DH convention, coordinate frame transformations, quaternions, dual quaternions, robotics
References:
[1] B. Siciliano, O. Khatib, T. Kroger, Handbook of robotics. Springer, Berlin, 2008.
[2] J.J. Craig, Introduction to robotics: mechanics and control, 3rd ed. Pearson Prentice Hall, Upper Saddle River, USA, 2005.
[3] P. Corke, Robot Arm Kinematics. In: Robotics, Vision and Control. Springer Tracts in Advanced Robotics. Springer, 118, 2017: 193-228. https://doi.org/10.1007/978-3-319-54413-7_7
[4] K. M. Lynch, F.C. Park, Modern Robotics: Mechanics, Planning and Control. Cambridge University Press, 2017.
[5] P. Mandić, M. Lazarević, Z. Stokić, T. Šekara, Dynamic modelling and control design of seven degrees of freedom robotic arm. 6th International Congress of Serbian Society of Mechanics, 19-21 June 2017, Tara, Serbia, pp.1-8.
[6] V. Covic, M. Lazarevic, Mehanika robota, second ed. Faculty of Mechanical Engineering, Belgrade, 2021. (in Serbian)
[7] M. Lazarevic, Mechanics of human locomotor system. FME Transactions, 34(2), 2006: 105-114.
[8] C. Faria, J.L. Vilaca, S. Monteiro, W. Erlhagen, E. Bicho, Automatic Denavit-Hartenberg parameter identification for serial manipulators. 45th Annual Conference of the IEEE Industrial Electronics Society (IECON), 1 October 2019, Lisbon, Portugal, pp.610-617. https://doi.org/10.1109/IECON.2019.8927455
[9] N.A. Aspragathos, J.K. Dimitros, A Comparative Study of Three Methods for Robot Kinematics. IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics, 28(2), 1998:135-145.
https://doi.org/10.1109/3477.662755
[10] J. Funda, R.H. Taylor, R.P. Paul, On homogeneous transformations, quaternions and computational efficiency. IEEE Transactions on Robotics and Automation, 6(3), 1990: 382-388.
https://doi.org/10.1109/70.56658
[11] J.Z. Vidakovic, M.P. Lazarevic, V.M. Kvrgic, Z.Z. Dancuo, G.Z. Ferenc, Advanced quaternion forward kinematics algorithm including overview of different methods for robot kinematics. FME Transactions, 42(3), 2014:189-199. https://doi.org/10.5937/fmet1403189V
[12] B.V. Adorno, Two-arm Manipulation: From Manipulators to Enhanced Human-Robot Collaboration (Ph.D. Thesis). Université Montpellier II – Sciences et Techniques du Languedoc, Montpellier, 2011.
[13] N.T. Dantam, Robust and efficient forward, differential and inverse kinematics using dual quaternions. International Journal of Robotics Research, 40(10-11), 2021: 1087-1105.
https://doi.org/10.1177/0278364920931948
[14] S. Kucuk, Z. Bingul, Robot Kinematics: Forward and Inverse Kinematics. Industrial Robotics: Theory, Modelling and Control, 2006: 117-148. https://doi.org/10.5772/5015
[15] N.T. Dantam, Practical Exponential Coordinates Using Implicit Dual Quaternions. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, 14, 2020. https://doi.org/10.1007/978-3-030-44051-0_37
[16] E. Özgür, Y. Mezouar, Kinematic modeling and control of a robot arm using unit dual quaternions. Robotics and Autonomous Systems, 77, 2016: 66-73. https://doi.org/10.1016/j.robot.2015.12.005
[17] Stanford Artificial Intelligence Laboratory, Robotic Operating System, 2018. https://www.ros.org (Accessed 27 December 2022).
[18] A. Valverde, P. Tsiotras, Spacecraft Robot Kinematics Using Dual Quaternions. Robotics, 7(4), 2018: 64. https://doi.org/10.3390/robotics7040064
[19] M.W. Spong, S. Hutchinson, M. Vidyasagar, Forward Kinematics. in Robot Modelling and Control, 2nd ed. Wiley, 2020, p.79.
[20] Github, RViz, 2022. https://github.com/ros-visualization/rviz.git (Accessed 28 March 2023)
[21] N. Zivkovic, J. Vidakovic, S. Mitrovic, M. Lazarevic, Implementation of Dual Quaternion- based Robot Forward Kinematics Algorithm in ROS. 11th Mediterranean Conference on Embedded Computing (MECO), 21 June 2022, Budva, Montenegro, pp.1-4. https://doi.org/10.1109/MECO55406.2022.9797160
[22] W. R. Hamilton, On Quaternions, or on a new system of imaginaries in algebra.
https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/OnQuat/ (Accessed 28 March 2023).
[23] W. R. Hamilton, Additional Applications of the theory of algebraic quaternions.
https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/QDynamics/(Accessed 28 March 2023).
[24] G. Ron, Understanding quaternions. Graphical models, 73(2), 2011: 21-49.
https://doi.org/10.1016/j.gmod.2010.10.004
[25] B. Kenwright, A Beginners Guide to Dual- Quaternions. 20th International Conference on Computer Graphics, Visualization and Computer Vision (WSCG), 26-28 June 2012, Plzen, Czech Republic, pp.1-10.
[26] J. Rooney, Wiliam Kingdon Clifford (1845-1879). In: M. Ceccarelli (Ed.), Distinguished Figures in Mechanism and Machine Science. History of Mechanism and Machine Science, 1, 2007.
https://doi.org/10.1007/978-1-4020-6366-4_4
[27] V. Brodsky, M. Shoham, Dual numbers representation of rigid body dynamics. Mechanism and Machine Theory, 34(5), 1999:693-718. https://doi.org/10.1016/S0094-114X(98)00049-4
[28] V. Kvrgic, J. Vidakovic, Efficient method for robot forward dynamics computation. Mechanism and Machine Theory, 145, 2020:103680. https://doi.org/10.1016/j.mechmachtheory.2019.103680
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0)
How to Cite
N.LJ. Zivkovic, J.Z. Vidakovic, M.P. Lazarevic, Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), 2023: pp.52–59.
https://doi.org/10.18485/aeletters.2023.8.2.2
More Citation Formats
Zivkovic, N.LJ., Vidakovic, J.Z. & Lazarevic, M.P. (2023). Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), pp.52–59. https://doi.org/10.18485/aeletters.2023.8.2.2
Nikola LJ. Zivkovic, et al. ”Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention.” Applied Engineering Letters, vol. 8, no. 2, 2023, pp. 52–59, https://doi.org/10.18485/aeletters.2023.8.2.2.
Nikola LJ. Zivkovic, Jelena Z Vidakovic, and Mihailo P Lazarevic. 2023. “Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention.” Applied Engineering Letters 8 (2): 52–59. https://doi.org/10.18485/aeletters.2023.8.2.2.
Zivkovic, N.LJ., Vidakovic, J.Z. and Lazarevic, M.P. (2023). Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), pp.52–59. doi: 10.18485/aeletters.2023.8.2.2.
FORWARD KINEMATICS ALGORITHM IN DUAL QUATERNION SPACE BASED ON DENAVIT-HARTENBERG CONVENTION
Authors:
Nikola LJ. Zivkovic1
,
,
1Lola Institute Ltd., Kneza Viseslava 70a, 11030 Belgrade, Serbia
2Faculty of Mechanical Engineering, Kraljice Marije 16, 11060 Belgrade, Serbia
Received: 31 March 2023
Revised: 26 May 2023
Accepted: 5 June 2023
Published: 30 June 2023
Abstract:
Forward kinematics is fundamental to robot design, control, and simulation. Different forward kinematics algorithms have been developed to deal with the complex geometry of a robot. This paper presents a robot forward kinematics algorithm in dual quaternion space. The presented method uses Denavit-Hartenberg (DH) convention for uniform definition of successive rotational and translational transformations in joints along the robot’s kinematic chain. This research aims to utilize the advantages of dual quaternions and DH convection for forward kinematics computation and make the algorithm, which is compact, intuitive, numerically robust, and computationally efficient as it uses the minimal number of parameters required for the computation, suitable for implementation in ROS and similar software. The algorithm is verified on the 6DoF industrial robot RL15, with the symbolic equations and numerical simulation presented.
Keywords:
Forward kinematics, kinematic modelling, DH convention, coordinate frame transformations, quaternions, dual quaternions, robotics
References:
[1] B. Siciliano, O. Khatib, T. Kroger, Handbook of robotics. Springer, Berlin, 2008.
[2] J.J. Craig, Introduction to robotics: mechanics and control, 3rd ed. Pearson Prentice Hall, Upper Saddle River, USA, 2005.
[3] P. Corke, Robot Arm Kinematics. In: Robotics, Vision and Control. Springer Tracts in Advanced Robotics. Springer, 118, 2017: 193-228. https://doi.org/10.1007/978-3-319-54413-7_7
[4] K. M. Lynch, F.C. Park, Modern Robotics: Mechanics, Planning and Control. Cambridge University Press, 2017.
[5] P. Mandić, M. Lazarević, Z. Stokić, T. Šekara, Dynamic modelling and control design of seven degrees of freedom robotic arm. 6th International Congress of Serbian Society of Mechanics, 19-21 June 2017, Tara, Serbia, pp.1-8.
[6] V. Covic, M. Lazarevic, Mehanika robota, second ed. Faculty of Mechanical Engineering, Belgrade, 2021. (in Serbian)
[7] M. Lazarevic, Mechanics of human locomotor system. FME Transactions, 34(2), 2006: 105-114.
[8] C. Faria, J.L. Vilaca, S. Monteiro, W. Erlhagen, E. Bicho, Automatic Denavit-Hartenberg parameter identification for serial manipulators. 45th Annual Conference of the IEEE Industrial Electronics Society (IECON), 1 October 2019, Lisbon, Portugal, pp.610-617. https://doi.org/10.1109/IECON.2019.8927455
[9] N.A. Aspragathos, J.K. Dimitros, A Comparative Study of Three Methods for Robot Kinematics. IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics, 28(2), 1998:135-145.
https://doi.org/10.1109/3477.662755
[10] J. Funda, R.H. Taylor, R.P. Paul, On homogeneous transformations, quaternions and computational efficiency. IEEE Transactions on Robotics and Automation, 6(3), 1990: 382-388.
https://doi.org/10.1109/70.56658
[11] J.Z. Vidakovic, M.P. Lazarevic, V.M. Kvrgic, Z.Z. Dancuo, G.Z. Ferenc, Advanced quaternion forward kinematics algorithm including overview of different methods for robot kinematics. FME Transactions, 42(3), 2014:189-199. https://doi.org/10.5937/fmet1403189V
[12] B.V. Adorno, Two-arm Manipulation: From Manipulators to Enhanced Human-Robot Collaboration (Ph.D. Thesis). Université Montpellier II – Sciences et Techniques du Languedoc, Montpellier, 2011.
[13] N.T. Dantam, Robust and efficient forward, differential and inverse kinematics using dual quaternions. International Journal of Robotics Research, 40(10-11), 2021: 1087-1105.
https://doi.org/10.1177/0278364920931948
[14] S. Kucuk, Z. Bingul, Robot Kinematics: Forward and Inverse Kinematics. Industrial Robotics: Theory, Modelling and Control, 2006: 117-148. https://doi.org/10.5772/5015
[15] N.T. Dantam, Practical Exponential Coordinates Using Implicit Dual Quaternions. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, 14, 2020. https://doi.org/10.1007/978-3-030-44051-0_37
[16] E. Özgür, Y. Mezouar, Kinematic modeling and control of a robot arm using unit dual quaternions. Robotics and Autonomous Systems, 77, 2016: 66-73. https://doi.org/10.1016/j.robot.2015.12.005
[17] Stanford Artificial Intelligence Laboratory, Robotic Operating System, 2018. https://www.ros.org (Accessed 27 December 2022).
[18] A. Valverde, P. Tsiotras, Spacecraft Robot Kinematics Using Dual Quaternions. Robotics, 7(4), 2018: 64. https://doi.org/10.3390/robotics7040064
[19] M.W. Spong, S. Hutchinson, M. Vidyasagar, Forward Kinematics. in Robot Modelling and Control, 2nd ed. Wiley, 2020, p.79.
[20] Github, RViz, 2022. https://github.com/ros-visualization/rviz.git (Accessed 28 March 2023)
[21] N. Zivkovic, J. Vidakovic, S. Mitrovic, M. Lazarevic, Implementation of Dual Quaternion- based Robot Forward Kinematics Algorithm in ROS. 11th Mediterranean Conference on Embedded Computing (MECO), 21 June 2022, Budva, Montenegro, pp.1-4. https://doi.org/10.1109/MECO55406.2022.9797160
[22] W. R. Hamilton, On Quaternions, or on a new system of imaginaries in algebra.
https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/OnQuat/ (Accessed 28 March 2023).
[23] W. R. Hamilton, Additional Applications of the theory of algebraic quaternions.
https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/QDynamics/(Accessed 28 March 2023).
[24] G. Ron, Understanding quaternions. Graphical models, 73(2), 2011: 21-49.
https://doi.org/10.1016/j.gmod.2010.10.004
[25] B. Kenwright, A Beginners Guide to Dual- Quaternions. 20th International Conference on Computer Graphics, Visualization and Computer Vision (WSCG), 26-28 June 2012, Plzen, Czech Republic, pp.1-10.
[26] J. Rooney, Wiliam Kingdon Clifford (1845-1879). In: M. Ceccarelli (Ed.), Distinguished Figures in Mechanism and Machine Science. History of Mechanism and Machine Science, 1, 2007.
https://doi.org/10.1007/978-1-4020-6366-4_4
[27] V. Brodsky, M. Shoham, Dual numbers representation of rigid body dynamics. Mechanism and Machine Theory, 34(5), 1999:693-718. https://doi.org/10.1016/S0094-114X(98)00049-4
[28] V. Kvrgic, J. Vidakovic, Efficient method for robot forward dynamics computation. Mechanism and Machine Theory, 145, 2020:103680. https://doi.org/10.1016/j.mechmachtheory.2019.103680
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0)
How to Cite
N.LJ. Zivkovic, J.Z. Vidakovic, M.P. Lazarevic, Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), 2023: pp.52–59.
https://doi.org/10.18485/aeletters.2023.8.2.2
More Citation Formats
Zivkovic, N.LJ., Vidakovic, J.Z. & Lazarevic, M.P. (2023). Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), pp.52–59. https://doi.org/10.18485/aeletters.2023.8.2.2
Nikola LJ. Zivkovic, et al. ”Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention.” Applied Engineering Letters, vol. 8, no. 2, 2023, pp. 52–59, https://doi.org/10.18485/aeletters.2023.8.2.2.
Nikola LJ. Zivkovic, Jelena Z Vidakovic, and Mihailo P Lazarevic. 2023. “Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention.” Applied Engineering Letters 8 (2): 52–59. https://doi.org/10.18485/aeletters.2023.8.2.2.
Zivkovic, N.LJ., Vidakovic, J.Z. and Lazarevic, M.P. (2023). Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), pp.52–59. doi: 10.18485/aeletters.2023.8.2.2.