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Open Access

Dynamic Modeling of Robotic Manipulator via an Augmented Deep Lagrangian Network

School of Automation, Beijing Information Science and Technology University, Beijing 100192, China
Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
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Abstract

Learning the accurate dynamics of robotic systems directly from the trajectory data is currently a prominent research focus. Recent physics-enforced networks, exemplified by Hamiltonian neural networks and Lagrangian neural networks, demonstrate proficiency in modeling ideal physical systems, but face limitations when applied to systems with uncertain non-conservative dynamics due to the inherent constraints of the conservation laws foundation. In this paper, we present a novel augmented deep Lagrangian network, which seamlessly integrates a deep Lagrangian network with a standard deep network. This fusion aims to effectively model uncertainties that surpass the limitations of conventional Lagrangian mechanics. The proposed network is applied to learn inverse dynamics model of two multi-degree manipulators including a 6-dof UR-5 robot and a 7-dof SARCOS manipulator under uncertainties. The experimental results clearly demonstrate that our approach exhibits superior modeling precision and enhanced physical credibility.

Keywords

deep Lagrangian networknonconservative dynamicsmulti-degree manipulatorinverse dynamic modeling

References

[1]

M. Spong, K. Khorasani, and P. Kokotovic, An integral manifold approach to the feedback control of flexible joint robots, IEEE J. Robot. Auto. , vol. RA-3, no. 4, pp. 291–300, 1987.
Crossref Google Scholar
[2]

S. V. Shah, S. K. Saha, and J. K. Dutt, Modular framework for dynamic modeling and analyses of legged robots, Mech. Mach. Theory , vol. 49, pp. 234–255, 2012.
Crossref Google Scholar
[3]

M. Jafarinasab, S. Sirouspour, and E. Dyer, Model-based motion control of a robotic manipulator with a flying multirotor base, IEEE-ASME Trans. Mechatron. , vol. 24, no. 5, pp. 2328–2340, 2019.
Crossref Google Scholar
[4]
K. Hitzler, F. Meier, S. Schaal, and T. Asfour, Learning and adaptation of inverse dynamics models: A comparison, in Proc. 2019 IEEE-RAS 19th Int. Conf. Humanoids Robot. (Humanoids), Toronto, Canada, 2019, pp. 491–498.
Crossref
[5]
M. Jansen, Learning an accurate neural model of the dynamics of a typical industrial robot, https://www.semanticscholar.org/paper/Learning-an-Accurate-Neural-Model-of-the-Dynamics-a-Jansen/28f6446fd74986bad9b179e21d6645faf5b88e22, 1994.
[6]
D. Nguyen-Tuong, J. Peters, M. Seeger, and B. Schlkopf, Learning inverse dynamics: A comparison, in Proc. 16th Eur. Symp. Artificial Neural Networks, Bruges, Belgium, 2008, pp. 13–18.
[7]
S. Greydanus, M. Dzamba, and J. Yosinski, Hamiltonian neural networks, in Proc. 33rd Int. Conf. Neural Inf. Process. Syst., Vancouver, Canada, 2019, pp. 15379–15389.
[8]

M. Raissi, Deep hidden physics models: Deep learning of nonlinear partial differential equations, J. Mach. Learn. Res. , vol. 19, no. 1, pp. 932–955, 2018.
Google Scholar
[9]
D. Y. Zhong, B. Dey, and A. Chakraborty, Symplectic ode-net: Learning hamiltonian dynamics with control, arXiv preprint arXiv:1909.12077, 2019.
[10]
S. Saemundsson, A. Terenin, K. Hofmann, and M. Deisenroth, Variational integrator networks for physically structured embeddings, arXiv preprint arXiv:1910.09349, 2020.
[11]
M. Lutter, R. Christian, and J. Peters, Deep Lagrangian Networks: Using physics as model prior for deep learning, arXiv preprint arXiv: 1907.04490, 2018.
[12]
M. Lutter, K. Listmann, and J. Peters, Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems, in 2019 IEEE/RSJ Int. Conf. Intel. Robots Sys. (IROS), Macau, China, 2019.
Crossref
[13]

M. Lutter, and J. Peters, Combining physics and deep learning to learn continuous-time dynamics models, Int. J. Robot. Res. , vol. 42, no. 3, pp. 83–107, 2023.
Crossref Google Scholar
[14]

X. Li, W. Shang, and S. Cong, Offline reinforcement learning of robotic control using deep kinematics and dynamics, IEEE-ASME Trans. Mechatron. , 2023.
Crossref Google Scholar
[15]
J. K. Gupta, K. Menda, Z. Manchester, and M. J. Kochenderfer, A general framework for structured learning of mechanical systems, arXiv preprint arXiv: 1902.08705, 2019.
[16]
M. Lutter, J. Silberbauer, J. Watson, and J. Peters, A differentiable Newton Euler algorithm for multi-body model learning, arXiv preprint arXiv:2010.09802 , 2020.
[17]
L. Liu, G. Zuo, J. Li, and J. Li, Dynamics modeling with realistic constraints for trajectory tracking control of manipulator, in Proc. 2022 IEEE Int. Conf. Real-time Comput. Robot. (RCAR), Guiyang, China, 2022, pp. 99–104.
Crossref
[18]
C. Ritter, Deep learning of inverse dynamic models, Master thesis, Technical University of Darmstadt, Darmstadt, Germany, 2018.
[19]

Z. Liu, B. Wang, Q. Meng, W. Chen, M. Tegmark, and T. Y. Liu, Machine-learning nonconservative dynamics for new-physics detection, Phys. Rev. E , vol. 104, no. 5, p. 055302, 2021.
Crossref Google Scholar
[20]
M. Cranmer, S. Greydanus, S. Hoyer, P. Battaglia, D. Spergel, and S. Ho, Lagrangian neural networks, arXiv preprint arXiv: 2003.04630 , 2020.
[21]
C. Huang and W. Yang, Inverse dynamics modeling of robots based on sparse spectral gaussian process regression, J. Phys. Conf. Ser., vol. 2010, no. 1, p. 012136, 2021.
Crossref
[22]

D. Nguyen-Tuong and J. Peters, Model learning for robot control: A survey, Cognit. Process. , vol. 12, no. 4, pp. 319–340, 2011.
Crossref Google Scholar
[23]

A. Wahrburg, J. Bös, K. D. Listmann, F. Dai, B. Matthias, and H. Ding, Motor-current-based estimation of cartesian contact forces and torques for robotic manipulators and its application to force control, IEEE Trans. Autom. Sci. Eng. , vol. 15, no. 2, pp. 879–886, 2017.
Crossref Google Scholar
[24]
B. Bona and M. Indri, Friction compensation in robotics: An overview, in Proc. 44th IEEE Conf. Decision Control, Seville, Spain, 2005, pp. 4360–4367.
[25]
A. Albu-Schäffer, Control of robots with elastic joints using the example of DLR lightweight arms, Ph.D. dissertation, Technical University of Munich, Munich, Germany, 2002.
[26]

D. Q. Cao and R. W. Tucker, Nonlinear dynamics of elastic rods using the Cosserat theory: Modelling and simulation, Int. J. Solids Struct. , vol. 45, no. 2, pp. 460–477, 2008.
Crossref Google Scholar
[27]

P. K. Khsla, Categorization of parameters in the dynamic robot model, IEEE Trans. Robot. Autom. , vol. 5, no. 3, pp. 261–268, 1989.
Crossref Google Scholar
[28]
J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, and S. Wanderman-Milne, JAX: Composable Transformations of Python+ NumPy Programs (v0. 2.5), Software available from https://github.com/google/jax, 2018.
[29]
E. Coumans and Y. Bai, PyBullet quickstart guide, https://usermanual.wiki/Doc-ument/PyBullet20Quickstart20Guide, 2023.
[30]

J. Y. Luh, M. W. Walker, and R. P. Paul, On-line computational scheme for mechanical manipulators, J. Dyn. Sys., Meas., Control , vol. 102, no. 2, pp. 69–76, 1980.
Crossref Google Scholar
[31]
S. Vijayakumar and S. Schaal, Locally weighted projection regression: An O(n) algorithm for incremental real time learning in high dimensional space, https://www.semanticscholar.org/paper/Locally-Weighted-Projection-Regression-:-An-O(n)-in-Vijayakumar-Schaal/749c81cc86c3a946424332f3866474b4a1e8014f3, 2000.
Tsinghua Science and Technology
Volume 29 Issue 5,
October 2024
Pages 1604-1614
DOI: 10.26599/TST.2024.9010011
Cite this article:
Wu S, Li Z, Chen W, et al. Dynamic Modeling of Robotic Manipulator via an Augmented Deep Lagrangian Network. Tsinghua Science and Technology, 2024, 29(5): 1604-1614. https://doi.org/10.26599/TST.2024.9010011

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Received: 02 September 2023
Revised: 04 December 2023
Accepted: 09 January 2024
Published: 02 May 2024
© The Author(s) 2024.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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