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Data-driven physical law learning model for chaotic robot dynamics prediction

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Abstract

A robot control system is a multivariable, nonlinear automatic control system, as well as a dynamic coupling system. To address the difficult problem of data prediction under a chaotic system, a data-driven physical law learning model (DPM) is proposed, which can learn the underlying physical rules that the data follow. First, two independent autoencoder neural networks are stacked and merged to explore potential physical rules. Then, a virtual Hamiltonian represented as the sum of kinetic energy and potential energy of chaotic data is introduced. Combined with the Hamiltonian equation, the learned Hamiltonian is transformed into a symplectic transformation, whose first-order differential w.r.t. the generalized coordinates and momentum can be regarded as a time-dependent prediction instead of a direct numerical approximation. Finally, the DPM continuously learns implicit Hamiltonian equations from chaotic data until it can fit the law of phase space motion in a chaotic environment. The experimental results show that the model has a better robot dynamics prediction ability in long-term chaotic systems than the existing SOTA methods.

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References

  1. Featherstone R, Orin DE (2016) Dynamics[M]. Springer Handbook of Robotics. Springer, Cham, pp 37–66

    Google Scholar 

  2. Godois LM, Adamatti DF, Emmendorfer LR (2020) A multi-agent-based algorithm for data clustering. Prog Artif Intell 9(4):305–313

    Article  Google Scholar 

  3. Wei C, Hindriks KV, Jonker CM (2016) Dynamic task allocation for multi-robot search and retrieval tasks. Appl Intell 45(2):383–401

    Article  Google Scholar 

  4. Sousa CD, Cortesao R (2019) Inertia tensor properties in robot dynamics identification: A linear matrix inequality approach[J]. IEEE Trans Mechatron 24(1):406–411

    Article  Google Scholar 

  5. Saadatzi M, Long DC, Celik O (2019) Comparison of human-robot interaction torque estimation methods in a wrist rehabilitation exoskeleton[J]. J Intell Robot Syst 94(3-4):565–581

    Article  Google Scholar 

  6. Miclosina CO, Cojocaru V, Korka ZI (2015) Dynamic simulation of a parallel topology robot operation[J]. Appl Mech Mater 762:107–112

    Article  Google Scholar 

  7. Xu D, Wu X, Chen YL, et al. (2015) Online dynamic gesture recognition for human robot interaction[J]. J Intell Robot Syst 77(3-4):583–596

    Article  Google Scholar 

  8. Pan H, Dai J, Chen L, et al. (2014) Multi-robot parallel dynamic bounding volume hierarchy tree collision detection algorithm[J]. J Computer-Aided Des Comput Graphics 26(11):1948–1956

    Google Scholar 

  9. Vanraj GD, Saini A, et al. (2016) Intelligent predictive maintenance of dynamic systems using condition monitoring and signal processing techniques - A review[C]. In: 2016 International conference on advances in computing, communication, & automation (ICACCA) (Spring), IEEE

  10. Liu Z, Wang X, Cai Y, et al. (2020) Dynamic risk assessment and active response strategy for industrial human-robot collaboration[J]. Comput Ind Eng 141:106302

    Article  Google Scholar 

  11. Sciavicco L, Siciliano B, Villani L (1995) Lagrange and newton-euler dynamic modeling of a gear-driven robot manipulator with inclusion of motor inertia effects[J]. Adv Robot 10(3):317– 334

    Article  Google Scholar 

  12. Lu S, Zhao J, Jiang L, et al. (2017) Solving the time-jerk optimal trajectory planning problem of a robot using augmented lagrange constrained particle swarm optimization[J]. Math Probl Eng 2017(pt.6):1–10

    Article  MathSciNet  MATH  Google Scholar 

  13. Morabito F, Teel AR, Zaccarian L (2004) Nonlinear antiwindup applied to Euler-Lagrange systems[J]. IEEE Trans Robot Autom 20(3):526–537

    Article  Google Scholar 

  14. Rahmani B, Belkheiri M (2019) Adaptive neural network output feedback control for flexible multi-link robotic manipulators[J]. Int J Control 92(10):2324–2338

    Article  MathSciNet  MATH  Google Scholar 

  15. Razzaghi P, Al Khatib E, Hurmuzlu Y (2019) Nonlinear dynamics and control of an inertially actuated jumper robot[J]. Nonlinear Dyn 97(1):161–176

    Article  MATH  Google Scholar 

  16. Lu Y, Yan D, Zhou M, et al. (2017) Maximum likelihood parameter estimation of dynamic systems by heuristic swarm search[J]. Intell Data Anal 21(1):97–116

    Article  Google Scholar 

  17. Borovykh A, Oosterlee CW, Bohté SM (1020) Generalization in fully-connected neural networks for time series forecasting[J]. J Comput Sci 36(10):2019

    MathSciNet  Google Scholar 

  18. Jiang Y, Chen J, Zhou H, et al. (2021) Residual learning of the dynamics model for feeding system modelling based on dynamic nonlinear correlate factor analysis. Appl Intell 51:5067–5080. https://doi.org/10.1007/s10489-020-02096-2

    Article  Google Scholar 

  19. Wang Z, Goldsmith P, Gu J (2009) Adaptive trajectory tracking control for Euler-Lagrange systems with application to robot manipulators[J]. Control Intell Syst 37(1):46–56

    MathSciNet  MATH  Google Scholar 

  20. Valverde A, Tsiotras P (2018) Modeling of spacecraft-mounted robot dynamics and control using dual quaternions[C]. In: IEEE Annual american control conference, 2018 pp 670–675

  21. Liang B, Li T, Chen Z, et al. (2018) Robot arm dynamics control based on deep learning and physical simulation[C]. In: 2018 37th Chinese control conference (CCC). IEEE, pp 2921–2925

  22. Bae HJ, Jin M, Suh J, et al. (2017) Control of robot manipulators using time-delay estimation and fuzzy logic systems[J]. J Electr Eng Technol 12(3):1271–1279

    Article  Google Scholar 

  23. Sun F, Sun Z, Woo PY (2001) Neural network-based adaptive controller design of robotic manipulators with an observer[J]. IEEE Trans Neural Netw 12(1):54–67

    Article  MathSciNet  Google Scholar 

  24. Mbede JB, Wei W, Zhang Q (2001) Fuzzy and recurrent neural network motion control among dynamic obstacles for robot manipulators[J]. J Intell Robot Syst 30(2):155–177

    Article  MATH  Google Scholar 

  25. Chu M, Song JZ, Jia QX, et al. (2013) Intelligent control for model-free robot joint with dynamic friction using wavelet neural networks. J Theor Appl Inf Technol 50(1):167–173

    Google Scholar 

  26. Saleki A, Fateh MM (2020) Model-free control of electrically driven robot manipulators using an extended state observer[J]. Comput Electr Eng 87:106768

    Article  Google Scholar 

  27. Asl HJ, Janabi-Sharifi F (2017) Adaptive neural network control of cable-driven parallel robots with input saturation[J]. Eng Appl Artif Intell 65:252–260

    Article  Google Scholar 

  28. Su H, Qi W, Yang C, et al. (2020) Deep neural network approach in robot tool dynamics identification for bilateral teleoperation[J]. IEEE Robot Autom Lett 5(2):2943–2949

    Article  Google Scholar 

  29. Luan F, Na J, Huang Y, et al. (2019) Adaptive neural network control for robotic manipulators with guaranteed finite-time convergence[J]. Neurocomputing 337:153–164

    Article  Google Scholar 

  30. Karpatne A, Atluri G, Faghmous JH, et al. (2017) Theory-guided data science: A new paradigm for scientific discovery from data[J]. IEEE Trans Knowl Data Eng 29(10):2318–2331

    Article  Google Scholar 

  31. Zhang P, Shen H, Zhai H (2018) Machine learning topological invariants with neural networks[J]. Phys Rev Lett 120(6): 066401

    Article  Google Scholar 

  32. Moret-Bonillo V (2018) Emerging technologies in artificial intelligence: quantum rule-based systems[J]. Prog Artif Intell 7(2):155–166

    Article  Google Scholar 

  33. Doan N, Polifke W, Magri L (2020) Physics-informed echo state networks[J]. J Comput Sci 47:101237

    Article  MathSciNet  Google Scholar 

  34. Dominguez DRC, Korutcheva E (2000) Three-state neural network: From mutual information to the Hamiltonian[J]. Phys Rev 62(2 Pt B):2620–2628

    Google Scholar 

  35. Yang B, Li HG, Sha XP, et al. (2012) A speed observer for robot based on hamiltonian theory and immersion & invariance[J]. Acta Automatica Sinica 38(11):1757

    Article  MathSciNet  Google Scholar 

  36. Rabinowitz PH (2010) Periodic solutions of Hamiltonian systems and related topics[J]. Commun Pure Appl Math 31(2):157– 184

    Article  Google Scholar 

  37. Leimkuhler BJ, Skeel RD (1994) Symplectic numerical integrators in constrained hamiltonian systems[J]. J Comput Phys 112(1):117–125

    Article  MathSciNet  MATH  Google Scholar 

  38. Greydanus SJ, Dzamba M, Yosinski J (2019) Hamiltonian neural networks. In: 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada

  39. Bertalan T, Dietrich F, Mezic I et al (2019) On learning Hamiltonian systems from data[J]. Chaos: An Interdiscip J Nonlinear Sci 29(12):121107

    Article  MathSciNet  Google Scholar 

  40. Miller ST, Lindner JF, Choudhary A, Sinha S, Ditto WL (2020) The scaling of physics-informed machine learning with data and dimensions. Chaos, Solitons & Fractals: X 5:100046

    Article  Google Scholar 

  41. Shirvany Y, Hayati M, Moradian R (2009) Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations[J]. Appl Soft Comput 9 (1):20–29

    Article  Google Scholar 

Download references

Acknowledgments

This paper is supported by the Nanjing Institute of Technology High-level Scientific Research Foundation for the introduction of talent (No. YKJ201918), the Natural Science Foundation Youth Fund of Jiangsu Province of China(No.BK20210931). The Natural Science Fondation of the Jiangsu Higher Education Institutions of China (No. 20KJB510049), and is partially supported by the National Natural Science Foundation of China (No. 61902179).

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  1. School of Automation, Nanjing Institute of Technology, Nanjing, China

    Kui Qian & Lei Tian

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  1. Kui Qian
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  2. Lei Tian
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Correspondence to Kui Qian.

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Qian, K., Tian, L. Data-driven physical law learning model for chaotic robot dynamics prediction. Appl Intell 52, 11160–11171 (2022). https://doi.org/10.1007/s10489-021-02902-5

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