Skip to main content

Advertisement

Log in

Development of a compact rotary series elastic actuator with neural network-driven model predictive control implementation

  • Original Research Paper
  • Published:
Intelligent Service Robotics Aims and scope Submit manuscript

Abstract

The development and control of a rotary series elastic actuator (SEA) are investigated in this paper. First, a rotary SEA is designed with a small volume and is lightweight, where the elastic element can be used as a torque sensor. We improve the structure of this rubber material elastic element, and its characteristics are analyzed. To provide a more comprehensive description of the entire system, motor dynamics are also taken into account while establishing the entire system dynamics model. Second, a neural network-driven model predictive control (NNMPC) method is proposed for the single-link SEA system. Since a real dynamic system for the SEA is hard to establish accurately due to disturbances, uncertainties, and varying mass of the load in different applications, a simple nonlinear autoregressive neural network using the rectified linear unit as the activation function (ReLU-NARX NN) is considered to approximate the system dynamic model, based on which a model predictive controller is developed. Finally, both numerical simulations and experiments are conducted for position and torque control. The simulation and experimental results demonstrate that the proposed method is superior to the conventional PD (proportional differential) method and the traditional MPC method. For position control, the NNMPC method is shown to be more effective, that is, it can suppress residual vibrations, reduce overshoots, arrive at a steady state quickly, and robust to different loads in a range. For torque control, the control performance is also satisfactory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Algorithm 1
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Paine N, Oh S, Sentis L (2014) Design and control considerations for high-performance series elastic actuators. IEEE/ASME Trans Mechatron 19:1080–1091

    Article  Google Scholar 

  2. Shao N, Zhou Q, Shao C, Zhao Y (2021) Adaptive control of robot series elastic drive joint based on optimized radial basis function neural network. Int J Soc Robot 13:1823–1832

    Article  Google Scholar 

  3. Negrello F et al (2015) A modular compliant actuator for emerging high performance and fall-resilient humanoids, 414–420. Seoul, Korea (South

    Google Scholar 

  4. Al-Dahiree OS, Raja Ghazilla RA, Yap HJ, Osman Tokhi M, Yoong GW (2022) Modeling and dynamic performance of energy storage -rotary series elastic actuator for lumbar support exoskeleton, 208–216. Malacca, Malaysia

    Google Scholar 

  5. dos Santos WM, Caurin GA, Siqueira AA (2017) Design and control of an active knee orthosis driven by a rotary series elastic actuator. Control Eng Pract 58:307–318

    Article  Google Scholar 

  6. Zhou Y (2023) Recent advances in wearable actuated ankle-foot orthoses: Medical effects, design, and control. Proc Inst Mech Eng [H] 237:163–178 (PMID: 36515408)

    Article  Google Scholar 

  7. Zhang T, Huang H (2019) Design and control of a series elastic actuator with clutch for hip exoskeleton for precise assistive magnitude and timing control and improved mechanical safety. IEEE/ASME Trans Mechatron 24:2215–2226

    Article  Google Scholar 

  8. Zhang T, Huang H (2018) A lower-back robotic exoskeleton: industrial handling augmentation used to provide spinal support. IEEE Robot Autom Mag 25:95–106

    Article  Google Scholar 

  9. Mrad F, Ahmad S (1992) Control of flexible joint robots. Robotics and computer-integrated manufacturing 9:137–144

    Article  Google Scholar 

  10. Weigand J, Gafur N, Ruskowski M (2021) Flatness based control of an industrial robot joint using secondary encoders. Robot Comput Integr Manufact 68:102039

    Article  Google Scholar 

  11. Qian Y, Han S, Aguirre-Ollinger G, Fu C, Yu H (2022) Design, modeling, and control of a reconfigurable rotary series elastic actuator with nonlinear stiffness for assistive robots. Mechatronics 86:102872

    Article  Google Scholar 

  12. Calanca A, Muradore R, Fiorini P (2017) Impedance control of series elastic actuators: Passivity and acceleration-based control. Mechatronics 47:37–48

    Article  Google Scholar 

  13. Yu H, Huang S, Chen G, Thakor N (2013) Control design of a novel compliant actuator for rehabilitation robots. Mechatronics 23:1072–1083

    Article  Google Scholar 

  14. Baldoni A et al (2018) Design and validation of a miniaturized sea transmission system. Mechatronics 49:149–156

    Article  Google Scholar 

  15. Toubar H et al (2022) Design, modeling, and control of a series elastic actuator with discretely adjustable stiffness (seadas). Mechatronics 86:102863

    Article  Google Scholar 

  16. Fotuhi MJ, Bingul Z (2021) Fuzzy torque trajectory control of a rotary series elastic actuator with nonlinear friction compensation. ISA Trans 115:206–217

    Article  Google Scholar 

  17. Cappello L et al (2019) Multistable series elastic actuators: design and control. Robot Auton Syst 118:167–178

    Article  Google Scholar 

  18. Ai L, Men X, Zhou T, Xiao X, Guo Z (2021) Design and control of a cable-driven series elastic actuator for exoskeleton. Wuhan, China, pp 335–339

  19. Seo H-T, Park J-I, Park J (2021) A compact series elastic element using a rubber compression mechanism. Rev Sci Instrum 92:065004

    Article  Google Scholar 

  20. Lee W (1990) Designing articulated legs for running machines. Ph.D. thesis, Massachusetts Institute of Technology

  21. Rollinson D, Ford S, Brown B, Choset H (2013) Design and modeling of a series elastic element for snake robots, vol 56123, V001T08A002 (Palo Alto, California, USA)

  22. Petit F, Lakatos D, Friedl W, Albu-Schäffer A (2012) Dynamic trajectory generation for serial elastic actuated robots. In: Proceedings of 10th IFAC symposium on robot control, vol 45, pp 636–643

  23. Sun L, Yin W, Wang M, Liu J (2017) Position control for flexible joint robot based on online gravity compensation with vibration suppression. IEEE Trans Industr Electron 65:4840–4848

    Article  Google Scholar 

  24. Spong MW (1987) Modeling and control of elastic joint robots. J Dyn Syst Meas Contr 109:310–318

    Article  Google Scholar 

  25. Tomei P (1991) A simple pd controller for robots with elastic joints. IEEE Trans Autom Control 36:1208–1213

    Article  MathSciNet  Google Scholar 

  26. De Luca A, Siciliano B, Zollo L (2005) Pd control with on-line gravity compensation for robots with elastic joints: theory and experiments. Automatica 41:1809–1819

    Article  MathSciNet  Google Scholar 

  27. Yin W, Sun L, Wang M, Liu J (2018) Nonlinear state feedback position control for flexible joint robot with energy shaping. Robot Auton Syst 99:121–134

    Article  Google Scholar 

  28. Abbasimoshaei A, Mohammadimoghaddam M, Kern TA (2020) Adaptive fuzzy sliding mode controller design for a new hand rehabilitation robot. Springer, pp 506–517

  29. Bae J, Kong K, Tomizuka M (2011) Gait phase-based control for a rotary series elastic actuator assisting the knee joint. J Med Devices 5:031010

    Article  Google Scholar 

  30. Soltanpour MR, Moattari M (2019) Voltage based sliding mode control of flexible joint robot manipulators in presence of uncertainties. Robot Autonom Syst 118:204–219

    Article  Google Scholar 

  31. Lanh LAK, Duong VT, Nguyen HH, Kim SB, Nguyen TT (2023) Hybrid adaptive control for series elastic actuator of humanoid robot. Int J Intell Unmanned Syst 11:359–377

    Article  Google Scholar 

  32. Laffranchi M et al (2014) Development and control of a series elastic actuator equipped with a semi active friction damper for human friendly robots. Robot Auton Syst 62:1827–1836

    Article  Google Scholar 

  33. Calanca A, Fiorini P (2014) Human-adaptive control of series elastic actuators. Robotica 32:1301–1316

    Article  Google Scholar 

  34. Jin M, Lee J, Tsagarakis NG (2017) Model-free robust adaptive control of humanoid robots with flexible joints. IEEE Trans Industr Electron 64:1706–1715

    Article  Google Scholar 

  35. Ma H, Zhou Q, Li H, Lu R (2022) Adaptive prescribed performance control of a flexible-joint robotic manipulator with dynamic uncertainties. IEEE Trans Cybern 52:12905–12915

    Article  Google Scholar 

  36. Pan Y, Li X, Wang H, Yu H (2018) Continuous sliding mode control of compliant robot arms: a singularly perturbed approach. Mechatronics 52:127–134

    Article  Google Scholar 

  37. Tarn T-J, Bejczy A, Yun X, Li Z (1991) Effect of motor dynamics on nonlinear feedback robot arm control. IEEE Trans Robot Autom 7:114–122

    Article  Google Scholar 

  38. Peng J, Ding S, Yang Z, Xin J (2020) Adaptive neural impedance control for electrically driven robotic systems based on a neuro-adaptive observer. Nonlinear Dyn 100:1359–1378

    Article  Google Scholar 

  39. Ding S, Peng J, Zhang H, Wang Y (2021) Neural network-based adaptive hybrid impedance control for electrically driven flexible-joint robotic manipulators with input saturation. Neurocomputing 458:99–111

    Article  Google Scholar 

  40. Vantilt J et al (2019) Model-based control for exoskeletons with series elastic actuators evaluated on sit-to-stand movements. J Neuroeng Rehabil 16:65

    Article  Google Scholar 

  41. Su H et al (2020) Improved recurrent neural network-based manipulator control with remote center of motion constraints: Experimental results. Neural Netw 131:291–299

    Article  Google Scholar 

  42. Tang Q, Chu Z, Qiang Y, Wu S, Zhou Z (2020) Trajectory tracking of robotic manipulators with constraints based on model predictive control. Italy, Rome, pp 23–28

  43. Wilson J, Charest M, Dubay R (2016) Non-linear model predictive control schemes with application on a 2 link vertical robot manipulator. Robot Comput Integrat Manufact 41:23–30

    Article  Google Scholar 

  44. Faroni M, Beschi M, Bianco Guarino Lo C, Visioli A (2020) Predictive joint trajectory scaling for manipulators with kinodynamic constraints. Control Eng Pract 95:104264

    Article  Google Scholar 

  45. Li S, Shi Y, Hu L, Sun Z (2021) A generalized model predictive control method for series elastic actuator driven exoskeleton robots. Comput Electric Eng 94:107328

    Article  Google Scholar 

  46. Bolívar-Nieto EA, Summers T, Gregg RD, Rezazadeh S (2021) A convex optimization framework for robust-feasible series elastic actuators. Mechatronics 79:102635

    Article  Google Scholar 

  47. Carron A et al (2019) Data-driven model predictive control for trajectory tracking with a robotic arm. IEEE Robot Autom Lett 4:3758–3765

    Article  Google Scholar 

  48. Rupert L, Hyatt P, Killpack MD (2015) Comparing model predictive control and input shaping for improved response of low-impedance robots, pp 256–263

  49. Scokaert P, Rawlings J, Meadows E (1997) Discrete-time stability with perturbations: application to model predictive control. Automatica 33:463–470

    Article  MathSciNet  Google Scholar 

  50. Goodwin GC, Kong H, Mirzaeva G, Seron MM (2014) Robust model predictive control: reflections and opportunities. J Control Decis 1:115–148

    Article  Google Scholar 

  51. Heirung TAN, Ydstie BE, Foss B (2017) Dual adaptive model predictive control. Automatica 80:340–348

    Article  MathSciNet  Google Scholar 

  52. Zhu B, Xia X (2016) Adaptive model predictive control for unconstrained discrete-time linear systems with parametric uncertainties. IEEE Trans Autom Control 61:3171–3176

  53. Yan Y et al (2018) Generalized dynamic predictive control for nonparametric uncertain systems with application to series elastic actuators. IEEE Trans Industr Inf 14:4829–4840

    Article  Google Scholar 

  54. Floriano BR, Vargas AN, Ishihara JY, Ferreira HC (2022) Neural-network-based model predictive control for consensus of nonlinear systems. Eng Appl Artif Intell 116:105327

    Article  Google Scholar 

  55. Hyatt P, Killpack MD (2020) Real-time nonlinear model predictive control of robots using a graphics processing unit. IEEE Robot Autom Lett 5:1468–1475

    Article  Google Scholar 

  56. Thuruthel TG, Falotico E, Renda F, Laschi C (2018) Model-based reinforcement learning for closed-loop dynamic control of soft robotic manipulators. IEEE Trans Rob 35:124–134

    Article  Google Scholar 

  57. Lenz I, Knepper RA, Saxena A (2015) Deepmpc: learning deep latent features for model predictive control. Italy, Rome

    Google Scholar 

  58. Li J, Yuan Z, Dong S, Sang X, Kang J (2022) A learning-based model predictive control scheme and its application in biped locomotion. Eng Appl Artif Intell 115:105246

    Article  Google Scholar 

  59. Abbasimoshaei A, Chinnakkonda Ravi AK, Kern TA (2023) Development of a new control system for a rehabilitation robot using electrical impedance tomography and artificial intelligence. Biomimetics 8

  60. Huang A-C, Chen Y-C (2004) Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties. IEEE Trans Control Syst Technol 12:770–775

    Article  Google Scholar 

  61. Slotine J-JE, Li W (1991) Applied nonlinear control, vol 199. Prentice hall Englewood Cliffs, NJ

    Google Scholar 

  62. Leontaritis I, Billings SA (1985) Input-output parametric models for non-linear systems part I: deterministic non-linear systems. Int J Control 41:303–328

    Article  Google Scholar 

  63. Lin T, Horne BG, Giles CL (1998) How embedded memory in recurrent neural network architectures helps learning long-term temporal dependencies. Neural Netw 11:861–868

    Article  Google Scholar 

  64. Camacho EF, Alba CB (2013) Model predictive control. Springer science and business media)

  65. Loshchilov I, Hutter F (2018) Fixing weight decay regularization in adam. Vancouver, Canada

  66. Thuruthel TG, Falotico E, Renda F, Laschi C (2019) Model-based reinforcement learning for closed-loop dynamic control of soft robotic manipulators. IEEE Trans Rob 35:124–134

    Article  Google Scholar 

  67. Kumar R, Srivastava S, Gupta JRP, Mohindru A (2019) Comparative study of neural networks for dynamic nonlinear systems identification. Soft Comput 23:101–114

    Article  Google Scholar 

  68. Fu J, Liao G, Yu M, Li P, Lai J (2016) Narx neural network modeling and robustness analysis of magnetorheological elastomer isolator. Smart Mater Struct 25:125019

    Article  Google Scholar 

Download references

Funding

The work is supported by the National Natural Science Foundation of China under Grant 62173118 and Shenzhen Key Laboratory of Control Theory and Intelligent Systems under grant ZDSYS20220330161800001.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhiyun Lin.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, A., Lin, Z., Wang, B. et al. Development of a compact rotary series elastic actuator with neural network-driven model predictive control implementation. Intel Serv Robotics 17, 641–660 (2024). https://doi.org/10.1007/s11370-024-00522-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11370-024-00522-9

Keywords