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.



























Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Paine N, Oh S, Sentis L (2014) Design and control considerations for high-performance series elastic actuators. IEEE/ASME Trans Mechatron 19:1080–1091
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
Negrello F et al (2015) A modular compliant actuator for emerging high performance and fall-resilient humanoids, 414–420. Seoul, Korea (South
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
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
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)
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
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
Mrad F, Ahmad S (1992) Control of flexible joint robots. Robotics and computer-integrated manufacturing 9:137–144
Weigand J, Gafur N, Ruskowski M (2021) Flatness based control of an industrial robot joint using secondary encoders. Robot Comput Integr Manufact 68:102039
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
Calanca A, Muradore R, Fiorini P (2017) Impedance control of series elastic actuators: Passivity and acceleration-based control. Mechatronics 47:37–48
Yu H, Huang S, Chen G, Thakor N (2013) Control design of a novel compliant actuator for rehabilitation robots. Mechatronics 23:1072–1083
Baldoni A et al (2018) Design and validation of a miniaturized sea transmission system. Mechatronics 49:149–156
Toubar H et al (2022) Design, modeling, and control of a series elastic actuator with discretely adjustable stiffness (seadas). Mechatronics 86:102863
Fotuhi MJ, Bingul Z (2021) Fuzzy torque trajectory control of a rotary series elastic actuator with nonlinear friction compensation. ISA Trans 115:206–217
Cappello L et al (2019) Multistable series elastic actuators: design and control. Robot Auton Syst 118:167–178
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
Seo H-T, Park J-I, Park J (2021) A compact series elastic element using a rubber compression mechanism. Rev Sci Instrum 92:065004
Lee W (1990) Designing articulated legs for running machines. Ph.D. thesis, Massachusetts Institute of Technology
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)
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
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
Spong MW (1987) Modeling and control of elastic joint robots. J Dyn Syst Meas Contr 109:310–318
Tomei P (1991) A simple pd controller for robots with elastic joints. IEEE Trans Autom Control 36:1208–1213
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
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
Abbasimoshaei A, Mohammadimoghaddam M, Kern TA (2020) Adaptive fuzzy sliding mode controller design for a new hand rehabilitation robot. Springer, pp 506–517
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
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
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
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
Calanca A, Fiorini P (2014) Human-adaptive control of series elastic actuators. Robotica 32:1301–1316
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
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
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
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
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
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
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
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
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
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
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
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
Bolívar-Nieto EA, Summers T, Gregg RD, Rezazadeh S (2021) A convex optimization framework for robust-feasible series elastic actuators. Mechatronics 79:102635
Carron A et al (2019) Data-driven model predictive control for trajectory tracking with a robotic arm. IEEE Robot Autom Lett 4:3758–3765
Rupert L, Hyatt P, Killpack MD (2015) Comparing model predictive control and input shaping for improved response of low-impedance robots, pp 256–263
Scokaert P, Rawlings J, Meadows E (1997) Discrete-time stability with perturbations: application to model predictive control. Automatica 33:463–470
Goodwin GC, Kong H, Mirzaeva G, Seron MM (2014) Robust model predictive control: reflections and opportunities. J Control Decis 1:115–148
Heirung TAN, Ydstie BE, Foss B (2017) Dual adaptive model predictive control. Automatica 80:340–348
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
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
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
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
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
Lenz I, Knepper RA, Saxena A (2015) Deepmpc: learning deep latent features for model predictive control. Italy, Rome
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
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
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
Slotine J-JE, Li W (1991) Applied nonlinear control, vol 199. Prentice hall Englewood Cliffs, NJ
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
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
Camacho EF, Alba CB (2013) Model predictive control. Springer science and business media)
Loshchilov I, Hutter F (2018) Fixing weight decay regularization in adam. Vancouver, Canada
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
Kumar R, Srivastava S, Gupta JRP, Mohindru A (2019) Comparative study of neural networks for dynamic nonlinear systems identification. Soft Comput 23:101–114
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
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
Corresponding author
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.
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11370-024-00522-9