目的：估计肘关节角度和提高模型的速度和精度。方法：建立并研究基于表面肌电信号（Surface electromyogram，sEMG） 的 Elman 神 经 网 络（Elman neural network，ENN）， 通 过 在 肱 二 头 肌（Biceps muscle，BM）和肱三头肌（Triceps muscle，TM）的皮肤表面上放置电极来采集 sEMG 信号，并通过惯性测量单元（Inertial measurement unit，IMU）记录实际的肘关节角度。结果：通过实验结果以及基于模型阶数和隐层神经元数量的参数讨论， 进一步证明了 ENN 可达到的最小均方根（Root mean square，RMS）误差为 18.1899 度。结论：在最优的参数下应用ENN估计肘关节角度时，均方根误差达到了可控范围。理论分析和实验结果都证明 ENN在估计关节角度方面是有效的。

Objective: To estimate the elbow joint angle and improve the rapidity and precision of the model. Methods: The elman neural network (ENN) based on surface electromyogram (sEMG) was established and investigated. The sEMG signals were collected by the electrodes placed on the skin surfaces of biceps muscle (BM) and triceps muscle (TM), and the actual elbow joint angle was recorded by an inertial measurement unit (IMU). Results: Theoretical analysis indicates that the ENN is feasible to be employed for estimating the elbow joint angle. Experimental results and the parameter discussion based on the model order and the number of hidden layer neurons further indicate that the minimum RMS error of ENN is 18.1899 degree. Conclusion: The RMS error is controllable when the ENN is used to estimate the elbow joint angle under the optimal parameter. Theoretical analysis and experimental results shows that the ENN is effective in estimation of joint angles.

收稿日期：2020-05-17  录用日期：2020-08-14

Received Date: 2020-05-17  Accepted Date: 2020-08-14

基金项目：国家自然科学基金项目（6187330）；中国博士后科学基金项目（2018M641784，2019T120240）；吉林省科技发展

计划项目（20200404208YY，20200201291JC）

Foundation Item: National Natural Science Foundation of China (61873304); China Postdoctoral Science Foundation Project (2018M641784, 2019T120240); Key Science and Technology Projects of Jilin Province, China (20200404208YY,

20200201291JC)

通讯作者：孙中波，E-mail：zhongbosun2012@163.com

Corresponding Author: SUN Zhongbo, Email: zhongbosun2012@163.com

引用格式：刘永柏，王刚，柴媛媛，等 . Elman 神经网络在表面肌电连续估计肘关节角度中的应用 [J]. 机器人外科学杂志（中英文），2021，2（4）：295-305.

Citation: LIU Y B, WANG G, CHAI Y Y, et al. Application of Elman neural network in continuous estimation of elbow joint angle with sEMG [J]. Chinese Journal of Robotic Surgery, 2021,2(4):295-305.

[1]Zorowitz R D, Gillard P J, Brainin M. Poststroke spasticity: sequelae and burden on stroke survivors and caregivers[J]. Neurology, 2013, 80(3): S45-S52.

[2]ZHANG Z J, ZHENG L N, YU J M, et al. Three recurrent neural networks and three numerical methods for solving a repetitive motion planning scheme of redundant robot manipulators[J]. IEEE-ASME Trans Mechatron, 2017, 22(3): 1423-1434.

[3]JIN L, LI S, LUO X, et al. Neural dynamics for cooperative control of redundant robot manipulators[J]. IEEE Trans Ind Informat, 2018, 14(9): 3812-3821.

[4] YANG C, GUO S X, BAO X Q, et al. A vascular interventional surgical robot based on surgeons operating skills[J]. Med Biol Eng Comput, 2019, 57(3):1999-2020.

[5]Kim Y M, Koo S Y, Lim J G, et al. A robust online touch pattern recognition for dynamic human-robot interaction[J]. IEEE Trans. Consum. Electron., 2010, 56(3): 1979-1987.

[6]LI Z J, SU C Y, LI G L, et al. Fuzzy approximation-based adaptive backstepping control of an exoskeleton for human upper limbs[J]. IEEE Trans Fuzzy Syst, 2015, 23(3): 555-566.

[7] Han J H, Lee S J, Kim J H, et al. Behavior hierarchy-based affordance map for recognition of human intention and its application to human-robot interaction[J]. IEEETrans Hum-Mach Syst, 2016, 46(5): 708-722.

[8]Nam Y, Koo B, Cichocki A, et al. GOM-Face: GKP, EOG, and EMG-based multimodal interface with application to humanoid robot control[J]. IEEE Trans Biomed. Eng, 2013, 61(2): 453-462.

[9] Kumar S, Sharma A. A new parameter tuning approach for enhanced motor imagery EEG signal classification[J].Med Biol Eng Comput, 2018, 56(10): 1861-1874.

[10] DUAN F, DAI L L, CHANG W N, et al. SEMG-based identification of hand motion commands using wavelet neural network combined with discrete wavelet transform[J]. IEEE Trans Ind Electron, 2015, 63(3):1923-1934.

[11] LIU Y J, LI J, TONG S, et al. Neural network control-based adaptive learning design for nonlinear systems with full-state constraints[J]. IEEE Trans Neural Netw Learn Syst, 2016, 27(7): 1562-1571.

[12] Artemiadis P K, Kyriakopoulos K J. An EMG-basedrobot control scheme robust to time-varying emg signal features[J]. IEEE T Inf Technol B, 2010, 14(3): 582-588.

[13] SHI J, ZHENG Y P, YAN Z Z. SVM for estimation of wrist angle from sonomyography and sEMG signals[C].IEEE International Conference on EMBS, 2007: 806-4809.

[14] Hill A V. The heat of shortening and the dynamic constants of muscle[J]. Proc. of Royal Society of London, Series B, 1938, 126(843): 136-195.

[15] HAN J D, DING Q C, XIONG A B, et al. A state-space EMG model for the estimation of continuous joint movements[J]. IEEE Trans Ind Electron, 2015, 62(7): 4267-4275.

[16] DING Q C, HAN J D, ZHAO X G. Continuous estimation of human multi-joint angles from semg using a state-space model[J]. IEEE Trans Neural Syst Rehabil Eng, 2016, 25(9): 1518-1528.

[17] XIA Y S, FENG G, WANG J. A primal-dual neural network for online resolving constrained kinematic redundancy in robot motion control[J]. IEEE Trans Cybern, 2005, 35(1): 54-64.

[18] JIN L, LI S, LIN B L, et al. Zeroing neural networks: a survey[J]. Neurocomputing, 2017, 267(6): 597-604.

[19] JIN L, LI S, YU JG, et al. Robot manipulator control using neural networks: a survey[J]. Neurocomputing, 2018, 285(12): 23-24.

[20] SUN Z B, LI F, ZHANG B C, et al. Different modified zeroing neural dynamics with inherent tolerance to noises for time-varying reciprocal problems: A control-theoretic approach[J]. Neurocomputing, 2019, 337:165-179.

[21] SUN Z B, LIU Y B, WEI L, et al. Two dtznn models of O (τ2) pattern for online solving dynamic system of linear equations: application to manipulator motion generation[J]. IEEE Access, 2020, 8: 36624-36638.

[22] ZHANG F, LI P F, HOU Z G, et al. sEMG-based continuous estimation of joint angles of human legs by using BP neural network[J]. Neurocomputing, 2012, 78(1): 139-148.

[23] Aung Y M, Al-jumail Y A. Estimation of upper limb joint angle using surface EMG signal[J]. Int J Adv Robot Syst, 2013, 10(369): 1-8.

[24] WANG G, LIU Y B, SHI T, et al. A novel estimation approach of semg-based joint movements via RBF neural network[C]. 2019 Chinese Automation Congress, 2020: 2059-2064.

[25] GAO X Z, GAO X M, Ovaska S J. A modified Elman neural network model with application to dynamical systems identification[C]. IEEE International Conference on Systems, 1996: 1376-1381.

[26] Boxtel A, Boelhouwer A J W, Bos A R. Optimal EMG signal bandwidth and interelectrode distance for the recording of acoustic, electrocutaneous, and photic blink reflexes[J]. Psychophysiology, 1998, 35(6): 690-697.

[27] Christie A, Greig Inglis J, Kamen G, et al. Relationships between surface EMG variables and motor unit firing rates[J]. Eur J Appl Physiol, 2009, 107(2): 177-185.