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Prediction of Passive Torque on Human Shoulder Joint Based on BPANN

Prediction of Passive Torque on Human Shoulder Joint Based on BPANN Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 8839791, 10 pages https://doi.org/10.1155/2020/8839791 Research Article Prediction of Passive Torque on Human Shoulder Joint Based on BPANN 1 1,2 1 Shuyang Li, Paolo Dario, and Zhibin Song Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China The BioRobotics Institute, Scuola Superiore Sant’Anna, Polo Sant’Anna Valdera, V.le R. Piaggio 34, Pontedera 56025, Italy Correspondence should be addressed to Zhibin Song; songzhibin@tju.edu.cn Received 2 June 2020; Revised 4 July 2020; Accepted 5 August 2020; Published 28 August 2020 Academic Editor: Wei Wei Copyright © 2020 Shuyang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In upper limb rehabilitation training by exploiting robotic devices, the qualitative or quantitative assessment of human active effort is conducive to altering the robot control parameters to offer the patients appropriate assistance, which is considered an effective rehabilitation strategy termed as assist-as-needed. Since active effort of a patient is changeable for the conscious or unconscious behavior, it is considered to be more feasible to determine the distributions of the passive resistance of the patient’s joints versus the joint angle in advance, which can be adopted to assess the active behavior of patients combined with the measurement of robotic sensors. However, the overintensive measurements can impose a burden on patients. Accordingly, a prediction method of shoulder joint passive torque based on a Backpropagation neural network (BPANN) was proposed in the present study to expand the passive torque distribution of the shoulder joint of a patient with less measurement data. The experiments recruiting three adult male subjects were conducted, and the results revealed that the BPANN exhibits high prediction accurate for each direction shoulder passive torque. The results revealed that the BPANN can learn the nonlinear relationship between the passive torque and the position of the shoulder joint and can make an accurate prediction without the need to build a force distribution function in advance, making it possible to draw up an assist-as-needed strategy with high accuracy while reducing the measurement burden of patients and physiotherapists. 1. Introduction [4]. Thus, compared with the stiff control strategy that moves the patient’s limbs along a desired trajectory in the training For patients suffering impaired upper limb function after process given the patient’s active motion ability, the so- stroke, adopting rehabilitation robots for rehabilitation exer- called “assist-as-needed” strategy that provides only the min- imum assistance required to maximize the patient’s active cise can reduce labor burden of therapists, with more accu- rate measurement of the position and force information in participation can enhance the efficiency of rehabilitation [5]. the rehabilitation training. Thus, the quantitative assessment One of the critical problems of the assist-as-needed reha- of the patient’s health state can be achieved. Recently, the bilitation strategy refers to the methods to assess the patient’s research and application of the rehabilitation robotics has active motion state, which will generate feedback to the been increasingly common [1, 2]. In therapeutic practice, robotic therapy devices to modify the control strategy. A not all patients lost all their active motion abilities; thus, common method complies with the surface electromyo- patients retaining part of the motion abilities can achieve sig- graphic (sEMG), as collected in real time in the rehabilitation nificantly improved training effect of their active participa- training and analyzed online to extract the patient’s move- tion in the rehabilitation training [3]. As revealed from ment intention [6, 7]. However, applying sEMG to calculate existing studies, overdose robotic assistance will reduce the the joint torque usually requires the integration of a complex patient’s active force output and energy consumption in musculoskeletal model that contains numerous parameters rehabilitation training, and the patient’s limbs appear to be difficult to measure in vivo. Moreover, for patients with neu- “slacking,” probably reducing the efficiency of rehabilitation rological impairment due to stroke, the sEMG can be 2 Applied Bionics and Biomechanics significantly increased compared with that of healthy sub- significantly inconsistent with that of the healthy people, and the real movement intention of the mentioned patients may jects. However, the stiffness value in this study was regarded be difficult to successfully extract with the sEMG. There is as a constant value, without considering the change of joint stiffness with a joint rotation angle. In 2019, the passive tor- another type of active motion state assessment method, cal- culating the patient’s active force/moment based on the que of shoulder joint during external rotation and internal dynamic model of the human-robot interaction system and rotation was measured by Wight et al., and the slope of the the determined value of the robotic device sensor. Obviously, best-fit line of the torque-angle curve was defined as stiffness the patients’ active force/torque intuitively manifests their [11]. However, in their study, the upper limb rotation was carried out in a fixed plane without considering the distribu- motion intention. In fact, the patient’s active force/torque is changeable for both of the conscious and unconscious behav- tion of passive torque in other planes. Obtaining the distri- iors in the rehabilitation training. Furthermore, unlike the bution of shoulder passive torque in a wider range is changeable active motion state, a stable nonlinear torque- beneficial to evaluating health status and drawing up the angle relationship is identified between the passive compo- rehabilitation strategies, but the measurement of the joint passive torque over the entire joint range of motion may take nents of the human joint (e.g., passive resistance of the soft tissues and gravitational torque, as well as the posture of limb a long time and make the patients fatigued. Thus, the joint for a patients). Thus, a measurement before rehabilitation passive torque assessment method with less measurement training to distribute passive components of force/torque of data can be beneficial. the human shoulder joint is critical to assess active motion Since the artificial neural network (ANN) is capable of approximating any rational function without the cognition states based on dynamic models. In general, the upper limb is affected by gravitational for- of the system constitutive model, a prediction method of ce/torque, passive resistance force/torque generated by joint the shoulder passive torque, as caused both by the gravity biological tissue, active muscle force/torque, and assisted for- and the joint soft tissues, was proposed in the present study ce/torque provided by the rehabilitation device during reha- based on BPANN, making the expansion of the passive tor- que distribution of shoulder joint possible. bilitation exercise. In addition, the influence of centrifugal force and inertial force should also be taken into account A passive upper limb abduction experiment was executed when the movement speed and acceleration is large. How- with the 7-DoF lightweight collaborative robot KUKA lbr iiwa extensively applied in the human-robot interaction ever, considering the safety and comfort of patients, the speed and acceleration of rehabilitation training are usually experiments [12]. The position and the force/torque applied to the robot by human upper limb were recorded by the robot small; thus, the centrifugal force and inertial force can be neglected. Since the main motion form of the upper limb sensor in the experimental motion. Subsequently, the kine- joints is rotation, the torque is usually concerned rather than matic analysis and static force analysis of the upper limb were conducted to calculate the motion and the resistance torque the force. Passive torque of the shoulder joint is mainly com- posed of the gravitational torque and the joint resistance tor- of the shoulder joint. Some of the mentioned angle-torque results were given into a three-layer BPANN as training data. que. The gravitational torque is determined by inertia parameters such as mass and centroid position. And the joint Next, the trained BPANN was adopted to assess the passive resistance torque is mainly determined by the viscoelastic torque of the rest joint posture data collected from the iden- tical subject. Afterwards, the torque assessed by BPANN was characteristics of joint biological tissue. In 1980, the shoulder joint resistance torque of 3 subjects under several simple compared with the torque calculated by static force analysis. The result suggested that the BPANN can accurately assess movement that was measured of upper arm was measured by Engin et al. [8]. The results showed that the magnitude the spatial distribution of shoulder passive torque. of the shoulder joint resistance torque is obviously different Results showed that the BPANN assessment method pro- posed in this study can predict the passive torque of the between subjects, but the trend of the torque-angle curves of different subjects is similar. Then, in 1986, Engin et al. shoulder joint during the upper limb abduction with high measured the shoulder joint resistance torque of the shoulder accuracy and make it possible to obtain more passive joint of 10 subjects beyond the active range of motion of each torque-angle distribution through less measurement data, subject, and a statistical database of the torque-angle rela- which is critical to reduce the burden on patients. tionship was formed which can be used in realistic dynamic simulations of human shoulder joint [9]. However, gravita- 2. Methods tional influence on the shoulder was factored out in their research by making the experimental motion performed only 2.1. Subjects. Three healthy male adults were recruited from in a horizontal equigravitational plane, which is not easy to the identical institution where the experiments of this study realize in actual rehabilitation state. In 2009, an upper limb were conducted. All subjects were voluntary to participant dynamic model is established by Zhang et al., where each seg- in the experiment; they were right-handed, with no history ment of the upper limb was regarded as a rigid body link, and of shoulder disease. the joint elastic resistance torque and gravitational torque are treated as a whole passive torque [10]. The rate of change of 2.2. Experimental Protocol. The subjects were seated at a high the joint rotation angle according to the dynamic force was chair. The subject’s right upper limb was connected to the defined as joint stiffness. The measurement experiment end tool flange of the robot through the orthosis (Figure 1). found that the joint stiffness of the subjects after stroke was To avoid the effect of forearm movement, the elbow joint of Applied Bionics and Biomechanics 3 X X X 1 X Y 0 0 Figure 2: World frame and flange frame of the robot. their muscle activity. As revealed from the results of preex- Figure 1: The orthosis of right upper limb. periment results, the subjects can maintain muscle relaxation during passive exercise. To avoid the interference of the elec- trode patches and the wires on the subject’s motion, no the orthosis was locked in a 90 posture, while the shoulder sEMG signal was harvested in the formal passive exercise joint movement was not restricted by the orthosis. The sub- experiment. jects were required to maintain the stability of their trunk The identical passive abduction trajectory was repeated 2 and avoid the rotation of their upper arm while their right times in a single experiment. If significant difference is iden- upper limb being dragged by the robot to complete abduction tified between the determined values of the two motion along movement in different planes of elevation. the identical trajectory, the data will be considered invalid. The motion path of the robot was generated by dragging The position data (axes angle) and force data of the experi- teaching method. In the preliminary stage, the robot was set ment were recorded with the DataRecorder function built to a low-stiffness impedance control mode, thus making it in the robot control software; thus, the data of the operation possible for the robot to follow the subject’s movement. In of the robot at the specified frequency (50 Hz in the present the dragging stage, the subject was required to move his study) can be recorded. upper limb along the specified abduction trajectory actively and dragging the compliant robot. The robot recorded the 2.3. Kinematics. The motion and force of real human upper rotation angle of each axis at a frequency of 100 Hz during limbs can be significantly complicated, and it is acceptable the dragging step automatically. Subsequently, the trajectory to make a reasonable simplification when performing kine- reproduction step was executed in the passive upper limb matic analysis. In the present study, the following assump- abduction, in which the robot was set to a impedance control tions were made: mode with higher stiffness, and the axes angle data recorded in the dragging step was transferred to the controller as the (1) The flexibility of the biological tissue is not consid- position parameter successively. Thus, the robot can regener- ered. The hand takes up a small proportion in the ate a similar trajectory of the dragging step. Though the upper limb, and the effect of its motion on the upper impedance control mode in trajectory reproduction step limb is negligible. The elbow motion is locked by the may lose some positioning accuracy compared with the posi- orthosis. In the mentioned case, the entire upper limb tion control mode for the effect of human upper limb, it can and the connected orthotics can be considered a comply with the natural movement trajectory of the upper whole rigid body for kinematic analysis limbs better, ensuring the safety of the robot and the subjects. Moreover, its compliant properties also helps avoid the sud- (2) The shoulder joint is simplified as a ball and socket den change of the joint torque of the robot attributed to the joint rotating around a fixed point on the human human upper limb as an uncertain load. Accordingly, the body, and the spatial position of the center of the impedance control mode is chosen for the passive abduction shoulder joint is assessed with the least-square experiment in the present study. To ensure the safety of reha- sphere-fitting method bilitation training, usually the speed during the motion is slow. Thus, this study only focused on the shoulder resistance Thus, the upper limb is considered a rigid body that rotates around the ball and socket joint at a fixed center. Sub- performance at low speed, and the speed of each axis of the robot was also limited to 1/10 of its maximum speed. sequently, the shoulder joint posture can be calculated from Before the start of the experiment, the subjects were the robot position data recorded by the DataRecorder func- required to fully warm up the upper limbs. During the pas- tion. The robot axes angle can be adopted to calculate the sive abduction, the upper limbs of the subjects should not feel position and posture of the flange frame relative to the world coordinate system of the robot by robot forward kinematics. being pulled or pushed by the robot obviously. To ensure the stability of the passive torque, all subjects were required to Besides, the world and the flange frames of the robot are illus- participate in the preexperiment before the formal experi- trated in Figure 2. ment to determine their muscle relaxation level in the passive To quantitatively express the movement of the shoulder abduction. Besides, the sEMG signals of the upper limb mus- joint, the local frame of the shoulder (Figure 3) was built according to the ISB recommendation [13] at its rotation cles related to the active motion were harvested to monitor 4 Applied Bionics and Biomechanics Y 600 R Motion 200 direction Figure 3: Shoulder joint frame system and upper limb stress. center. In the preliminary stage of the experiment, the sub- 0 300 400 500 600 700 800 900 jects altered their sitting posture as guided by the experiment X/mm supervisor, thereby making the coronal, sagittal, and vertical axes of their body parallel to the X -axis, Y -axis, and Z -axis 0 0 0 Figure 4: Projection of motion trajectory on XZ plane. of the robot world frame, respectively. The upper limb and the orthosis are considered a rigid body, and the orthosis is rigidly fixed on the robot flange, present study, the two angles globographic method was so the homogeneous transformation matrix between the adopted to describe the shoulder motion, excluding the robot flange frame and the shoulder frame is considered rotational effect of the upper arm. The globographic angles invariant with upper limb motion. The actual value of the were calculated by a landmark point fixed on upper arm, transformation matrix was determined, to be specific, the which was taken as the elbow point. The elbow point was robot axes angle when the shoulder joint was on its initial obtained by manual measurement. posture where shoulder abduction/adduction angle, flexio- Though the subjects were required to move their upper limb n/extension angle, and internal rotation/external rotation within a single plane in the passive abduction movement exper- angle were 0 on the whole. Subsequently, the position and iments, the elbow joint sampling points did not exhibit the single posture of the flange frame could be calculated, while the plane distribution. The mentioned finding is because the move- shoulder frame posture was already known (all rotation angle ment trajectories were generated by the subjects themselves and was 0 ). Thus, the rotation matrix between the two frames because the designated primary movement tended to be accom- was calculated. Besides, by employing the radius from the panied by an unconscious “secondary movement” [15]. shoulder rotation center sphere-fitting, the translation vec- It was found in the experiments that the results of sphere tor between the two frames was calculated. With the rota- fitting were quite different at different stages of a same move- ment, especially at the end stage. For example, the projection tion matrix and the translation vector, the homogeneous transformation matrix between the robot flange frame and of an abduction trajectory in 0 plane of elevation of subject the shoulder joint frame was determined, which can be S1 on the XY plane was shown in Figure 4. The trajectory adopted to calculate the posture of shoulder frame from curve displays a significantly different curvature between the robot axes angle as expressed Equation (1), where T the initial and final stages. This is primarily attributed to the translation of the shoulder joint center and for the denotes the homogeneous transformation matrix of shoul- der joint frame relative to the robot world frame, T repre- rigid connection between upper limb and robot that made sents the homogeneous transformation matrix of robot the rotation of the robot axis more difficult under the flange frame calculated by forward kinematics relative to larger rotation angle; the effect of the center translation was more obvious than in human natural voluntary move- the robot world frame, and T indicates the homogeneous ment. Accordingly, for the data of each motion trajectory, transformation matrix of the shoulder joint frame relative the former part was taken for sphere fitting, and the shoulder to the robot flange frame. joint angle was calculated by the intersection point of the line connecting the sample point and the fitting sphere center and T = T T ð1Þ s FF the fitting sphere. The fitting sphere with the same trajectory shown in Figure 4 and its corresponding intersection point Overall, the posture of rigid body is not expressed by the on the sphere is illustrated in Figure 5. rotation matrix which contains 9 elements directly, whereas it is decomposed into 3 rotation angles in a certain order. 2.4. Static Force Analyses. The passive abduction experiment The ISB recommended by adopting the YXY order Euler in the present study was conducted at a slow speed, so the human-robot system is considered quasi-static, and the effect angle to present the shoulder joint (GH joint, actually) pos- ture. However, some existing studies suggested that the of inertial force was ignored. Moreover, low-speed also YXY sequence Euler angles gives gimbal deadlock problem, reduced the effect of velocity-related viscous part in the pas- and the clinical amplitude coherence is poor [14]. In the sive torque of the shoulder joint. Z/mm Applied Bionics and Biomechanics 5 0.7 W jk ij 0.6 X Y 1 1 0.5 0.4 0.3 0.2 0.1 3 0.4 0.2 Input layer Hidden layer Output layer Figure 6: The topological structure of BPANN. –0.2 1.2 1.1 Y/m 0.9 0.8 0.7 0.6 X/m torque on the robot joint calculated by the robot based on its torque sensor measurements with the built-in dynamic Sample point model, and J indicates the pseudo-inverse matrix of the Intersection point 7×6 robot Jacobian matrix. The external torque data were Figure 5: Sphere-fitting results. smoothed with a moving average filter to reducing the influence of high-frequency noise. The force/torque applied on the upper limb under quasi- "# static is illustrated in Figure 3. The robot applies an assist force f = = J τ : ð4Þ F on the original point of the flange frame and an assist tor- que M to the upper limb through the orthosis. The shoulder joint generated a resistance force F applied on its rotation The gravity and the center of mass of the orthosis was center and a resistance torque M . The gravity G was applied determined in advance; its effect was removed from the on the center of mass of the upper limb. Furthermore, the result. The passive torque of shoulder joint M can be cal- gravity G and assist force F would generate torque M and R G culated as Equation (5). M at the shoulder rotation center, respectively. FR In fact, the rigidly connected robot flange provided con- M = M + M = −M − M : ð5Þ straints of all 6 DoF for the upper limb, and the shoulder P s G R FR joint, which was approximated as a ball and socket joint, gen- erated additional constraints for the upper limb; thus, the 2.5. ANN Prediction. Unlike conventional function fitting methods, the ANN expresses the mapping relationship upper limb static force system became an overdetermined problem. For this reason, there are infinite sets of solutions between input data and output data through the structure for the static equilibrium state of the system in theory. How- and parameters (e.g., weights and biases here) of the layered network. A three-layer feedforward ANN was used here to ever, an ideal ball and socket joint would only provide force constraints without torque constraints. Likewise, in a specific express the torque-angle relationship of shoulder joint. The joint angle, the resistance force F number of units of the input layer was two and that of the out- of shoulder joint may change following the external force/torque, whereas the resis- put layer was three. The number of the hidden units was deter- tance torque M is relatively stable, primarily determined by mined initially by an empirical equation and altered according to assessed effects. After the network structure was deter- the joint tissue characteristics. Moreover, the experimental results revealed that the high repeatability of M and F of mined, the weights and biases of the network could be altered R R by training. Backpropagation (BP) algorithm is commonly a specific subject in the identical trajectory. The static equilibrium equation is written in Equation used in ANN training, calculating the gradient of the error (3). with respect to the weights for a given input by propagating error backwards through the network [16]. The topological ð2Þ structure of BPANN is illustrated in Figure 6. F +F +G = 0, s R Two globographic angles were selected as the input data and the three components of shoulder passive torque relative M + M + M + M =0: ð3Þ s R G FR to the direction of robot world frame calculated in section 2.4. The activation functions of the hidden and output units The robot assist force F and assist torque M were cal- R R culated by the robot joint external torque by Equation (4) were sigmoid. All data were normalized before being trans- derived from the principle of virtual work, where f denotes ferred to a neural network. The training of the BPANN was the generalized force of the robot, τ represents the external carried out in the Neural Network Toolbox of MATLAB. In Z/m 6 Applied Bionics and Biomechanics 120 120 100 100 60 60 0 1 23456789 0 5 10 15 Time/s Time/s Plane of elevation angle Plane of elevation angle Abduction angle Abduction angle (a) (b) ° ° Figure 7: Globographic angle results. (a) Globographic angle of abduction in 0 plane of elevation. (b) Globographic angle of abduction in 30 plane of elevation. –5 –5 –10 –10 0 5 10 15 0123456789 Time (s) Time/s Torque X Torque X Torque Y Torque Y Torque Z Torque Z (a) (b) Figure 8: Shoulder joint passive torque results. (a) Passive torque components of abduction in 0 plane of elevation. (b) Passive torque components of abduction in about 30 plane of elevation. terms of the training parameters, the maximum number of vation of subject S1 were shown in Figures 7(a) and 7(b), training epochs was 1000, the performance goal is 0.001 where respectively. The angle curves suggested that a secondary the performance was measured by the mean square error movement took place, especially in the moment as presented (MSE) of the network output, and the learning rate is 0.01. in Figure 7(b). The Levenberg-Marquardt optimization was chosen to be the backpropagation algorithm due to its faster training speed. 3.2. Shoulder Passive Torques. The passive torque calculation results of the two moments in Figure 7 are, respectively, 3. Results shown in Figures 8(a) and 8(b). It can be seen that the passive torque on the shoulder joint is quite different in different 3.1. Kinematics. The globographic angle results of the abduc- ° ° motion trajectories of the same subject. tion trajectories in 0 plane of elevation and 30 plane of ele- Torque/N·m Angle/degree Torque X (N·m) Angle/degree Applied Bionics and Biomechanics 7 Hidden layer units is 5 Hidden layer units is 10 1 1 10 10 0 0 10 10 –1 –1 10 10 –2 –2 10 10 –3 –3 10 10 –4 –4 10 10 0 100 200 300 400 500 600 700 800 900 1000 0 1020304050607080 1000 epochs 88 epochs Hidden layer units is 15 Hidden layer units is 20 –1 –1 –2 –2 10 10 –3 –3 10 10 –4 –4 02468 10 12 14 16 01 234 56 6 epochs 16 epochs Train Goal Figure 9: Performance of the BPANN with different hidden layer units. is small, the network needs more training epochs to achieve 3.3. BPANN Prediction. In the two motions of subject S1 as presented in Figure 7, 1123 groups of angle-torque data were the performance goal. Especially when the number of units collected. First, 500 groups of data were selected randomly to is very small, the network cannot meet the performance goal, train the BPANN, and the rest groups of data acted as test set even after more training epochs than 1000. For example, to verify the prediction effect of the network. when the number of hidden layer units is 5, the network per- formance hardly changed with iterative calculation after 84 The number of hidden layer units impacted the predic- tion effect of the BPANN. Generally, with the increase of training epochs, which can not meet the set accuracy goal the number of neural network layers and hidden layer ele- (0.001). However, although more units can make the net- ments, the nonlinear fitting ability of neural network is work reach the specified accuracy with fewer training epochs, enhanced. However, too complicated network structure will the computational complexity of each epoch is larger. In this increase the calculate complexity and may lead to over-fit- paper, the number of the hidden layer units was chosen to be ting, thus reducing the generalization ability of the BPANN. 9, with which the structure of the network will not be too Therefore, the network structure should be determined complicated, and at the same time, the accuracy target can according to the prediction effect in practical application. be achieved at a relatively fast speed. In this paper, the training performance of the network with The passive torque prediction error of the test set data in 5~20 hidden layer units was tested, and the training curves each direction was shown in Figure 10. For clarity of illustra- of the networks with different hidden layer units were shown tion, not all sample points in the test set were shown in in Figure 9. It can be seen that when the number of the units Figure 10, and one point was taken for every 5 points for Mean squared error (mse) Mean squared error (mse) Mean squared error (mse) Mean squared error (mse) 8 Applied Bionics and Biomechanics –2 –4 –6 –8 –10 0 200 400 600 800 1000 1200 Sample point number Error Prediction results (a) –5 0 200 400 600 800 1000 1200 Sample point number Error Prediction results (b) –2 –4 –6 –8 –10 0 200 400 600 800 1000 1200 Sample point number Error Prediction results (c) Figure 10: Assessment results and errors in each direction. Torque Z/N·m Torque X/N·m Torque Y/N·m Applied Bionics and Biomechanics 9 the joint position for a specific individual and expand the Table 1: MAV and MSE of ANN assessment. spatial distribution with less measurement data. MAV[N·m] MSE[N·m] RE X 6.399 0.093 0.0145 Data Availability Y 5.172 0.139 0.0269 The position data and force/torque data used to support the Z 1.728 0.104 0.0602 findings of this study are included within the article. plotting. It can be seen that the prediction error was small Conflicts of Interest compared with the magnitude of each passive torque compo- The authors declare there is no conflict of interest regarding nent, and the specific mean absolute value (MAV) and mean square error (MSE) of the passive torque prediction are listed this publication. in Table 1. The relative error (RE) is defined as the ratio of the MSE to MAV. The results showed that the BPANN can pre- Acknowledgments dict the torque of the shoulder joint with high accuracy. For subject S2 and S3, similar accurate passive torque This research is supported by the National Key Research and Development Program of China (No. 2018YFB1307803) and perditions can be conducted by BPANN, which was not repeated in this paper for the sake of length. Although the the Natural Science Foundation of China (Project No. 51775367, 51975401, 51535008). upper limb is often treated as a rigid body link system, in fact, the biological tissue is not rigid and its characteristics, such as inertial parameters and elastic characteristics, will change References with the limb motion. Especially for the shoulder joint, its actual motion is coupled by the common motion of the gle- [1] R. Colombo, F. Pisano, S. 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Hegde, “Designing neural networks using genetic algorithms,” International conference on genetic algorithms, 1989. [17] C. Högfors, B. Peterson, G. Sigholm, and P. Herberts, “Biome- chanical model of the human shoulder joint—ii. The shoulder rhythm,” Journal of Biomechanics, vol. 24, no. 8, pp. 699–709, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Bionics and Biomechanics Hindawi Publishing Corporation

Prediction of Passive Torque on Human Shoulder Joint Based on BPANN

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Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 8839791, 10 pages https://doi.org/10.1155/2020/8839791 Research Article Prediction of Passive Torque on Human Shoulder Joint Based on BPANN 1 1,2 1 Shuyang Li, Paolo Dario, and Zhibin Song Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China The BioRobotics Institute, Scuola Superiore Sant’Anna, Polo Sant’Anna Valdera, V.le R. Piaggio 34, Pontedera 56025, Italy Correspondence should be addressed to Zhibin Song; songzhibin@tju.edu.cn Received 2 June 2020; Revised 4 July 2020; Accepted 5 August 2020; Published 28 August 2020 Academic Editor: Wei Wei Copyright © 2020 Shuyang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In upper limb rehabilitation training by exploiting robotic devices, the qualitative or quantitative assessment of human active effort is conducive to altering the robot control parameters to offer the patients appropriate assistance, which is considered an effective rehabilitation strategy termed as assist-as-needed. Since active effort of a patient is changeable for the conscious or unconscious behavior, it is considered to be more feasible to determine the distributions of the passive resistance of the patient’s joints versus the joint angle in advance, which can be adopted to assess the active behavior of patients combined with the measurement of robotic sensors. However, the overintensive measurements can impose a burden on patients. Accordingly, a prediction method of shoulder joint passive torque based on a Backpropagation neural network (BPANN) was proposed in the present study to expand the passive torque distribution of the shoulder joint of a patient with less measurement data. The experiments recruiting three adult male subjects were conducted, and the results revealed that the BPANN exhibits high prediction accurate for each direction shoulder passive torque. The results revealed that the BPANN can learn the nonlinear relationship between the passive torque and the position of the shoulder joint and can make an accurate prediction without the need to build a force distribution function in advance, making it possible to draw up an assist-as-needed strategy with high accuracy while reducing the measurement burden of patients and physiotherapists. 1. Introduction [4]. Thus, compared with the stiff control strategy that moves the patient’s limbs along a desired trajectory in the training For patients suffering impaired upper limb function after process given the patient’s active motion ability, the so- stroke, adopting rehabilitation robots for rehabilitation exer- called “assist-as-needed” strategy that provides only the min- imum assistance required to maximize the patient’s active cise can reduce labor burden of therapists, with more accu- rate measurement of the position and force information in participation can enhance the efficiency of rehabilitation [5]. the rehabilitation training. Thus, the quantitative assessment One of the critical problems of the assist-as-needed reha- of the patient’s health state can be achieved. Recently, the bilitation strategy refers to the methods to assess the patient’s research and application of the rehabilitation robotics has active motion state, which will generate feedback to the been increasingly common [1, 2]. In therapeutic practice, robotic therapy devices to modify the control strategy. A not all patients lost all their active motion abilities; thus, common method complies with the surface electromyo- patients retaining part of the motion abilities can achieve sig- graphic (sEMG), as collected in real time in the rehabilitation nificantly improved training effect of their active participa- training and analyzed online to extract the patient’s move- tion in the rehabilitation training [3]. As revealed from ment intention [6, 7]. However, applying sEMG to calculate existing studies, overdose robotic assistance will reduce the the joint torque usually requires the integration of a complex patient’s active force output and energy consumption in musculoskeletal model that contains numerous parameters rehabilitation training, and the patient’s limbs appear to be difficult to measure in vivo. Moreover, for patients with neu- “slacking,” probably reducing the efficiency of rehabilitation rological impairment due to stroke, the sEMG can be 2 Applied Bionics and Biomechanics significantly increased compared with that of healthy sub- significantly inconsistent with that of the healthy people, and the real movement intention of the mentioned patients may jects. However, the stiffness value in this study was regarded be difficult to successfully extract with the sEMG. There is as a constant value, without considering the change of joint stiffness with a joint rotation angle. In 2019, the passive tor- another type of active motion state assessment method, cal- culating the patient’s active force/moment based on the que of shoulder joint during external rotation and internal dynamic model of the human-robot interaction system and rotation was measured by Wight et al., and the slope of the the determined value of the robotic device sensor. Obviously, best-fit line of the torque-angle curve was defined as stiffness the patients’ active force/torque intuitively manifests their [11]. However, in their study, the upper limb rotation was carried out in a fixed plane without considering the distribu- motion intention. In fact, the patient’s active force/torque is changeable for both of the conscious and unconscious behav- tion of passive torque in other planes. Obtaining the distri- iors in the rehabilitation training. Furthermore, unlike the bution of shoulder passive torque in a wider range is changeable active motion state, a stable nonlinear torque- beneficial to evaluating health status and drawing up the angle relationship is identified between the passive compo- rehabilitation strategies, but the measurement of the joint passive torque over the entire joint range of motion may take nents of the human joint (e.g., passive resistance of the soft tissues and gravitational torque, as well as the posture of limb a long time and make the patients fatigued. Thus, the joint for a patients). Thus, a measurement before rehabilitation passive torque assessment method with less measurement training to distribute passive components of force/torque of data can be beneficial. the human shoulder joint is critical to assess active motion Since the artificial neural network (ANN) is capable of approximating any rational function without the cognition states based on dynamic models. In general, the upper limb is affected by gravitational for- of the system constitutive model, a prediction method of ce/torque, passive resistance force/torque generated by joint the shoulder passive torque, as caused both by the gravity biological tissue, active muscle force/torque, and assisted for- and the joint soft tissues, was proposed in the present study ce/torque provided by the rehabilitation device during reha- based on BPANN, making the expansion of the passive tor- que distribution of shoulder joint possible. bilitation exercise. In addition, the influence of centrifugal force and inertial force should also be taken into account A passive upper limb abduction experiment was executed when the movement speed and acceleration is large. How- with the 7-DoF lightweight collaborative robot KUKA lbr iiwa extensively applied in the human-robot interaction ever, considering the safety and comfort of patients, the speed and acceleration of rehabilitation training are usually experiments [12]. The position and the force/torque applied to the robot by human upper limb were recorded by the robot small; thus, the centrifugal force and inertial force can be neglected. Since the main motion form of the upper limb sensor in the experimental motion. Subsequently, the kine- joints is rotation, the torque is usually concerned rather than matic analysis and static force analysis of the upper limb were conducted to calculate the motion and the resistance torque the force. Passive torque of the shoulder joint is mainly com- posed of the gravitational torque and the joint resistance tor- of the shoulder joint. Some of the mentioned angle-torque results were given into a three-layer BPANN as training data. que. The gravitational torque is determined by inertia parameters such as mass and centroid position. And the joint Next, the trained BPANN was adopted to assess the passive resistance torque is mainly determined by the viscoelastic torque of the rest joint posture data collected from the iden- tical subject. Afterwards, the torque assessed by BPANN was characteristics of joint biological tissue. In 1980, the shoulder joint resistance torque of 3 subjects under several simple compared with the torque calculated by static force analysis. The result suggested that the BPANN can accurately assess movement that was measured of upper arm was measured by Engin et al. [8]. The results showed that the magnitude the spatial distribution of shoulder passive torque. of the shoulder joint resistance torque is obviously different Results showed that the BPANN assessment method pro- posed in this study can predict the passive torque of the between subjects, but the trend of the torque-angle curves of different subjects is similar. Then, in 1986, Engin et al. shoulder joint during the upper limb abduction with high measured the shoulder joint resistance torque of the shoulder accuracy and make it possible to obtain more passive joint of 10 subjects beyond the active range of motion of each torque-angle distribution through less measurement data, subject, and a statistical database of the torque-angle rela- which is critical to reduce the burden on patients. tionship was formed which can be used in realistic dynamic simulations of human shoulder joint [9]. However, gravita- 2. Methods tional influence on the shoulder was factored out in their research by making the experimental motion performed only 2.1. Subjects. Three healthy male adults were recruited from in a horizontal equigravitational plane, which is not easy to the identical institution where the experiments of this study realize in actual rehabilitation state. In 2009, an upper limb were conducted. All subjects were voluntary to participant dynamic model is established by Zhang et al., where each seg- in the experiment; they were right-handed, with no history ment of the upper limb was regarded as a rigid body link, and of shoulder disease. the joint elastic resistance torque and gravitational torque are treated as a whole passive torque [10]. The rate of change of 2.2. Experimental Protocol. The subjects were seated at a high the joint rotation angle according to the dynamic force was chair. The subject’s right upper limb was connected to the defined as joint stiffness. The measurement experiment end tool flange of the robot through the orthosis (Figure 1). found that the joint stiffness of the subjects after stroke was To avoid the effect of forearm movement, the elbow joint of Applied Bionics and Biomechanics 3 X X X 1 X Y 0 0 Figure 2: World frame and flange frame of the robot. their muscle activity. As revealed from the results of preex- Figure 1: The orthosis of right upper limb. periment results, the subjects can maintain muscle relaxation during passive exercise. To avoid the interference of the elec- trode patches and the wires on the subject’s motion, no the orthosis was locked in a 90 posture, while the shoulder sEMG signal was harvested in the formal passive exercise joint movement was not restricted by the orthosis. The sub- experiment. jects were required to maintain the stability of their trunk The identical passive abduction trajectory was repeated 2 and avoid the rotation of their upper arm while their right times in a single experiment. If significant difference is iden- upper limb being dragged by the robot to complete abduction tified between the determined values of the two motion along movement in different planes of elevation. the identical trajectory, the data will be considered invalid. The motion path of the robot was generated by dragging The position data (axes angle) and force data of the experi- teaching method. In the preliminary stage, the robot was set ment were recorded with the DataRecorder function built to a low-stiffness impedance control mode, thus making it in the robot control software; thus, the data of the operation possible for the robot to follow the subject’s movement. In of the robot at the specified frequency (50 Hz in the present the dragging stage, the subject was required to move his study) can be recorded. upper limb along the specified abduction trajectory actively and dragging the compliant robot. The robot recorded the 2.3. Kinematics. The motion and force of real human upper rotation angle of each axis at a frequency of 100 Hz during limbs can be significantly complicated, and it is acceptable the dragging step automatically. Subsequently, the trajectory to make a reasonable simplification when performing kine- reproduction step was executed in the passive upper limb matic analysis. In the present study, the following assump- abduction, in which the robot was set to a impedance control tions were made: mode with higher stiffness, and the axes angle data recorded in the dragging step was transferred to the controller as the (1) The flexibility of the biological tissue is not consid- position parameter successively. Thus, the robot can regener- ered. The hand takes up a small proportion in the ate a similar trajectory of the dragging step. Though the upper limb, and the effect of its motion on the upper impedance control mode in trajectory reproduction step limb is negligible. The elbow motion is locked by the may lose some positioning accuracy compared with the posi- orthosis. In the mentioned case, the entire upper limb tion control mode for the effect of human upper limb, it can and the connected orthotics can be considered a comply with the natural movement trajectory of the upper whole rigid body for kinematic analysis limbs better, ensuring the safety of the robot and the subjects. Moreover, its compliant properties also helps avoid the sud- (2) The shoulder joint is simplified as a ball and socket den change of the joint torque of the robot attributed to the joint rotating around a fixed point on the human human upper limb as an uncertain load. Accordingly, the body, and the spatial position of the center of the impedance control mode is chosen for the passive abduction shoulder joint is assessed with the least-square experiment in the present study. To ensure the safety of reha- sphere-fitting method bilitation training, usually the speed during the motion is slow. Thus, this study only focused on the shoulder resistance Thus, the upper limb is considered a rigid body that rotates around the ball and socket joint at a fixed center. Sub- performance at low speed, and the speed of each axis of the robot was also limited to 1/10 of its maximum speed. sequently, the shoulder joint posture can be calculated from Before the start of the experiment, the subjects were the robot position data recorded by the DataRecorder func- required to fully warm up the upper limbs. During the pas- tion. The robot axes angle can be adopted to calculate the sive abduction, the upper limbs of the subjects should not feel position and posture of the flange frame relative to the world coordinate system of the robot by robot forward kinematics. being pulled or pushed by the robot obviously. To ensure the stability of the passive torque, all subjects were required to Besides, the world and the flange frames of the robot are illus- participate in the preexperiment before the formal experi- trated in Figure 2. ment to determine their muscle relaxation level in the passive To quantitatively express the movement of the shoulder abduction. Besides, the sEMG signals of the upper limb mus- joint, the local frame of the shoulder (Figure 3) was built according to the ISB recommendation [13] at its rotation cles related to the active motion were harvested to monitor 4 Applied Bionics and Biomechanics Y 600 R Motion 200 direction Figure 3: Shoulder joint frame system and upper limb stress. center. In the preliminary stage of the experiment, the sub- 0 300 400 500 600 700 800 900 jects altered their sitting posture as guided by the experiment X/mm supervisor, thereby making the coronal, sagittal, and vertical axes of their body parallel to the X -axis, Y -axis, and Z -axis 0 0 0 Figure 4: Projection of motion trajectory on XZ plane. of the robot world frame, respectively. The upper limb and the orthosis are considered a rigid body, and the orthosis is rigidly fixed on the robot flange, present study, the two angles globographic method was so the homogeneous transformation matrix between the adopted to describe the shoulder motion, excluding the robot flange frame and the shoulder frame is considered rotational effect of the upper arm. The globographic angles invariant with upper limb motion. The actual value of the were calculated by a landmark point fixed on upper arm, transformation matrix was determined, to be specific, the which was taken as the elbow point. The elbow point was robot axes angle when the shoulder joint was on its initial obtained by manual measurement. posture where shoulder abduction/adduction angle, flexio- Though the subjects were required to move their upper limb n/extension angle, and internal rotation/external rotation within a single plane in the passive abduction movement exper- angle were 0 on the whole. Subsequently, the position and iments, the elbow joint sampling points did not exhibit the single posture of the flange frame could be calculated, while the plane distribution. The mentioned finding is because the move- shoulder frame posture was already known (all rotation angle ment trajectories were generated by the subjects themselves and was 0 ). Thus, the rotation matrix between the two frames because the designated primary movement tended to be accom- was calculated. Besides, by employing the radius from the panied by an unconscious “secondary movement” [15]. shoulder rotation center sphere-fitting, the translation vec- It was found in the experiments that the results of sphere tor between the two frames was calculated. With the rota- fitting were quite different at different stages of a same move- ment, especially at the end stage. For example, the projection tion matrix and the translation vector, the homogeneous transformation matrix between the robot flange frame and of an abduction trajectory in 0 plane of elevation of subject the shoulder joint frame was determined, which can be S1 on the XY plane was shown in Figure 4. The trajectory adopted to calculate the posture of shoulder frame from curve displays a significantly different curvature between the robot axes angle as expressed Equation (1), where T the initial and final stages. This is primarily attributed to the translation of the shoulder joint center and for the denotes the homogeneous transformation matrix of shoul- der joint frame relative to the robot world frame, T repre- rigid connection between upper limb and robot that made sents the homogeneous transformation matrix of robot the rotation of the robot axis more difficult under the flange frame calculated by forward kinematics relative to larger rotation angle; the effect of the center translation was more obvious than in human natural voluntary move- the robot world frame, and T indicates the homogeneous ment. Accordingly, for the data of each motion trajectory, transformation matrix of the shoulder joint frame relative the former part was taken for sphere fitting, and the shoulder to the robot flange frame. joint angle was calculated by the intersection point of the line connecting the sample point and the fitting sphere center and T = T T ð1Þ s FF the fitting sphere. The fitting sphere with the same trajectory shown in Figure 4 and its corresponding intersection point Overall, the posture of rigid body is not expressed by the on the sphere is illustrated in Figure 5. rotation matrix which contains 9 elements directly, whereas it is decomposed into 3 rotation angles in a certain order. 2.4. Static Force Analyses. The passive abduction experiment The ISB recommended by adopting the YXY order Euler in the present study was conducted at a slow speed, so the human-robot system is considered quasi-static, and the effect angle to present the shoulder joint (GH joint, actually) pos- ture. However, some existing studies suggested that the of inertial force was ignored. Moreover, low-speed also YXY sequence Euler angles gives gimbal deadlock problem, reduced the effect of velocity-related viscous part in the pas- and the clinical amplitude coherence is poor [14]. In the sive torque of the shoulder joint. Z/mm Applied Bionics and Biomechanics 5 0.7 W jk ij 0.6 X Y 1 1 0.5 0.4 0.3 0.2 0.1 3 0.4 0.2 Input layer Hidden layer Output layer Figure 6: The topological structure of BPANN. –0.2 1.2 1.1 Y/m 0.9 0.8 0.7 0.6 X/m torque on the robot joint calculated by the robot based on its torque sensor measurements with the built-in dynamic Sample point model, and J indicates the pseudo-inverse matrix of the Intersection point 7×6 robot Jacobian matrix. The external torque data were Figure 5: Sphere-fitting results. smoothed with a moving average filter to reducing the influence of high-frequency noise. The force/torque applied on the upper limb under quasi- "# static is illustrated in Figure 3. The robot applies an assist force f = = J τ : ð4Þ F on the original point of the flange frame and an assist tor- que M to the upper limb through the orthosis. The shoulder joint generated a resistance force F applied on its rotation The gravity and the center of mass of the orthosis was center and a resistance torque M . The gravity G was applied determined in advance; its effect was removed from the on the center of mass of the upper limb. Furthermore, the result. The passive torque of shoulder joint M can be cal- gravity G and assist force F would generate torque M and R G culated as Equation (5). M at the shoulder rotation center, respectively. FR In fact, the rigidly connected robot flange provided con- M = M + M = −M − M : ð5Þ straints of all 6 DoF for the upper limb, and the shoulder P s G R FR joint, which was approximated as a ball and socket joint, gen- erated additional constraints for the upper limb; thus, the 2.5. ANN Prediction. Unlike conventional function fitting methods, the ANN expresses the mapping relationship upper limb static force system became an overdetermined problem. For this reason, there are infinite sets of solutions between input data and output data through the structure for the static equilibrium state of the system in theory. How- and parameters (e.g., weights and biases here) of the layered network. A three-layer feedforward ANN was used here to ever, an ideal ball and socket joint would only provide force constraints without torque constraints. Likewise, in a specific express the torque-angle relationship of shoulder joint. The joint angle, the resistance force F number of units of the input layer was two and that of the out- of shoulder joint may change following the external force/torque, whereas the resis- put layer was three. The number of the hidden units was deter- tance torque M is relatively stable, primarily determined by mined initially by an empirical equation and altered according to assessed effects. After the network structure was deter- the joint tissue characteristics. Moreover, the experimental results revealed that the high repeatability of M and F of mined, the weights and biases of the network could be altered R R by training. Backpropagation (BP) algorithm is commonly a specific subject in the identical trajectory. The static equilibrium equation is written in Equation used in ANN training, calculating the gradient of the error (3). with respect to the weights for a given input by propagating error backwards through the network [16]. The topological ð2Þ structure of BPANN is illustrated in Figure 6. F +F +G = 0, s R Two globographic angles were selected as the input data and the three components of shoulder passive torque relative M + M + M + M =0: ð3Þ s R G FR to the direction of robot world frame calculated in section 2.4. The activation functions of the hidden and output units The robot assist force F and assist torque M were cal- R R culated by the robot joint external torque by Equation (4) were sigmoid. All data were normalized before being trans- derived from the principle of virtual work, where f denotes ferred to a neural network. The training of the BPANN was the generalized force of the robot, τ represents the external carried out in the Neural Network Toolbox of MATLAB. In Z/m 6 Applied Bionics and Biomechanics 120 120 100 100 60 60 0 1 23456789 0 5 10 15 Time/s Time/s Plane of elevation angle Plane of elevation angle Abduction angle Abduction angle (a) (b) ° ° Figure 7: Globographic angle results. (a) Globographic angle of abduction in 0 plane of elevation. (b) Globographic angle of abduction in 30 plane of elevation. –5 –5 –10 –10 0 5 10 15 0123456789 Time (s) Time/s Torque X Torque X Torque Y Torque Y Torque Z Torque Z (a) (b) Figure 8: Shoulder joint passive torque results. (a) Passive torque components of abduction in 0 plane of elevation. (b) Passive torque components of abduction in about 30 plane of elevation. terms of the training parameters, the maximum number of vation of subject S1 were shown in Figures 7(a) and 7(b), training epochs was 1000, the performance goal is 0.001 where respectively. The angle curves suggested that a secondary the performance was measured by the mean square error movement took place, especially in the moment as presented (MSE) of the network output, and the learning rate is 0.01. in Figure 7(b). The Levenberg-Marquardt optimization was chosen to be the backpropagation algorithm due to its faster training speed. 3.2. Shoulder Passive Torques. The passive torque calculation results of the two moments in Figure 7 are, respectively, 3. Results shown in Figures 8(a) and 8(b). It can be seen that the passive torque on the shoulder joint is quite different in different 3.1. Kinematics. The globographic angle results of the abduc- ° ° motion trajectories of the same subject. tion trajectories in 0 plane of elevation and 30 plane of ele- Torque/N·m Angle/degree Torque X (N·m) Angle/degree Applied Bionics and Biomechanics 7 Hidden layer units is 5 Hidden layer units is 10 1 1 10 10 0 0 10 10 –1 –1 10 10 –2 –2 10 10 –3 –3 10 10 –4 –4 10 10 0 100 200 300 400 500 600 700 800 900 1000 0 1020304050607080 1000 epochs 88 epochs Hidden layer units is 15 Hidden layer units is 20 –1 –1 –2 –2 10 10 –3 –3 10 10 –4 –4 02468 10 12 14 16 01 234 56 6 epochs 16 epochs Train Goal Figure 9: Performance of the BPANN with different hidden layer units. is small, the network needs more training epochs to achieve 3.3. BPANN Prediction. In the two motions of subject S1 as presented in Figure 7, 1123 groups of angle-torque data were the performance goal. Especially when the number of units collected. First, 500 groups of data were selected randomly to is very small, the network cannot meet the performance goal, train the BPANN, and the rest groups of data acted as test set even after more training epochs than 1000. For example, to verify the prediction effect of the network. when the number of hidden layer units is 5, the network per- formance hardly changed with iterative calculation after 84 The number of hidden layer units impacted the predic- tion effect of the BPANN. Generally, with the increase of training epochs, which can not meet the set accuracy goal the number of neural network layers and hidden layer ele- (0.001). However, although more units can make the net- ments, the nonlinear fitting ability of neural network is work reach the specified accuracy with fewer training epochs, enhanced. However, too complicated network structure will the computational complexity of each epoch is larger. In this increase the calculate complexity and may lead to over-fit- paper, the number of the hidden layer units was chosen to be ting, thus reducing the generalization ability of the BPANN. 9, with which the structure of the network will not be too Therefore, the network structure should be determined complicated, and at the same time, the accuracy target can according to the prediction effect in practical application. be achieved at a relatively fast speed. In this paper, the training performance of the network with The passive torque prediction error of the test set data in 5~20 hidden layer units was tested, and the training curves each direction was shown in Figure 10. For clarity of illustra- of the networks with different hidden layer units were shown tion, not all sample points in the test set were shown in in Figure 9. It can be seen that when the number of the units Figure 10, and one point was taken for every 5 points for Mean squared error (mse) Mean squared error (mse) Mean squared error (mse) Mean squared error (mse) 8 Applied Bionics and Biomechanics –2 –4 –6 –8 –10 0 200 400 600 800 1000 1200 Sample point number Error Prediction results (a) –5 0 200 400 600 800 1000 1200 Sample point number Error Prediction results (b) –2 –4 –6 –8 –10 0 200 400 600 800 1000 1200 Sample point number Error Prediction results (c) Figure 10: Assessment results and errors in each direction. Torque Z/N·m Torque X/N·m Torque Y/N·m Applied Bionics and Biomechanics 9 the joint position for a specific individual and expand the Table 1: MAV and MSE of ANN assessment. spatial distribution with less measurement data. MAV[N·m] MSE[N·m] RE X 6.399 0.093 0.0145 Data Availability Y 5.172 0.139 0.0269 The position data and force/torque data used to support the Z 1.728 0.104 0.0602 findings of this study are included within the article. plotting. It can be seen that the prediction error was small Conflicts of Interest compared with the magnitude of each passive torque compo- The authors declare there is no conflict of interest regarding nent, and the specific mean absolute value (MAV) and mean square error (MSE) of the passive torque prediction are listed this publication. in Table 1. The relative error (RE) is defined as the ratio of the MSE to MAV. The results showed that the BPANN can pre- Acknowledgments dict the torque of the shoulder joint with high accuracy. For subject S2 and S3, similar accurate passive torque This research is supported by the National Key Research and Development Program of China (No. 2018YFB1307803) and perditions can be conducted by BPANN, which was not repeated in this paper for the sake of length. Although the the Natural Science Foundation of China (Project No. 51775367, 51975401, 51535008). upper limb is often treated as a rigid body link system, in fact, the biological tissue is not rigid and its characteristics, such as inertial parameters and elastic characteristics, will change References with the limb motion. Especially for the shoulder joint, its actual motion is coupled by the common motion of the gle- [1] R. Colombo, F. Pisano, S. 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Journal

Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Aug 28, 2020

References