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Prediction Algorithm of Parameters of Toe Clearance in the Swing Phase

Prediction Algorithm of Parameters of Toe Clearance in the Swing Phase Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4502719, 10 pages https://doi.org/10.1155/2019/4502719 Research Article Prediction Algorithm of Parameters of Toe Clearance in the Swing Phase 1 2 2 Tamon Miyake , Masakatsu G. Fujie, and Shigeki Sugano Graduate School of Creative Science and Engineering, Waseda University, Tokyo, Japan Faculty of Science and Engineering, Waseda University, Tokyo, Japan Correspondence should be addressed to Tamon Miyake; tamon-tamonc3@ruri.waseda.jp Received 22 March 2019; Revised 30 June 2019; Accepted 23 July 2019; Published 14 August 2019 Academic Editor: Loredana Zollo Copyright © 2019 Tamon Miyake 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. The adaptive control of gait training robots is aimed at improving the gait performance by assisting motion. In conventional robotics, it has not been possible to adjust the robotic parameters by predicting the toe motion, which is considered a tripping risk indicator. The prediction of toe clearance during walking can decrease the risk of tripping. In this paper, we propose a novel method of predicting toe clearance that uses a radial basis function network. The input data were the angles, angular velocities, and angular accelerations of the hip, knee, and ankle joints in the sagittal plane at the beginning of the swing phase. In the experiments, seven subjects walked on a treadmill for 360 s. The radial basis function network was trained with gait data ranging from 20 to 200 data points and tested with 100 data points. The root mean square error between the true and predicted values was 3.28 mm for the maximum toe clearance in the earlier swing phase and 2.30 mm for the minimum toe clearance in the later swing phase. Moreover, using gait data of other five subjects, the root mean square error between the true and predicted values was 4.04 mm for the maximum toe clearance and 2.88 mm for the minimum toe clearance when the walking velocity changed. This provided higher prediction accuracy compared with existing methods. The proposed algorithm used the information of joint movements at the start of the swing phase and could predict both the future maximum and minimum toe clearances within the same swing phase. 1. Introduction which allows patients to walk in a matter that is different from the desired trajectory determined for a healthy person Robotic technology for physical human-robot interaction [4–6]. LOPES II, which is an end-effector type robot, is able has the potential to improve human locomotion. More- to switch between low and high mechanical impedance modes using admittance control [7]. These robots adapt to over, robotic assistance can guide gait motion and provide direct somatosensory information. Robotic guidance is individual differences and adjust their reference trajectory effective because the effects of training last longer when to recover motor functioning for gait trajectory generation. people instinctively modify their motion, compared with Conventional algorithms are adaptive after human action, when they consciously modify their motion [1]. Assistance and assistance methods for determining the robotic parame- should be provided only when it is required because the ters by previously predicting the gait motion have not yet human movement ability decreases when it is not actively been established. used [2]. Hence, there is a need for developing adaptive Falling is one of the most serious problems with locomo- robotic assistance technology that encourages maximum tion. The risk of falling encourages people to stay indoors, active patient participation. which leads to the weakening of their bodies. Moreover, The human-centered control of robotics for gait training tripping accounts for 53% of falling incidents [8]. Older is being investigated in an attempt to make robotic systems individuals are in more risk of tripping while taking small more human-friendly [3]. Gait training robots, such as ALEX steps because it is difficult for them to assess the height and Lokomat, have an interaction force field controller, difference at the edges of rugs or carpets [9]. Toe clearance 2 Applied Bionics and Biomechanics Normalized must be ensured to avoid falling and controlled to reduce the data dispersion. The possibility of tripping occurs if the toe Extract angular Regression with approaches the ground at an arbitrary point in the gait cycle. information Input RBFN The prediction of toe clearance can reduce the risk of Output tripping. For robotic assistance to increase the toe clearance Hip when it decreases in the gait cycle, a method of predicting toe clearance is required. Calculation techniques with wearable sensors deriving Knee the toe clearance have been developed mainly for ambulatory estimation and monitoring of the toe clearance without a Toe trajectory Ankle camera system [10–14]. The integration of the inertial Swing starts parameters of the inertial measurement unit (IMU), which consists of triaxial accelerometers and gyroscopes, was Figure 1: Overview of the dataflow of the proposed algorithm. carried out to estimate the toe parameters [10–12]. The dedrifted integration of two wirelesses IMUs attached to the feet can estimate the foot clearance with an error of approx- among the gait cycles. Moreover, we assumed that adding the imately 20 mm [12]. Owing to this large error, the integration angular velocity and acceleration of the lower limb joint method has a large limitation with regard to calculating the would be beneficial because these parameters contain information regarding the movement over time. Previous position. A machine learning method has been developed to estimate the gait parameters after the learning phase in studies have investigated computational technology, such each person [13–15]. Using machine learning with Gaussian as accelerometers [19, 20], gyroscopes [21, 22], and IMUs functions and a hill-climbing feature-selection method, the [23], for the detection of foot-contact state using wearable root mean square error (RMSE) of 6.6 mm was estimated sensors and machine learning strategies implementing support vector machines (SVM) [24], linear discriminant for young individuals [14]. In previous research, the parameters of toe clearance were predicted by a regression analysis (LDA) [25], Gaussian mixture model (GMM) model [15]. To the best of our knowledge, Gaussian func- [26], and hidden Markov model (HMM) [27, 28]. Notably, tions that were applied using acceleration features through none of these methods can detect the characteristic points the double differentiation of the toe position captured with of phase change in the angular trajectory. In a previous work, we extracted the characteristic angular point with a motion capture system could predict the minimum toe clearance most accurately (an RMSE of 3.7 mm) for one consideration to the change of synergy between the hip, gait cycle ahead. knee, and ankle joints and only predicted the minimum The existing prediction method has a limitation with toe clearance with higher accuracy [17]. However, the regard to establishing robotic assistance that increases the wearable sensor tends to deviate while people walk, and the sensed values always contain noises. Compensation is toe clearance when it decreases, because the system does not use wearable sensors that can communicate with a robot required for the deviation of the sensed values. controller. The estimation accuracy is lower when the wear- In this study, we established an algorithm to predict the able inertial sensor is used, compared with when the motion characteristic toe clearance parameters in the swing phase capture system is used to extract the input data. Moreover, using the angles, angular velocities, and angular accelerations of the lower limb joints. We applied machine learning-based the existing method is not sufficiently accurate for handling the toe clearance variability between the gait cycles. Addi- regression with Gaussian functions to probabilistically pre- tionally, it has been reported that the interquartile range of dict the toe clearance with consideration to the noise of the input data. Additionally, we investigated the relationship the minimum toe clearance is approximately 4.3 mm for young individuals and approximately 5.3 mm for older between the number of training data and the prediction accu- individuals [16]. Detecting a lower value for the minimum racy, and we evaluated the prediction algorithm to investigate toe clearance with a probability of more than 50% may be whether our method could more accurately predict the toe difficult using this method. Hence, a more accurate toe clearance and detect the lower value of toe clearance. clearance prediction method that uses wearable sensors to obtain the input data is required for robotic assistance. 2. Materials and Methods We developed a prediction algorithm of minimum toe clearance using the angular information of the lower limb The proposed method consisted of extraction of input data joints [17]. Our hypothesis is that the articular motion infor- and a regression algorithm using the radial basis function mation at the lower limb joints at the time when people start network (RBFN) to predict the characteristic parameters of to swing their leg is related to the future toe clearance because the toe clearance as shown in Figure 1. The algorithm was the toe motion is generated by the swing motion of the lower designed to automatically extract the input data points in limb. People control their leg motion based on interjoint an earlier swing phase and normalize these input values to coordination, and the angular coordination maintains low reduce the effect of the deviation of the sensor. dispersion at the limb end points [18]. Therefore, we The characteristic phase of input data was extracted with assumed that the difference between the angular information consideration to the synergy between the hip, knee, and ankle in a certain phase is related to the difference of toe clearance joints. The angular trajectory in the angular space is on the Hip joint angle (°) Applied Bionics and Biomechanics 3 Detect transition of the planes 1. Calculation of planes 1. Calculates plane Angular data were 2. Detect plane that sensed angular data belong to extracted from the The plane is calculated middle of each motion ① Swing up ④ Support ③ Loading response ② Swing down Average G Eigen vector w −2 −4 2. Detection of plane that sensed angular data belong to −6 −8 Plane B Q Q −10 60 (t-2) (t) Q Convergent point Q (t-1) (t) Plane A −12 is switching point −20 from plane A to plane B −10 −20 Q: sensed angular data Figure 2: Overview of the algorithm for deriving the four planes in the angular space of the hip, knee, and ankle joints and for detecting the transitions of the planes. planes during walking [29], and the planes of these angles are the parts of the angular data corresponding to the motion different in the phases [30]. Detecting the change from the of supporting the body were extracted when the hip joint stance phase to the swing plane can be done more clearly in was in extension and the ankle joint was in dorsiflexion. the planes, whereas detecting changes with the angle readings The robot extracted the angular data in the middle of the is difficult owing to the presence of noise and fluctuations in swing or stance phase based on the hip angle readings. the angle range. As shown in Figure 2, the controller explores Two basis vectors constituting the plane can be derived four planes in one gait cycle because the gait motion of the using principal component analysis (PCA) and the extracted lower limb consists of the swing of the leg to lift the foot parts of the angular data. The controller calculates the eigen- (swing up), the swing of the leg to prepare foot-ground con- vectors of the first and second components, which are the tact (swing down), the loading response to absorb the shock basis vectors of the plane, using PCA. The vector from the of foot contact (loading response), and support for the body preprojection coordinates to the postprojection coordinates (support). First, the controller derives basis vectors of the is orthogonal to the basis vectors of the plane. Moreover, planes by extracting parts of the angular data in each phase the two eigenvectors w and w are perpendicular to each 1 2 (block 1 of Figure 1). Second, the controller detects the other. Using this relationship, the coordinates P on the plane switching points from the support phase to the swing up are defined as follows: phase in an angular space so as to detect the time points when the swing phase starts (block 2 of Figure 1). P = a w + a w + G, 1 1 2 2 Parts of the angular data were extracted based on the hip angle to derive the planes for deriving the basis vectors of the a = Q · w − G · w , 1 1 1 1 planes (block 1 of the Figure 1). The maximum angle was a = Q · w − G · w , defined as 100%, and the minimum angle was defined as 2 2 2 0%. First, the angular data were categorized as belonging to the motion of the swing up and were extracted when the where a and a are the coefficients of the eigenvectors, 1 2 hip motion was in more than 10% flexion and the knee joint G denotes the coordinates of the mean angle data, and was in flexion. Next, the angular data corresponding to the Q denotes the sensed coordinates of the lower limb motion of the swing down were extracted when the knee joint articular angular space before projection. a and a are 1 2 extended and the hip flexion angle was within 30% after the calculated using the inner product of the eigenvectors swinging motion. Additionally, angular data corresponding and orthogonal vectors. to the loading response (i.e., dual-support phase) were The algorithm calculates the distance from the preprojec- extracted when the hip joint was in extension, the knee joint tion coordinates to the postprojection coordinates on each was in flexion, and the dorsiflexion angle of the ankle joint plane to derive the switching points of the planes (block 2 was less than 10% from the second minimum value. Finally, of Figure 1). Additionally, the algorithm calculates the inner Knee joint angle (°) Ankle joint angle (°) Eigen vector w 2 4 Applied Bionics and Biomechanics Section plane The angular point that is closest to the section plane is extracted in each gait cycle Section Angular Angular plane points trajectory Angular trajectory Figure 3: Extraction method of input values by finding the angular point that is the closest to the section plane when the gait state changes from the stance phase to the swing phase. Extracted time points 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Time (s) Figure 4: Gait phase detection result of extracting time points for use as input to the prediction algorithm. product between the unit vector from a previously sensed vector. Finally, as shown in Figure 4, the angular points for angular point to the currently sensed angular point and the the input data are extracted by finding the time point where unit vector from a previous projected point to the current the distance from the sensed angular point to the point projected point. The sensed angular data are recognized as projected onto the section plane is minimum. a phase whose plane is closer to the data, compared with The parameters of toe clearance were calculated using the RBFN with Gaussian functions, as shown in Figure 5. The the other planes, when the distance is the local minimum and the inner product is more than 0.9. RBFN is the linear sum of the radial basis functions, such The phase when the swing starts can be derived by as the Gaussian functions, for nonlinear curve fitting. The observing whether the angular trajectory passes through the RBFN consists of an input layer, a hidden layer with radial section plane that was previously calculated using the plane basis functions, and an output layer. This network calculates structure as shown in Figure 3. The section plane is calculated the distance between the vector of the input data and the because it is difficult to detect the switching points of the centroids of each Gaussian, which are derived using the planes in real time owing to the shifting of the plane during K-means clustering algorithm to partition the dataset into walking. First, the switching points from the plane of support a predetermined number of groups according to the Euclid- to the plane of swing up were derived using the data obtained ean distance. The RBFN structure is expressed as follows: from the 20 gait cycles. Next, the section plane of the angular N 2 trajectory is calculated when the swing phase starts. The x − c y = 〠 w exp − + α, 3 average switching point is estimated, and the normal vector k k=1 of the section plane is calculated by deriving the vector from the detected switching points to the next sensed angular where y denotes the output vector, w is the weight vector, x point. The orthogonal vector v of the normal vector can be is the input vector, c is the centroid vector, N is the number calculated as follows: of RBF units, α is a variable coefficient, and σ is a variable related to the standard deviation of the Gaussian function. v=2bc, –ac, –ab , 2 σ is derived as follows [31]: where a, b, and c denote the hip, knee, and ankle joint angles max σ = , 4 that constitute the normal vector, respectively. The basis Nm vectors of the section plane are two orthogonal vectors of the normal vector, which is calculated by deriving the cross where d denotes the maximum distance among the data max product between the first orthogonal vector and the normal and m is the dimension of the data. Toe height (mm) Applied Bionics and Biomechanics 5 2 Goniometer Input Output Figure 5: Structure of the radial basis function network (RBFN). Marker The angles of the hip, knee, and ankle joints in the sagittal plane were sensed with wearable angle sensors. The angular velocity and angular acceleration of these joints were derived Figure 6: Experimental image of subjects walking on a treadmill. by differentiating the angles with a pseudo differential. The angles were smoothed using a low-pass filter (with a cutoff frequency of 6 Hz). The equation of the pseudo differential phase were measured to give characteristic toe clearance data. based on an s-plane to z-plane transformation is expressed The toe coordinates of the right foot were measured with a as follows: motion capture system (Raptor-E; Motion Analysis, Santa Rosa, CA, USA). The marker for the measurement was X − X + T Y n n−1 d n−1 Y = , 5 n attached to the first metatarsophalangeal joint of the foot. ΔT The angles of the right hip, knee, and ankle joints were measured with goniometers (SG110 and SG150, Biometrics where T denotes the time constant, ΔT denotes the Ltd., Newport, UK), which are wearable angle sensors. The sampling time, which was 8.33 ms, and Y and X denote n n th th subjects walked on a treadmill as shown in Figure 6. the n differential value and n input value, respectively. The 6 subjects were instructed to continue walking for In this study, T was considered 167 ms to differentiate the 360 s at a preferred constant speed ranging from 2.1 km/h data whose frequency was lower than 6 Hz. to 3.0 km/h in the first experiment. We investigated the All input values were normalized to reduce the effect of number of training data points required for the RBFN to attachment position deviation of the wearable angle sensors. improve the prediction accuracy. We used 20 to 200 gait The minimum values in the previous gait cycle were cycle data points for the training and 100 gait cycle data subtracted from the input values. Moreover, all input values points for the RBFN test. The number of RBF units was set were divided by their range of values in the first gait cycle from two to twenty. in the training phase for RBFN so as to decrease the effect The 5 subjects walked for 600 s at 2.0 km/h, 2.5 km/h, of the range of values. and 3.0 km/h in the second experiment. The duration of walking at 2.5 km/h was 360 s, and the duration of walking 3. Human Walking Experiment at 2.0 km/h and 3.0 km/h was 120 s. We investigated Four healthy younger adults (three men and one woman; aged whether the RBFN could predict the toe clearance if the 27 ± 5 years, body weight 57 ± 13 kg,height 1 walking speed changed. Approximately 160 cycle data of 64 ± 0 13 cm) and two healthy older adults (two men; aged 65 ± 2 years, 2.5 km/h walking were used as the training data based body weight 62 ± 1 kg,height 1 68 ± 0 03 cm) were recruited on the result of the first experiment, and the 100 gait cycle in the first experiment. Five healthy young adults (four men data points of 2.0 km/h and 3.0 km/h were used as the test and one woman; aged 25 ± 3 years, body weight 58 ± 9 kg, data. The number of RBF units was set from two to twenty. Moreover, we added the goniometers for a left height 1 63 ± 0 7cm) were recruited in the second experi- ment. All of them did not have neurological injuries or leg in this experiment. gait disorders. Before the experiment, the subjects were We derived the time from the time point where the provided with a detailed account of our experimental system extracted the input data to the time points for objectives and were informed that they could withdraw the maximum and minimum toe clearances. We calculated from the experiment whenever they desired, and we the average time of all training data and the standard devia- obtained their consent. This experiment was also approved tion to evaluate whether the system could have previously by the institutional review board at Waseda University predicted both the maximum and minimum clearances. We normalized the maximum and minimum toe clear- (No. 2017-085). Because the maximum values are an indicator of how ance values by defining the average of the training data as high people raise their foot and the minimum values are an zero as shown in Figure 7. The toe clearance values that were indicator of how high people can keep their foot above the lower than the average were negative (minus sign), while the ground, the maximum toe clearance in the earlier swing values that were higher than the average were positive (plus sign). We calculated the RMSE between the true value and phase and the minimum toe clearance in the later swing 6 Applied Bionics and Biomechanics 0.3 Dispersion of 0.25 toe clearance 0.2 0.15 0 Median 0.1 0.05 Maximum Minimum Figure 7: Normalization of toe clearance data. toe clearance toe clearance the predicted value of the maximum and minimum toe Figure 8: Time from points where the system extracted the input clearances, as follows: data to the points of the maximum and minimum toe clearances. The error bar indicates the standard deviation. ∑ y − y k=1 k k RMSE = , 6 where y denotes the true value, y denotes the predicted k k value, and n is the number of data points. Additionally, we estimated the accuracy percentage of the predicted data according to the accuracy of the plus or minus signs and counted the number of predicted values with the same sign as the true value, which was then divided by the total number of data points. 0 50 100 150 200 Number of training data points 4. Results and Discussion Subject 1 Subject 4 Figure 8 shows the time from the time points where the Subject 2 Subject 5 system extracted the input data to the time points of the Subject 3 Subject 6 maximum or minimum toe clearances. The input data were extracted 0.1 s before the toe clearance reached the maximum Figure 9: Prediction result for maximum toe clearance using 100 value in the earlier swing phase. test gait data (RMSE). Figures 9 and 10 show the RMSE between the true and predicted data for the maximum and minimum toe clear- ances corresponding to the number of training data points. The RMSE tended to decrease as the number of training data increased. Particularly, the RMSE was minimum when the 6 number of training data points was 200 for subjects 1, 3, and 6. The other subjects had a minimum RMSE when the number of training data points was between 80 and 180. For the maximum toe clearance, the average minimum RMSE was 2.99 mm, and the lowest RMSE was 2.31 mm. For the minimum toe clearance, the average minimum 0 50 100 150 200 RMSE was 2.34 mm, and the lowest RMSE was 1.79 mm. Number of training data points The number of RBF units that minimized the RMSE was Subject 1 Subject 4 approximately five. Subject 2 Subject 5 Figures 11 and 12 show the accuracy rate of the predicted Subject 3 Subject 6 data for the maximum and minimum toe clearances corre- sponding to the number of training data points. The average Figure 10: Prediction result for minimum toe clearance using 100 accuracy rate was 71% for the maximum toe clearance and test gait data (RMSE). 68% for the minimum toe clearance. Figure 8 shows the average time from the time points where the system extracted the input data to the time points imately 1.4 s in this experiment. The variance in the detection where the maximum or minimum toe clearances were time plays a role in reducing the time. By improving the accu- positive. This means that the proposed algorithm was able racy of phase detection, the prediction can be made earlier. to extract the input data before the toe clearance reached its As shown in Figures 9 and 10, the RMSE between the real maximum value in the earlier swing phase. However, time toe clearance measured by the motion capture system and the was not always constant. The standard deviation was large predicted toe clearance was the lowest between 80 and 200 compared with the time of the gait cycle, which was approx- training data points. Moreover, the accuracy rate tended to RMSE (mm) RMSE (mm) Time (s) Applied Bionics and Biomechanics 7 100 between cycles increased. The probability of detecting a value lower than that of the median toe clearance was higher than 68%; that is, the probability was higher than the probability of random detection. Figures 13 and 14 show the RMSE and the accuracy rate of the predicted data for the maximum and minimum toe clearances of 100 test data by training the RBFN using approximately 160 training data in the case of the walking 0 50 100 150 200 velocity. The prediction error of the minimum toe clearance Number of training data points was lower compared with the previous researches even when Subject 1 Subject 4 the walking speed changed after the RBFN was learned with a Subject 2 Subject 5 constant walking speed. Moreover, the proposed algorithm Subject 3 Subject 6 could detect the value lower than that of the median toe Figure 11: Prediction result for maximum toe clearance using 100 clearance with the probability that was higher than the test gait data (accuracy rate). probability of random detection if walking velocity changed. We assumed that the RBFN parameters reflected the differ- ence of foot kinematics related to the change of the walking velocity because the input data were related to the kinematics of the lower limb. However, the RMSE of the minimum toe clearance and the maximum toe clearance increased when the walking velocity changed. It will be beneficial to train the RMSE with the input data in several conditions for generalized regression. Besides, the standard deviation of the RMSE of all subjects decreased when the left leg joints’ information was included as the input values. We assumed that it indicated that more numbers of input parameters 050 100 150 200 related to foot kinematics improved the prediction accuracy. Number of training data points As a future work, we will focus on both the feet and increase Subject 1 Subject 4 of the input parameters of joints of both lower limbs. Subject 2 Subject 5 The proposed algorithm has an advantage of deriving the Subject 3 Subject 6 toe clearance preliminarily in real time while most previous calculation methods were developed for the estimation of Figure 12: Prediction result for minimum toe clearance using 100 test gait data (accuracy rate). toe clearance [10–14]. Moreover, the prediction accuracy of the proposed algorithm was higher than that of the previous increase when the number of training data points increased. method [15]. Although we normalized the data of the toe Therefore, a higher number of training data points tended clearance for evaluating whether the algorithm could detect to improve the prediction accuracy, presumably because it the value lower than that of the median toe clearance, the became easier to extract the characteristics of the input data toe height from the ground could be derived because the subtracted value is clear. The proposed system has a limita- space when more training data were provided. The RBFN clusters the input data and calculates the median values of tion because learning is needed in each person, which is each cluster in the training phase. The output values are similar to previous MTC estimation methods using wearable determined according to the distance of the input data values sensors. Therefore, it requires a learning phase with a camera from the median values of each cluster. If the number of system before using the algorithm. The accuracy was lower for subjects whose gait motion training data points decreases, it becomes difficult to pre- cisely determine the RBFN parameters because the effect of and planes in an angular space tended to vary. The angular the input data noise increases. In this experiment, the cluster- information always changes with time within one gait cycle. ing of training data points and the derivation of the median One point on the periodic trajectory in an angular space required approximately 100 to 200 training data points to was extracted in each gait cycle. If phase detection errors occur, it is difficult to compare the articular angle, angular reduce the variance and the effect of the noise that is always present in data. velocity, and angular acceleration differences between the As shown in Figures 9 and 10, the RMSE was 2.99 mm for gait cycles. We used the planes of the articular space for the the maximum toe clearance and 2.34 mm for the minimum hip, knee, and ankle joints to detect the phase of the angular toe clearance, which is a more accurate prediction compared periodic trajectory. Because the trajectory varied between gait cycles, the planar vectors varied throughout the experiment. with previous methods. The RMSE of the maximum toe clearance was higher than the RMSE of the minimum toe The proposed algorithm considered the change of planes by clearance, because the variance of the maximum toe calculating the section plane of the trajectory around the clearance was higher than the variance of the minimum toe switching points, which was detected by calculating the clearance. The individual difference between the RMSE planes in each gait cycle. However, the phase when the input data were extracted might vary. This study demonstrated that tended to be higher as the variance of the toe clearance Accuracy rate (%) Accuracy rate (%) 8 Applied Bionics and Biomechanics 5.5 4.5 3.5 2.5 1.5 0.5 Minimum Maximum Minimum Maximum toe clearance toe clearance toe clearance toe clearance With three leg’s joints With six leg’s joints Figure 13: The prediction result using 100 test gait data when the walking velocity changes (RMSE). The values are the mean, and the error var means the standard deviation among the five subjects. Minimum Maximum Minimum Maximum toe clearance toe clearance toe clearance toe clearance With six leg’s joints With three leg’s joints Figure 14: The prediction result using 100 test gait data when the walking velocity changes (accuracy rate). The values are the mean, and the error var means the standard deviation among the five subjects. the toe clearance parameters can be predicted using only a robot using this algorithm may be able to influence the angular information in the sagittal plane. The accuracy of gait variance of human toe clearance. phase detection and the prediction of toe clearance may In a future work, we will improve the gait phase detection improve by increasing the input parameters, such as the method. Moreover, we will conduct experiments to investi- angles in the coronal plane or the foot contact information. gate the effect of robotic assistance with the proposed toe clearance prediction algorithm on older people. 5. Conclusions Data Availability This paper proposes a novel toe clearance prediction algo- rithm with an RBFN using the angles, angular velocities, The data used to support the findings of this study are available from the corresponding author upon request. and angular accelerations of the hip, knee, and ankle joints in the sagittal plane. The proposed algorithm can predict both the maximum toe clearance in the earlier swing phase Conflicts of Interest and the minimum toe clearance in the later swing phase at the same time. The error was 2.99 mm for the maximum The authors declare that there is no conflict of interest toe clearance and 2.34 mm for the minimum toe clearance. regarding the publication of this paper. Moreover, the root mean square error between the true and predicted values was 4.04 mm for the maximum toe Acknowledgments clearance, and 2.88 mm for the minimum toe clearance when the walking velocity changed. The errors of the minimum toe This work was supported in part by the Program for Leading clearance are smaller compared with previous methods. The Graduate Schools, “Graduate Program for Embodiment probability of detecting a value lower than the median toe Informatics” of the Ministry of Education, Culture, Sports, clearance was higher than 68%; that is, the probability was Science and Technology (MEXT) of Japan and Tateisi higher than the probability of random detection. Therefore, Science and Technology Foundation and supported by the Accuracy rate (%) RMSE (mm) Applied Bionics and Biomechanics 9 toe clearance using inertial measurement units,” Journal of Research Institute for Science and Engineering, Waseda Uni- Biomechanics, vol. 48, no. 16, pp. 4309–4316, 2015. versity. We thank Edanz Group (https://www.edanzediting .com/ac) for editing the draft of this manuscript. [15] D. T. Lai, S. B. Taylor, and R. K. 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Prediction Algorithm of Parameters of Toe Clearance in the Swing Phase

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Copyright © 2019 Tamon Miyake 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.
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Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 4502719, 10 pages https://doi.org/10.1155/2019/4502719 Research Article Prediction Algorithm of Parameters of Toe Clearance in the Swing Phase 1 2 2 Tamon Miyake , Masakatsu G. Fujie, and Shigeki Sugano Graduate School of Creative Science and Engineering, Waseda University, Tokyo, Japan Faculty of Science and Engineering, Waseda University, Tokyo, Japan Correspondence should be addressed to Tamon Miyake; tamon-tamonc3@ruri.waseda.jp Received 22 March 2019; Revised 30 June 2019; Accepted 23 July 2019; Published 14 August 2019 Academic Editor: Loredana Zollo Copyright © 2019 Tamon Miyake 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. The adaptive control of gait training robots is aimed at improving the gait performance by assisting motion. In conventional robotics, it has not been possible to adjust the robotic parameters by predicting the toe motion, which is considered a tripping risk indicator. The prediction of toe clearance during walking can decrease the risk of tripping. In this paper, we propose a novel method of predicting toe clearance that uses a radial basis function network. The input data were the angles, angular velocities, and angular accelerations of the hip, knee, and ankle joints in the sagittal plane at the beginning of the swing phase. In the experiments, seven subjects walked on a treadmill for 360 s. The radial basis function network was trained with gait data ranging from 20 to 200 data points and tested with 100 data points. The root mean square error between the true and predicted values was 3.28 mm for the maximum toe clearance in the earlier swing phase and 2.30 mm for the minimum toe clearance in the later swing phase. Moreover, using gait data of other five subjects, the root mean square error between the true and predicted values was 4.04 mm for the maximum toe clearance and 2.88 mm for the minimum toe clearance when the walking velocity changed. This provided higher prediction accuracy compared with existing methods. The proposed algorithm used the information of joint movements at the start of the swing phase and could predict both the future maximum and minimum toe clearances within the same swing phase. 1. Introduction which allows patients to walk in a matter that is different from the desired trajectory determined for a healthy person Robotic technology for physical human-robot interaction [4–6]. LOPES II, which is an end-effector type robot, is able has the potential to improve human locomotion. More- to switch between low and high mechanical impedance modes using admittance control [7]. These robots adapt to over, robotic assistance can guide gait motion and provide direct somatosensory information. Robotic guidance is individual differences and adjust their reference trajectory effective because the effects of training last longer when to recover motor functioning for gait trajectory generation. people instinctively modify their motion, compared with Conventional algorithms are adaptive after human action, when they consciously modify their motion [1]. Assistance and assistance methods for determining the robotic parame- should be provided only when it is required because the ters by previously predicting the gait motion have not yet human movement ability decreases when it is not actively been established. used [2]. Hence, there is a need for developing adaptive Falling is one of the most serious problems with locomo- robotic assistance technology that encourages maximum tion. The risk of falling encourages people to stay indoors, active patient participation. which leads to the weakening of their bodies. Moreover, The human-centered control of robotics for gait training tripping accounts for 53% of falling incidents [8]. Older is being investigated in an attempt to make robotic systems individuals are in more risk of tripping while taking small more human-friendly [3]. Gait training robots, such as ALEX steps because it is difficult for them to assess the height and Lokomat, have an interaction force field controller, difference at the edges of rugs or carpets [9]. Toe clearance 2 Applied Bionics and Biomechanics Normalized must be ensured to avoid falling and controlled to reduce the data dispersion. The possibility of tripping occurs if the toe Extract angular Regression with approaches the ground at an arbitrary point in the gait cycle. information Input RBFN The prediction of toe clearance can reduce the risk of Output tripping. For robotic assistance to increase the toe clearance Hip when it decreases in the gait cycle, a method of predicting toe clearance is required. Calculation techniques with wearable sensors deriving Knee the toe clearance have been developed mainly for ambulatory estimation and monitoring of the toe clearance without a Toe trajectory Ankle camera system [10–14]. The integration of the inertial Swing starts parameters of the inertial measurement unit (IMU), which consists of triaxial accelerometers and gyroscopes, was Figure 1: Overview of the dataflow of the proposed algorithm. carried out to estimate the toe parameters [10–12]. The dedrifted integration of two wirelesses IMUs attached to the feet can estimate the foot clearance with an error of approx- among the gait cycles. Moreover, we assumed that adding the imately 20 mm [12]. Owing to this large error, the integration angular velocity and acceleration of the lower limb joint method has a large limitation with regard to calculating the would be beneficial because these parameters contain information regarding the movement over time. Previous position. A machine learning method has been developed to estimate the gait parameters after the learning phase in studies have investigated computational technology, such each person [13–15]. Using machine learning with Gaussian as accelerometers [19, 20], gyroscopes [21, 22], and IMUs functions and a hill-climbing feature-selection method, the [23], for the detection of foot-contact state using wearable root mean square error (RMSE) of 6.6 mm was estimated sensors and machine learning strategies implementing support vector machines (SVM) [24], linear discriminant for young individuals [14]. In previous research, the parameters of toe clearance were predicted by a regression analysis (LDA) [25], Gaussian mixture model (GMM) model [15]. To the best of our knowledge, Gaussian func- [26], and hidden Markov model (HMM) [27, 28]. Notably, tions that were applied using acceleration features through none of these methods can detect the characteristic points the double differentiation of the toe position captured with of phase change in the angular trajectory. In a previous work, we extracted the characteristic angular point with a motion capture system could predict the minimum toe clearance most accurately (an RMSE of 3.7 mm) for one consideration to the change of synergy between the hip, gait cycle ahead. knee, and ankle joints and only predicted the minimum The existing prediction method has a limitation with toe clearance with higher accuracy [17]. However, the regard to establishing robotic assistance that increases the wearable sensor tends to deviate while people walk, and the sensed values always contain noises. Compensation is toe clearance when it decreases, because the system does not use wearable sensors that can communicate with a robot required for the deviation of the sensed values. controller. The estimation accuracy is lower when the wear- In this study, we established an algorithm to predict the able inertial sensor is used, compared with when the motion characteristic toe clearance parameters in the swing phase capture system is used to extract the input data. Moreover, using the angles, angular velocities, and angular accelerations of the lower limb joints. We applied machine learning-based the existing method is not sufficiently accurate for handling the toe clearance variability between the gait cycles. Addi- regression with Gaussian functions to probabilistically pre- tionally, it has been reported that the interquartile range of dict the toe clearance with consideration to the noise of the input data. Additionally, we investigated the relationship the minimum toe clearance is approximately 4.3 mm for young individuals and approximately 5.3 mm for older between the number of training data and the prediction accu- individuals [16]. Detecting a lower value for the minimum racy, and we evaluated the prediction algorithm to investigate toe clearance with a probability of more than 50% may be whether our method could more accurately predict the toe difficult using this method. Hence, a more accurate toe clearance and detect the lower value of toe clearance. clearance prediction method that uses wearable sensors to obtain the input data is required for robotic assistance. 2. Materials and Methods We developed a prediction algorithm of minimum toe clearance using the angular information of the lower limb The proposed method consisted of extraction of input data joints [17]. Our hypothesis is that the articular motion infor- and a regression algorithm using the radial basis function mation at the lower limb joints at the time when people start network (RBFN) to predict the characteristic parameters of to swing their leg is related to the future toe clearance because the toe clearance as shown in Figure 1. The algorithm was the toe motion is generated by the swing motion of the lower designed to automatically extract the input data points in limb. People control their leg motion based on interjoint an earlier swing phase and normalize these input values to coordination, and the angular coordination maintains low reduce the effect of the deviation of the sensor. dispersion at the limb end points [18]. Therefore, we The characteristic phase of input data was extracted with assumed that the difference between the angular information consideration to the synergy between the hip, knee, and ankle in a certain phase is related to the difference of toe clearance joints. The angular trajectory in the angular space is on the Hip joint angle (°) Applied Bionics and Biomechanics 3 Detect transition of the planes 1. Calculation of planes 1. Calculates plane Angular data were 2. Detect plane that sensed angular data belong to extracted from the The plane is calculated middle of each motion ① Swing up ④ Support ③ Loading response ② Swing down Average G Eigen vector w −2 −4 2. Detection of plane that sensed angular data belong to −6 −8 Plane B Q Q −10 60 (t-2) (t) Q Convergent point Q (t-1) (t) Plane A −12 is switching point −20 from plane A to plane B −10 −20 Q: sensed angular data Figure 2: Overview of the algorithm for deriving the four planes in the angular space of the hip, knee, and ankle joints and for detecting the transitions of the planes. planes during walking [29], and the planes of these angles are the parts of the angular data corresponding to the motion different in the phases [30]. Detecting the change from the of supporting the body were extracted when the hip joint stance phase to the swing plane can be done more clearly in was in extension and the ankle joint was in dorsiflexion. the planes, whereas detecting changes with the angle readings The robot extracted the angular data in the middle of the is difficult owing to the presence of noise and fluctuations in swing or stance phase based on the hip angle readings. the angle range. As shown in Figure 2, the controller explores Two basis vectors constituting the plane can be derived four planes in one gait cycle because the gait motion of the using principal component analysis (PCA) and the extracted lower limb consists of the swing of the leg to lift the foot parts of the angular data. The controller calculates the eigen- (swing up), the swing of the leg to prepare foot-ground con- vectors of the first and second components, which are the tact (swing down), the loading response to absorb the shock basis vectors of the plane, using PCA. The vector from the of foot contact (loading response), and support for the body preprojection coordinates to the postprojection coordinates (support). First, the controller derives basis vectors of the is orthogonal to the basis vectors of the plane. Moreover, planes by extracting parts of the angular data in each phase the two eigenvectors w and w are perpendicular to each 1 2 (block 1 of Figure 1). Second, the controller detects the other. Using this relationship, the coordinates P on the plane switching points from the support phase to the swing up are defined as follows: phase in an angular space so as to detect the time points when the swing phase starts (block 2 of Figure 1). P = a w + a w + G, 1 1 2 2 Parts of the angular data were extracted based on the hip angle to derive the planes for deriving the basis vectors of the a = Q · w − G · w , 1 1 1 1 planes (block 1 of the Figure 1). The maximum angle was a = Q · w − G · w , defined as 100%, and the minimum angle was defined as 2 2 2 0%. First, the angular data were categorized as belonging to the motion of the swing up and were extracted when the where a and a are the coefficients of the eigenvectors, 1 2 hip motion was in more than 10% flexion and the knee joint G denotes the coordinates of the mean angle data, and was in flexion. Next, the angular data corresponding to the Q denotes the sensed coordinates of the lower limb motion of the swing down were extracted when the knee joint articular angular space before projection. a and a are 1 2 extended and the hip flexion angle was within 30% after the calculated using the inner product of the eigenvectors swinging motion. Additionally, angular data corresponding and orthogonal vectors. to the loading response (i.e., dual-support phase) were The algorithm calculates the distance from the preprojec- extracted when the hip joint was in extension, the knee joint tion coordinates to the postprojection coordinates on each was in flexion, and the dorsiflexion angle of the ankle joint plane to derive the switching points of the planes (block 2 was less than 10% from the second minimum value. Finally, of Figure 1). Additionally, the algorithm calculates the inner Knee joint angle (°) Ankle joint angle (°) Eigen vector w 2 4 Applied Bionics and Biomechanics Section plane The angular point that is closest to the section plane is extracted in each gait cycle Section Angular Angular plane points trajectory Angular trajectory Figure 3: Extraction method of input values by finding the angular point that is the closest to the section plane when the gait state changes from the stance phase to the swing phase. Extracted time points 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Time (s) Figure 4: Gait phase detection result of extracting time points for use as input to the prediction algorithm. product between the unit vector from a previously sensed vector. Finally, as shown in Figure 4, the angular points for angular point to the currently sensed angular point and the the input data are extracted by finding the time point where unit vector from a previous projected point to the current the distance from the sensed angular point to the point projected point. The sensed angular data are recognized as projected onto the section plane is minimum. a phase whose plane is closer to the data, compared with The parameters of toe clearance were calculated using the RBFN with Gaussian functions, as shown in Figure 5. The the other planes, when the distance is the local minimum and the inner product is more than 0.9. RBFN is the linear sum of the radial basis functions, such The phase when the swing starts can be derived by as the Gaussian functions, for nonlinear curve fitting. The observing whether the angular trajectory passes through the RBFN consists of an input layer, a hidden layer with radial section plane that was previously calculated using the plane basis functions, and an output layer. This network calculates structure as shown in Figure 3. The section plane is calculated the distance between the vector of the input data and the because it is difficult to detect the switching points of the centroids of each Gaussian, which are derived using the planes in real time owing to the shifting of the plane during K-means clustering algorithm to partition the dataset into walking. First, the switching points from the plane of support a predetermined number of groups according to the Euclid- to the plane of swing up were derived using the data obtained ean distance. The RBFN structure is expressed as follows: from the 20 gait cycles. Next, the section plane of the angular N 2 trajectory is calculated when the swing phase starts. The x − c y = 〠 w exp − + α, 3 average switching point is estimated, and the normal vector k k=1 of the section plane is calculated by deriving the vector from the detected switching points to the next sensed angular where y denotes the output vector, w is the weight vector, x point. The orthogonal vector v of the normal vector can be is the input vector, c is the centroid vector, N is the number calculated as follows: of RBF units, α is a variable coefficient, and σ is a variable related to the standard deviation of the Gaussian function. v=2bc, –ac, –ab , 2 σ is derived as follows [31]: where a, b, and c denote the hip, knee, and ankle joint angles max σ = , 4 that constitute the normal vector, respectively. The basis Nm vectors of the section plane are two orthogonal vectors of the normal vector, which is calculated by deriving the cross where d denotes the maximum distance among the data max product between the first orthogonal vector and the normal and m is the dimension of the data. Toe height (mm) Applied Bionics and Biomechanics 5 2 Goniometer Input Output Figure 5: Structure of the radial basis function network (RBFN). Marker The angles of the hip, knee, and ankle joints in the sagittal plane were sensed with wearable angle sensors. The angular velocity and angular acceleration of these joints were derived Figure 6: Experimental image of subjects walking on a treadmill. by differentiating the angles with a pseudo differential. The angles were smoothed using a low-pass filter (with a cutoff frequency of 6 Hz). The equation of the pseudo differential phase were measured to give characteristic toe clearance data. based on an s-plane to z-plane transformation is expressed The toe coordinates of the right foot were measured with a as follows: motion capture system (Raptor-E; Motion Analysis, Santa Rosa, CA, USA). The marker for the measurement was X − X + T Y n n−1 d n−1 Y = , 5 n attached to the first metatarsophalangeal joint of the foot. ΔT The angles of the right hip, knee, and ankle joints were measured with goniometers (SG110 and SG150, Biometrics where T denotes the time constant, ΔT denotes the Ltd., Newport, UK), which are wearable angle sensors. The sampling time, which was 8.33 ms, and Y and X denote n n th th subjects walked on a treadmill as shown in Figure 6. the n differential value and n input value, respectively. The 6 subjects were instructed to continue walking for In this study, T was considered 167 ms to differentiate the 360 s at a preferred constant speed ranging from 2.1 km/h data whose frequency was lower than 6 Hz. to 3.0 km/h in the first experiment. We investigated the All input values were normalized to reduce the effect of number of training data points required for the RBFN to attachment position deviation of the wearable angle sensors. improve the prediction accuracy. We used 20 to 200 gait The minimum values in the previous gait cycle were cycle data points for the training and 100 gait cycle data subtracted from the input values. Moreover, all input values points for the RBFN test. The number of RBF units was set were divided by their range of values in the first gait cycle from two to twenty. in the training phase for RBFN so as to decrease the effect The 5 subjects walked for 600 s at 2.0 km/h, 2.5 km/h, of the range of values. and 3.0 km/h in the second experiment. The duration of walking at 2.5 km/h was 360 s, and the duration of walking 3. Human Walking Experiment at 2.0 km/h and 3.0 km/h was 120 s. We investigated Four healthy younger adults (three men and one woman; aged whether the RBFN could predict the toe clearance if the 27 ± 5 years, body weight 57 ± 13 kg,height 1 walking speed changed. Approximately 160 cycle data of 64 ± 0 13 cm) and two healthy older adults (two men; aged 65 ± 2 years, 2.5 km/h walking were used as the training data based body weight 62 ± 1 kg,height 1 68 ± 0 03 cm) were recruited on the result of the first experiment, and the 100 gait cycle in the first experiment. Five healthy young adults (four men data points of 2.0 km/h and 3.0 km/h were used as the test and one woman; aged 25 ± 3 years, body weight 58 ± 9 kg, data. The number of RBF units was set from two to twenty. Moreover, we added the goniometers for a left height 1 63 ± 0 7cm) were recruited in the second experi- ment. All of them did not have neurological injuries or leg in this experiment. gait disorders. Before the experiment, the subjects were We derived the time from the time point where the provided with a detailed account of our experimental system extracted the input data to the time points for objectives and were informed that they could withdraw the maximum and minimum toe clearances. We calculated from the experiment whenever they desired, and we the average time of all training data and the standard devia- obtained their consent. This experiment was also approved tion to evaluate whether the system could have previously by the institutional review board at Waseda University predicted both the maximum and minimum clearances. We normalized the maximum and minimum toe clear- (No. 2017-085). Because the maximum values are an indicator of how ance values by defining the average of the training data as high people raise their foot and the minimum values are an zero as shown in Figure 7. The toe clearance values that were indicator of how high people can keep their foot above the lower than the average were negative (minus sign), while the ground, the maximum toe clearance in the earlier swing values that were higher than the average were positive (plus sign). We calculated the RMSE between the true value and phase and the minimum toe clearance in the later swing 6 Applied Bionics and Biomechanics 0.3 Dispersion of 0.25 toe clearance 0.2 0.15 0 Median 0.1 0.05 Maximum Minimum Figure 7: Normalization of toe clearance data. toe clearance toe clearance the predicted value of the maximum and minimum toe Figure 8: Time from points where the system extracted the input clearances, as follows: data to the points of the maximum and minimum toe clearances. The error bar indicates the standard deviation. ∑ y − y k=1 k k RMSE = , 6 where y denotes the true value, y denotes the predicted k k value, and n is the number of data points. Additionally, we estimated the accuracy percentage of the predicted data according to the accuracy of the plus or minus signs and counted the number of predicted values with the same sign as the true value, which was then divided by the total number of data points. 0 50 100 150 200 Number of training data points 4. Results and Discussion Subject 1 Subject 4 Figure 8 shows the time from the time points where the Subject 2 Subject 5 system extracted the input data to the time points of the Subject 3 Subject 6 maximum or minimum toe clearances. The input data were extracted 0.1 s before the toe clearance reached the maximum Figure 9: Prediction result for maximum toe clearance using 100 value in the earlier swing phase. test gait data (RMSE). Figures 9 and 10 show the RMSE between the true and predicted data for the maximum and minimum toe clear- ances corresponding to the number of training data points. The RMSE tended to decrease as the number of training data increased. Particularly, the RMSE was minimum when the 6 number of training data points was 200 for subjects 1, 3, and 6. The other subjects had a minimum RMSE when the number of training data points was between 80 and 180. For the maximum toe clearance, the average minimum RMSE was 2.99 mm, and the lowest RMSE was 2.31 mm. For the minimum toe clearance, the average minimum 0 50 100 150 200 RMSE was 2.34 mm, and the lowest RMSE was 1.79 mm. Number of training data points The number of RBF units that minimized the RMSE was Subject 1 Subject 4 approximately five. Subject 2 Subject 5 Figures 11 and 12 show the accuracy rate of the predicted Subject 3 Subject 6 data for the maximum and minimum toe clearances corre- sponding to the number of training data points. The average Figure 10: Prediction result for minimum toe clearance using 100 accuracy rate was 71% for the maximum toe clearance and test gait data (RMSE). 68% for the minimum toe clearance. Figure 8 shows the average time from the time points where the system extracted the input data to the time points imately 1.4 s in this experiment. The variance in the detection where the maximum or minimum toe clearances were time plays a role in reducing the time. By improving the accu- positive. This means that the proposed algorithm was able racy of phase detection, the prediction can be made earlier. to extract the input data before the toe clearance reached its As shown in Figures 9 and 10, the RMSE between the real maximum value in the earlier swing phase. However, time toe clearance measured by the motion capture system and the was not always constant. The standard deviation was large predicted toe clearance was the lowest between 80 and 200 compared with the time of the gait cycle, which was approx- training data points. Moreover, the accuracy rate tended to RMSE (mm) RMSE (mm) Time (s) Applied Bionics and Biomechanics 7 100 between cycles increased. The probability of detecting a value lower than that of the median toe clearance was higher than 68%; that is, the probability was higher than the probability of random detection. Figures 13 and 14 show the RMSE and the accuracy rate of the predicted data for the maximum and minimum toe clearances of 100 test data by training the RBFN using approximately 160 training data in the case of the walking 0 50 100 150 200 velocity. The prediction error of the minimum toe clearance Number of training data points was lower compared with the previous researches even when Subject 1 Subject 4 the walking speed changed after the RBFN was learned with a Subject 2 Subject 5 constant walking speed. Moreover, the proposed algorithm Subject 3 Subject 6 could detect the value lower than that of the median toe Figure 11: Prediction result for maximum toe clearance using 100 clearance with the probability that was higher than the test gait data (accuracy rate). probability of random detection if walking velocity changed. We assumed that the RBFN parameters reflected the differ- ence of foot kinematics related to the change of the walking velocity because the input data were related to the kinematics of the lower limb. However, the RMSE of the minimum toe clearance and the maximum toe clearance increased when the walking velocity changed. It will be beneficial to train the RMSE with the input data in several conditions for generalized regression. Besides, the standard deviation of the RMSE of all subjects decreased when the left leg joints’ information was included as the input values. We assumed that it indicated that more numbers of input parameters 050 100 150 200 related to foot kinematics improved the prediction accuracy. Number of training data points As a future work, we will focus on both the feet and increase Subject 1 Subject 4 of the input parameters of joints of both lower limbs. Subject 2 Subject 5 The proposed algorithm has an advantage of deriving the Subject 3 Subject 6 toe clearance preliminarily in real time while most previous calculation methods were developed for the estimation of Figure 12: Prediction result for minimum toe clearance using 100 test gait data (accuracy rate). toe clearance [10–14]. Moreover, the prediction accuracy of the proposed algorithm was higher than that of the previous increase when the number of training data points increased. method [15]. Although we normalized the data of the toe Therefore, a higher number of training data points tended clearance for evaluating whether the algorithm could detect to improve the prediction accuracy, presumably because it the value lower than that of the median toe clearance, the became easier to extract the characteristics of the input data toe height from the ground could be derived because the subtracted value is clear. The proposed system has a limita- space when more training data were provided. The RBFN clusters the input data and calculates the median values of tion because learning is needed in each person, which is each cluster in the training phase. The output values are similar to previous MTC estimation methods using wearable determined according to the distance of the input data values sensors. Therefore, it requires a learning phase with a camera from the median values of each cluster. If the number of system before using the algorithm. The accuracy was lower for subjects whose gait motion training data points decreases, it becomes difficult to pre- cisely determine the RBFN parameters because the effect of and planes in an angular space tended to vary. The angular the input data noise increases. In this experiment, the cluster- information always changes with time within one gait cycle. ing of training data points and the derivation of the median One point on the periodic trajectory in an angular space required approximately 100 to 200 training data points to was extracted in each gait cycle. If phase detection errors occur, it is difficult to compare the articular angle, angular reduce the variance and the effect of the noise that is always present in data. velocity, and angular acceleration differences between the As shown in Figures 9 and 10, the RMSE was 2.99 mm for gait cycles. We used the planes of the articular space for the the maximum toe clearance and 2.34 mm for the minimum hip, knee, and ankle joints to detect the phase of the angular toe clearance, which is a more accurate prediction compared periodic trajectory. Because the trajectory varied between gait cycles, the planar vectors varied throughout the experiment. with previous methods. The RMSE of the maximum toe clearance was higher than the RMSE of the minimum toe The proposed algorithm considered the change of planes by clearance, because the variance of the maximum toe calculating the section plane of the trajectory around the clearance was higher than the variance of the minimum toe switching points, which was detected by calculating the clearance. The individual difference between the RMSE planes in each gait cycle. However, the phase when the input data were extracted might vary. This study demonstrated that tended to be higher as the variance of the toe clearance Accuracy rate (%) Accuracy rate (%) 8 Applied Bionics and Biomechanics 5.5 4.5 3.5 2.5 1.5 0.5 Minimum Maximum Minimum Maximum toe clearance toe clearance toe clearance toe clearance With three leg’s joints With six leg’s joints Figure 13: The prediction result using 100 test gait data when the walking velocity changes (RMSE). The values are the mean, and the error var means the standard deviation among the five subjects. Minimum Maximum Minimum Maximum toe clearance toe clearance toe clearance toe clearance With six leg’s joints With three leg’s joints Figure 14: The prediction result using 100 test gait data when the walking velocity changes (accuracy rate). The values are the mean, and the error var means the standard deviation among the five subjects. the toe clearance parameters can be predicted using only a robot using this algorithm may be able to influence the angular information in the sagittal plane. The accuracy of gait variance of human toe clearance. phase detection and the prediction of toe clearance may In a future work, we will improve the gait phase detection improve by increasing the input parameters, such as the method. Moreover, we will conduct experiments to investi- angles in the coronal plane or the foot contact information. gate the effect of robotic assistance with the proposed toe clearance prediction algorithm on older people. 5. Conclusions Data Availability This paper proposes a novel toe clearance prediction algo- rithm with an RBFN using the angles, angular velocities, The data used to support the findings of this study are available from the corresponding author upon request. and angular accelerations of the hip, knee, and ankle joints in the sagittal plane. The proposed algorithm can predict both the maximum toe clearance in the earlier swing phase Conflicts of Interest and the minimum toe clearance in the later swing phase at the same time. The error was 2.99 mm for the maximum The authors declare that there is no conflict of interest toe clearance and 2.34 mm for the minimum toe clearance. regarding the publication of this paper. Moreover, the root mean square error between the true and predicted values was 4.04 mm for the maximum toe Acknowledgments clearance, and 2.88 mm for the minimum toe clearance when the walking velocity changed. 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