Gait_analysis_of_people_relying_on_mobility_aids_by_using_laser_range_finder.pdf

Gait analysis of people relying on mobility aids by using laser range finder 1st Tao Jiang School of Logistics Engineering Wuhan University of Technology Wuhan, China [email protected] 2nd Yanhong Ge School of Logistics Engineering Wuhan University of Technology Wuhan, China [email protected] Abstra...

Gait analysis of people relying on mobility aids by using laser range finder 1st Tao Jiang School of Logistics Engineering Wuhan University of Technology Wuhan, China [email protected] 2nd Yanhong Ge School of Logistics Engineering Wuhan University of Technology Wuhan, China [email protected] Abstract—Gait analysis provides an effective way for the elderly to monitor abnormal gait, predict fall risk, and evaluate rehabilitation training. The laser range finder mounted on the mobility aids is used to analyze gait characteristics in this paper. The leg data segment recognition method based on Kalman filtering and difference measure is proposed to estimate legs position. The system is developed that detects gait cycle by integrating the zero-point constraint and the crests-based detection method and extracts spatiotemporal gait characteristics. The experimental results demonstrate the effectiveness of the methods. Keywords—mobility aids, gait analysis, laser range finder, segment recognition, detecting gait cycle I. INTRODUCTION The mobility problems of the elderly for the decline in walking ability cause great inconvenience in daily life[1]. Walker, manual wheelchair, electric wheelchair and other mobility aids provide a reliable way for walking, so the demand of mobility aids for the elderly is increasing. Gait characteristics, as an external manifestation of walking ability, change accordingly, which have great significance for the diagnosis of abnormal gait and prediction of fall risk to the elderly. Various methods have been proposed for gait analysis. The image-based gait analysis system with high accuracy includes 3D motion capture system[2] and the video image processing system[3], but this way is expensive and complicated in data processing. Gait analysis methods based on wearable sensors, including MEMS inertial sensors[4], pressure sensors[5], and EMG sensors[6], analyze gait characteristics from changes in wearable sensor signals during walking by a low cost but invasive way. Gait analysis method based on laser sensors can avoid intrusive problems, gait characteristics are extracted by detecting the changes of distance between human legs and the laser range finder [7] [8]. The drawback of this way is static sensors with a limited detection range. The aim of this research is to perform gait analysis for the elderly in a non-invasive and continuous monitoring way without restricted movement range. Based on the increase of the elderly’s usage and demand of mobility aids , this research mounts laser sensor on the mobility aids to scan and obtain the movement of the legs, which is used to analyze the gait characteristics. Identification and tracking method for leg data segments based on Kalman filtering and difference measure is proposed to identify the leg data segment, determine its relative position and exclude the influence of interferences that may exist during walking for determining the leg coordinate accurately. Besides, it develops a system that detects gait cycle by integrating the China Disabled Persons' Federation for the development of disabled assistive devices (No. CJFJRRB01-2019). 3rd *Wenfeng Li School of Logistics Engineering Wuhan University of Technology Wuhan, China [email protected] zero-point constraint and the traditional crests-based detection method and extracts spatiotemporal gait characteristics associated with the mobility aids’ use. II. THE FRAMEWORK OF GAIT ANALYSIS SYSTEM In this research, the laser sensor is mounted on the mobility aids with a height of 30 cm from the ground. The gait characteristics are analyzed by measuring the relative displacement between the human leg and the mobility aids, as shown in Fig. 1 (a). The relative coordinate system is established by taking the laser sensor on the mobility aids as the origin and the forward direction as the X axis, as shown in Fig. 1 (b). The main workflow of the system is shown in Fig. 2. There are two procedures for data of each scan frame, including determining leg coordinates and gait analysis. Determining leg coordinates includes two processes: preprocession, segmentation and circular fitting, leg data segment recognition. Gait analysis is performed by the vibration of leg coordinate sequence, which includes two processes: gait cycle detection and gait characteristics analysis in one gait cycle. III. DETERMINING LEG COORDINATES We can obtain the original scan data by the laser sensor, which is used to determine two legs coordinates in the relative coordinate system. (a) (b) Fig. 1 (a) A mobility aids equipped with a laser sensor aiming to analyze gait characteristics. (b) Relative coordinate system of the mobility aids Determining Leg Coordinates Gait Analysis Preprocession ǃ Segmentation and Circular Fitting Gait Characteristics Leg Data Segment Recognition Gait Cycle Detection Fig. 2 The workflow of gait analysis system 978-1-7281-5871-6/20/$31.00 ©2020 IEEE Authorized licensed use limited to: CUNY Central ( City University of New York). Downloaded on November 15,2023 at 17:18:47 UTC from IEEE Xplore. Restrictions apply. A. Pre-procession, Segmentation and Circular Fitting For the limited motion range of the human when using mobility aids, a rectangular area of 1 m in length and 0.6m in width is defined as the scanning window of the laser sensor. For the data of each frame, Median filtering is used to eliminate noise. The data segment is divided according to the continuity between the scanning points. If the Euclidean distance between the continuous scanning points is higher than the threshold, the new data segment is divided. Taking into account the noise caused by factors such as laser sensor, data segments with lower number of points are deleted. The contour of human leg is approximately circular, so we perform circular fitting for the segment by using the least square method, and the center coordinates of the fitted circle are used as the position of the corresponding segment. B. Leg Data Segment Recognition Based on Kalman Filtering and Difference Measure We predict the motion state of the leg of next frame based on the Kalman filtering[9], determine the search domain of the leg data segment through the predicted value and propose a difference measurement rule by combining multiple spatial features of the leg during walking for the data segment in the search domain. The segment with the lowest difference is used as the leg data segment, and we use the measured value of this segment to modify the predicted value to determine the optimal coordinates of leg data segment. 1) Leg state estimation based on Kalman filtering The model of leg motion can be expressed as follows: ܺ௧ ൌ ‫ ܣ‬ൈ ܺ௧ିଵ ൅ ‫ ܤ‬ൈ ܷ௧ ൅ ܹ௧ ሺͳሻ where ‫ ܤ‬ൌ ܷ௧ ൌ Ͳ, ܹ௧ is gaussian white noise with mean 0 and covariance Q. ܺ௧ ൌ ሾ‫ݔ‬௧ ǡ ‫ݕ‬௧ ǡ ‫ݔݒ‬௧ ǡ ‫ݕݒ‬௧ ሿ, ሺ‫ݔ‬௧ ǡ ‫ݕ‬௧ ሻis the predicted position,ሺ‫ݔݒ‬௧ ǡ ‫ݕݒ‬௧ ሻis the predicted velocity. ͳ Ͳ Ͳ ͳ ‫ܣ‬ൌ൦ Ͳ Ͳ Ͳ Ͳ where ο‫ ݐ‬is scan cycle. The follows: ο‫Ͳ ݐ‬ Ͳ ο‫ݐ‬ ሺʹሻ ൪ ͳ Ͳ Ͳ ͳ measurement model is as ሺ͵ሻ ܻ௧ ൌ ‫ ܪ‬ൈ ܺ௧ ൅ ܸ௧ ͳ Ͳ Ͳ Ͳ ቃ, ܸ is gaussian white noise with where ൌ ቂ Ͳ ͳ Ͳ Ͳ ௧ mean 0 and covariance R. 2) The search domain The prediction status of the current frame is ൣ‫ݔ‬௧ȁ௧ିଵ ǡ ‫ݕ‬௧ȁ௧ିଵ ǡ ‫ݔݒ‬௧ȁ௧ିଵ ǡ ‫ݕݒ‬௧ȁ௧ିଵ ൧. The center of the search domian is the predicted position ൫‫ݔ‬௧ȁ௧ିଵ ǡ ‫ݕ‬௧ȁ௧ିଵ ൯ and the search radius ‫ݎ‬௧ is: ‫ݎ‬௧ ൌ ʹ ൈ ο‫ ݐ‬ൈ ฮ‫ݒ‬௧ȁ௧ିଵ ฮ ଶ ሺͶሻ where ‫ݒ‬௧ȁ௧ିଵ ൌ ሺ‫ݔݒ‬௧ȁ௧ିଵ ǡ ‫ݕݒ‬௧ȁ௧ିଵ ሻ. The deviation ɉ௘ of the measurement position ‫݌‬௧௘ of the e-th data segment of the current frame and the predicted position of the previous frame is: ் ɉ௘ ൌ ට൫‫݌‬௧௘ െ ‫݌‬௧ȁ௧ିଵ ൯ ൈ ሺܵ௧ ሻିଵ ൈ ൫‫݌‬௧௘ െ ‫݌‬௧ȁ௧ିଵ ൯ ሺͷሻ Where ‫݌‬௧ȁ௧ିଵ ൌ ൫‫ݔ‬௧ȁ௧ିଵ ǡ ‫ݕ‬௧ȁ௧ିଵ ൯ and ܵ௧ is the covariance matrix of the difference between the measured position and the estimated position vector. The data segment in the search domain needs to meet the following condition: ɉ௘ ଶ ൏ ‫ݎ‬௧ ሺ͸ሻ 3) Difference Measure The basis of difference measure is to extract the appropriate features of the segment and combine multiple features as the final difference index. For data segment e: The length is: ௡ మ ݈௘ ൌ ෍ ඥሺ‫ݔ‬௜ െ ‫ݔ‬௜ାଵ ሻଶ ൅ ሺ‫ݕ‬௜ െ ‫ݕ‬௜ାଵ ሻଶ  ሺ͹ሻ ௜ୀଵ where ሺ‫ݔ‬௜ ǡ ‫ݕ‬௜ ሻ is the point coordinates of the segment, ݊ is the total number of points of the segment. The endpoint distance is: మ ‫ݑ‬௘ ൌ ඥሺ‫ݔ‬ଵ െ ‫ݔ‬௡ ሻଶ ൅ ሺ‫ݕ‬ଵ െ ‫ݕ‬௡ ሻଶ ሺͺሻ The curvature is: ܿ௘ ൌ ݈௘ ‫ݑ‬௘ ሺͻሻ The total difference measure ܵ௙ǡ௘ is calculated by combining the deviation between the features of the leg segment ݂ in previous frame and the corresponding features of the e data segment in current frame. ܵ௙ǡ௘ ൌ ߙଵ ൈ ห݈௙ െ ݈௘ ห ห‫ݑ‬௙ െ ‫ݑ‬௘ ห หܿ௙ െ ܿ௘ ห ሺͳͲሻ ൅ ߙଶ ൈ ൅ ߙଷ ൈ ݈௙ ‫ݑ‬௙ ܿ௙ where ߙଵ ߙଶ ߙଷ correspond to weighting coefficients. The segment ݂ ǡ with the lowest difference in current frame is used as the corresponding segment of segment ݂: ܵ௙ǡ௙ǡ ൑ ܵ௙ǡ௘ ǡ ܵ௙ǡ௘ ‫ܩ א‬ ሺͳͳሻ where ‫ ܩ‬is the collection of differences corresponding to all segments in the search domain. IV. EXTRACTING GAIT CHARACTERISTICS After determining the leg coordinates, the gait analysis is performed through the leg coordinate sequence, including gait cycle detecting and gait characteristics analysis. A. The Overview of Gait Characteristics There are two main phases in one gait cycle: the support phase when the foot is on the ground, the swing phase when that same foot is swinging without touching the ground in preparation for the next heel strike[10]. The support phase can be subdivided into two separate phases: double support phase when both feet are touching the ground, single support phase when only one foot is touching the ground and the other foot is swinging forward. The spatiotemporal characteristics of gait mainly include step length, stride, velocity, step duration, stride duration. The step length is the distance from the point of one heel touching the ground to the point of the other heel touching the ground in the forward direction. The stride is the distance from the point of one heel touching the ground to the point of the same heel touching the ground next time in the forward direction. The Authorized licensed use limited to: CUNY Central ( City University of New York). Downloaded on November 15,2023 at 17:18:47 UTC from IEEE Xplore. Restrictions apply. step duration corresponds to the elapsed time in one step and the stride duration corresponds to the time elapsed in one stride[11]. B. Gait Cycle Detection Method Based on Crests and Zero-Point Constraint Fig. 3 shows the periodic variation of the leg coordinates in the forward direction during walking. The trough represents the smallest distance between human leg and the mobility aids, corresponding to the “heel strike ground” event, which is the turning point of swing phase to support phase. The crests represent that the largest distance between human leg and the mobility aids, corresponding to the “toe off ground” event, which is the turning point of support phase to swing phase. We take the trough of a curve to the next trough of the curve as a gait cycle. The intersection of the two curves is defined as the zero-point, where the distance between two legs in the forward direction is 0. The crests-based gait cycle detection method is susceptible to the influence of pseudo crests and troughs[12]. Considering that zero-point will appear twice in one gait cycle ,we integrate the zero-point constraint with the traditional crests-based detection method to detect gait cycle. The specific process are as follows: (1) Finding the first zero-point. (2) Finding the second zero-point after a trough appears in one curve and a crest appears in the other curve, (3) Using the interval between two zero-points as the first zero-point interval, and recording the time corresponding to the maximum crest and the lowest trough in the interval. (4) Using the end point of the previous zero-point interval as the start point of next zero-point interval. Repeating the step (2) and step (3) twice to determine the second and third zero-point intervals. Taking the interval between the lowest trough in first zero-point interval and the lowest trough in third zero-point interval as a gait cycle. (5) Using the third zero-point interval as the first zeropoint interval of the next state cycle. Repeating the step (4) and step (5). C. Analysis of Gait Characteristics in One Gait Cycle After determining the gait cycle, we analyze the spatiotemporal characteristics in one gait cycle, as is shown in Fig.4. We use ݂௟ ሺ‫ݐ‬ሻ and ݂௥ ሺ‫ݐ‬ሻ to respectively represent the relationship between the X-coordinate of left and right legs and time t. At t0, the left heel touches the ground, closest to the origin, and the left swing phase turns to the left support Fig. 3 Leg coordinate sequence Fig. 4 Gait characteristics in a gait cycle phase. At t1, the right toe is off the ground, farthest from the origin, and the right support phase turns to the right swing phase. Therefore, the interval between t0 and t1 corresponds to the double support phase. At t2, the right heel touches the ground, and the right swing phase turns to the right support phase. Therefore, the interval between t1 and t2 corresponds to the right swing phase and the left single support phase, and the interval between t0 and t2 corresponds to the right step duration. From t0 to t2, the left foot is in the support phase and its absolute position does not change. So the right step length is the difference of X-coordinates of legs at t2, which is ൫݂௟ ሺ‫ʹݐ‬ሻ െ ݂௥ ሺ‫ʹݐ‬ሻ൯ . We can analyze the gait characteristics from t2 to t4 in the same way. Table I shows the value of each characteristics in this gait cycle. V. EXPERIMENTS AND RESULTS A. Experiment Description In this paper, the distance between legs and the mobility aids is measured by the “RPLidar” laser sensor. The scanning cycle is about 150ms. The experimenters passed a corridor with the support of a mobility aids to verify the proposed methods. B. Experimental Results We use the data of one experimenter to verify the effectiveness of the method to extract the spatiotemporal gait characteristics. In the experiment, the actual walking time is 31.60s, the distance is 28.13m, and the step count is 61. Fig. 5 shows the spatial gait characteristics data of the experimenter. The fluctuation range of the step length is (0.381m, 0.513m), which corresponds to the actual average Table I. Gait Characteristics Gait Characteristics Value Double Support Phase ‫ ͳݐ‬െ ‫Ͳݐ‬ሺ‫ ͵ݐ‬െ ‫)ʹݐ‬ Right Swing Phase ‫ ʹݐ‬െ ‫ͳݐ‬ Left Swing Phase ‫ݐ‬Ͷ െ ‫͵ݐ‬ Right Step Duration ‫ ʹݐ‬െ ‫Ͳݐ‬ Left Step Duration ‫ݐ‬Ͷ െ ‫ʹݐ‬ Stride Duration ‫ݐ‬Ͷ െ ‫Ͳݐ‬ Right Step Length ȁ݂௟ ሺ‫ʹݐ‬ሻ െ ݂௥ ሺ‫ʹݐ‬ሻȁ Left Step Length ȁ݂௟ ሺ‫ݐ‬Ͷሻ െ ݂௥ ሺ‫ݐ‬Ͷሻȁ Stride ȁ݂௟ ሺ‫ʹݐ‬ሻ െ ݂௥ ሺ‫ʹݐ‬ሻȁ ൅ ȁ݂௟ ሺ‫ݐ‬Ͷሻ െ ݂௥ ሺ‫ݐ‬Ͷሻȁ Velocity ห݂݈ ሺ‫ʹݐ‬ሻെ݂‫ ݎ‬ሺ‫ʹݐ‬ሻห൅ห݂݈ ሺ‫ݐ‬Ͷሻെ݂‫ ݎ‬ሺ‫ݐ‬Ͷሻห ‫ݐ‬Ͷെ‫Ͳݐ‬ Authorized licensed use limited to: CUNY Central ( City University of New York). Downloaded on November 15,2023 at 17:18:47 UTC from IEEE Xplore. Restrictions apply. step length of 0.461m. The fluctuation range of the stride is (0.806m, 1.153m), which corresponds to the actual average stride of 0.922m. The fluctuation range of the velocity is (0.782m/s, 0.956m/s), corresponding to the actual average velocity of 0.890 m/s. Fig. 6 shows the temporal gait characteristics data of the experimenter. The fluctuation range of the step duration is (0.44s, 0.59s), corresponding to the actual average value of 0.52s. The fluctuation range of the stride duration is (0.99s, 1.14s), corresponding to the actual average value of 1.04s. The fluctuation range of the proportion of swing phase is (0.32, 0.47), and the fluctuation range of the proportion of support phase is (0.54, 0.67). Each gait characteristics fluctuates by a small margin around its corresponding actual average value. The normal proportion of swing phase is about 0.4, and the normal proportion of support phase is about 0.6[13]. It can be seen that the proportion of gait phase extracted by this method is consistent with the existing research. Considering that the stride and velocity are extracted through the step size, in order to verify the accuracy further, 30 gait cycle data of 3 experimenters is taken to calculate the absolute percentage error between the step length extracted and the actual step length. The results are shown in Table II. The absolute percentage error of both legs are very close, and the absolute percentage error of three experimenters also varies little. The gait characteristics can be extracted by this method with little error. detection method based on crests and zero-point constraints are proposed respectively. The validity of the method is verified by experiments. It has certain significance for the abnormal gait diagnosis and fall prediction of the elderly who rely on a mobility aids. The future work mainly includes two aspects. The first is to use real elderly data for gait studies, and the second is to perform gait studies when the human body is going straight, turning, as well as more complicated and maneuvering motions that appear in daily activities. ACKNOWLEDGMENT This work is financially supported by the research fund under China Disabled Persons' Federation for the development of disabled assistive devices (No. CJFJRRB01-2019). 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