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Measurement and Analysis of Gait Pattern during Stair Walk for Improvement of Robotic Locomotion Rehabilitation System

Measurement and Analysis of Gait Pattern during Stair Walk for Improvement of Robotic Locomotion... Hindawi Applied Bionics and Biomechanics Volume 2019, Article ID 1495289, 12 pages https://doi.org/10.1155/2019/1495289 Research Article Measurement and Analysis of Gait Pattern during Stair Walk for Improvement of Robotic Locomotion Rehabilitation System 1 1 2 1,3 1,4 Sang-Eun Park, Ye-Ji Ho, Min Ho Chun, Jaesoon Choi , and Youngjin Moon Biomedical Engineering Research Center, Asan Institute for Life Sciences, Asan Medical Center, Seoul, Republic of Korea Department of Rehabilitation Medicine, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Republic of Korea Department of Biomedical Engineering, College of Medicine, University of Ulsan, Seoul, Republic of Korea Department of Convergence Medicine, College of Medicine, University of Ulsan, Seoul, Republic of Korea Correspondence should be addressed to Youngjin Moon; jacobian@amc.seoul.kr Received 9 April 2019; Revised 26 June 2019; Accepted 13 August 2019; Published 13 October 2019 Academic Editor: Loredana Zollo Copyright © 2019 Sang-Eun Park 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. Background. Robotic locomotion rehabilitation systems have been used for gait training in patients who have had a stroke. Most commercialized systems allow patients to perform simple exercises such as balancing or level walking, but an additional function such as stair-walk training is required to provide a wide range of recovery cycle rehabilitation. In this study, we analyzed stair-gait patterns and applied the result to a robotic rehabilitation system that can provide a vertical motion of footplates. Methods. To obtain applicable data for the robotic system with vertically movable footplates, stair-walk action was measured using an optical marker-based motion capture system. The spatial position data of joints during stair walking was obtained from six healthy adults who participated in the experiment. The measured marker data were converted into joint kinematic data by using an algorithm that included resampling and normalization. The spatial position data are represented as angular trajectories and the relative displacement of each joint on the anatomical sagittal plane and movements of hip joints on ° ° the anatomical transverse plane. Results. The average range of motion (ROM) of each joint was estimated as (−6:75 ,48:69 )at ° ° ° ° ° ° ° ° the hip, ð8:20 ,93:78 Þ at the knee, and ð−17:78 ,11:75 Þ at the ankle during ascent and as ð6:41 ,31:67 Þ at the hip, ð7:38 ,91:93 Þ ° ° at the knee, and ð−24:89 ,24:18 Þ at the ankle during descent. Additionally, we attempted to create a more natural stair-gait pattern by analyzing the movement of the hip on the anatomical transverse plane. The hip movements were estimated to within ± ° ° 1:57 cm and ±2:00 cm for hip translation and to within ±2:52 and ±2:70 for hip rotation during stair ascent and stair descent, respectively. Conclusions. Based on the results, standard patterns of stair ascent and stair descent were derived and applied to a lower-limb rehabilitation robot with vertically movable footplates. The relative trajectory from the experiment ascertained that the function of stair walking in the robotic system properly worked within a normal ROM. 1. Background is one of the main goals for people who have had a stroke. Traditional therapies usually focus on treadmill training to According to a report by the United Nations, every year, restore the functional mobility of the affected limbs [3, 4]. During such rehabilitation training, a patient is made to more than 795,000 people in the United States have a stroke. Stroke patients 85 years of age and older make up 17% of all stand on a treadmill with his/her body supported by a sus- stroke patients. The worldwide percentage of the population pension system [5], and several physiotherapists make and/or 65 years of age or older is projected to grow from 9.1% to assist the walking movements of the patients’ legs by manual 15.9% between 2015 and 2050. Because of rapid aging, over handwork [6, 7]. However, the task is very difficult and labo- rious for therapists, and the procedure is complex to the the period from 2010 to 2050, the number of incident strokes is expected to more than double [1, 2]. Strokes are the most extent that their excessive burden can lead to inconsistent representative cause of serious long-term disabilities such as quality of the task or reduced duration of net training. For hemiplegia in adults. Therefore, rehabilitation of locomotion these reasons, various robotic locomotion therapy systems 2 Applied Bionics and Biomechanics Sagittal plane ang Joint angle [Y Z ] (norm) (norm) traj Joint trajectory ang Average of Motion Normalization Time traj each capture of body segment resampling trans D D parameter system D (resmp) length (norm) (raw) Transverse plane rot Hip translation trans [X Z ] (norm) (norm) rot Hip rotation (a) (b) (c) (d) Figure 1: Protocol for analyzing a stair-walk pattern: (a) experiment and data acquisition with a motion capture system, (b) normalization of time and body segment length, (c) calculation of each parameter to analyze motion during stair ascent/descent, and (d) averaging every dataset to unify stair-gait pattern. Table 1: Information about each subject. Length of Length of the Subject no. Gender the thigh (cm) lower leg (cm) 28 cm Sub 1 Male 36.67 38.09 Sub 2 Female 34.41 33.85 Sub 3 Male 40.04 41.69 17 cm Sub 4 Male 36.38 40.79 Sub 5 Female 36.19 35.08 Figure 2: The experimental staircase was designed to have five Sub 6 Male 40.81 39.90 steps. It had a 17 cm riser height and a 28 cm tread length Mean value of the length according to the Korean building standards law. 37.42 (2.47) 38.23 (3.18) (standard deviation) have been developed, and some of them have been used to train patients in the clinical field [8–11]. Usually, these systems are based on treadmill-type ASIS trainers in combination with exoskeletons and body weight Sacrum Hip support (BWS) systems. The Lokomat® (Hocoma AG, Thigh Switzerland) uses linear actuators that control the joint angles at the hip and knee. The system is synchronized with Knee the speed of the treadmill to assure precise matching between Shank the speed of the orthosis and the treadmill [12–14]. Similarly, Ankle the ReoAmbulator™ (Motorika, USA) employs powered leg Heel orthosis and robotic arms, which enable patients to contrib- Toe ute during walking on the treadmill. The robotic arms are (a) (b) attached laterally to the thigh and shank of the patient for control of the lower limbs [15, 16]. The LokoHelp (Lokohelp Figure 3: Markers were placed on a subject at the hip, thigh, knee, Group, Germany) aids the gait-training program on the shank, ankle, and toe on both the right and the left sides including treadmill without the use of exoskeletons on a patients’ legs. ASIS. (a) Front side. (b) Back side. It consists of an ankle orthosis for foot-drop prevention and a harness [17]. Such treadmill-type devices provide training programs exclusively for level walking owing to their exercises or level walking because the activities require more mechanical structure. muscle strength, balancing abilities, and complex movements In traditional rehabilitation, therapists allow patients to [9, 18–20]. However, such an additional function can be perform special gaits such as ascending or descending aided by just a few robotic systems of the footplate type. stairs. This training is more effective in improving the gait The G-EO System™ (Reha Technology AG, Switzerland) is ability of patients with low severity impairments than simple composed of robotic end-effector devices that allow Applied Bionics and Biomechanics 3 Camera (Right) Z (left) (Right) Z (left) (a) (b) Figure 4: (a) Experimental environment for a camera setup (blue circles). (b) Position of the staircase. Yellow, red, and white arrows on the figures define the axes in coordinate space. simulation of stair ascent and stair descent with a BWS sys- the anatomical sagittal and transverse planes. Finally, the tem [21]. The GaitMaster5 system by the University of average of each motion parameter was estimated as a stan- Tsukuba in Japan, is a lower-limb orthosis system; the patient dard stair-walk pattern. straps his/her feet into pads connected to motion platforms. These platforms can move the user’s foot forward (simulat- 2. Methods ing walking) or up and down, similar to climbing [22]. The footplates guide the feet, thereby reproducing the gait trajec- To make a patient train with a natural gait pattern, hip tory of the ankle joint. These technologies tend to focus on motion in the medial-lateral direction and hip rotation, as movements of the ankle joint; furthermore, the absence of well as the movement of each joint on the sagittal plane, need an exoskeleton or other structure that can control the hip to be applied to the robot. Figure 1 indicates the process of and knee does not allow support of the joints. As a result, it analyzing stair-gait motion. The protocol has four steps: (a) may become challenging for patients to train correctly and position data acquisition, (b) data rescaling on the time and effectively using systems where those joints are uncon- body segment length, (c) calculation of parameters for strained [10]. motion analysis, and (d) creation of a standard gait pattern. The robotic lower-limb rehabilitation system gait trainer, M181-1, was developed by Cyborg-Lab, Korea [23]. The 2.1. Experiment for Data Acquisition. For the test, a labora- system facilitates level walking using robotic linkages and tory staircase composed of five steps and having a riser height separate left and right footplates that track a patient’s foot and tread length of 17 cm and 28 cm, respectively, was pre- motion on the ground plane. As an improvement in the func- pared according to the Korean building standards law [24]. tionality of the system, the function of stair walking can be The prepared staircase is shown in Figure 2. Six healthy par- considered and a rehabilitation system that includes stair ticipants, four males and two females, participated in this walking is expected to actively train patients. This rehabilita- study. Table 1 summarizes information about the subjects. tion system is a hybrid of the footplate and treadmill types To generate a reference standard gait pattern, the because the system has footplates but the feet of a user do experiment was planned with subjects having no disorders not always touch the plates. If the footplates of the robot in their lower limbs. The subjects were asked to repeatedly are vertically and independently controlled, the patient can ascend and descend stairs at a self-selected velocity (normal train not only for level walking but also for stair walking. In pace) five times. The mean stride speeds were approximately other words, this robotic system can be designed to provide 0.88 m/s in stair ascent and 0.96 m/s in stair descent. The patients with various gait exercises by combining exoskeletal method of stair walking was step-to-step, and a stride cycle links with spatially movable footplates. was defined as the motion from the contact of the right foot In this study, a standard gait pattern of stair walking was of the first (third) step to the foot contact of the third (fifth) created and converted into applicable data that implemented step, as described in [25]. Briefly, two cycles of stair-gaits the stair-walking function in the M181-1 system. Thus, this were measured from the six subjects. study focused on the analysis of joint movement in stair The highly complicated structure of the human skeleton ascent and stair descent for the application to the joint actu- enables movement with high degrees of freedom. Each body ators of the robotic locomotion rehabilitation system. The part moves in an unpredictable and complex motion trajec- first step of the protocol involved an experiment to acquire tory. There are many types of systems for measuring body motion data using a motion capture system. The second movements, such as optical marker-based tracking systems, was processing the data and calculating the parameters on markerless visual systems, and inertial measurement unit- 4 Applied Bionics and Biomechanics d d d d r1[0] r1[9] n1[0] n1[9] (resmp)1 (raw)1 d d d r2[0] r2[8] n2[0] d n2[9] (resmp)2 (raw)2 d d r3[0] r3[11] d d n3[0] n3[9] (resmp)3 (raw)3 (a) (b) Figure 5: (a) Example of resampling datasets that have different lengths. (b) The vertical red lines are replaced using points by the cubic spline algorithm. (x ,y ,z ) (x ,y ,z ) (x ,y ,z ) (X ,Y ,Z ) 0 0 0 1 1 1 0 0 0 norm norm norm Origin Normalization Real norm Figure 6: Normalization of body segment length. Hip ° Knee hip Ankle ankle knee Toe Ground 0° (a) (b) (c) Figure 7: Definition of joint angles S : (a) flexion/extension of hip joint θ , (b) flexion/extension of the knee joint θ , and (c) ðangÞ hip knee dorsi-/plantar-flexion of ankle joint θ . The red points indicate joints, and the red/blue arrows denote the positive/negative sign of ankle angular direction. Left hip (IMU-) based systems, which can be used to capture irregular human motion [26]. Because the optical marker-based sys- tem is frequently used in medicine [27–29] owing to its rela- Center of hip tively high accuracy and minimal uncertainty of the subject’s movement, the optical marker-based system was used to T [m] trans Walking direction measure the normal stair-gait pattern in this study. To acquire the position data of each joint in three- dimensional (3D) space, 17 optical markers were placed, Right hip one on the subject’s sacrum, and two on the left and right anterior superior iliac spine (ASIS), hip, thigh, knee, shank, Figure 8: Definition of mediolateral movement, T . trans ankle, heel, and toe. Figure 3 presents the arrangement of the markers on the front and back sides of a subject. The placements of the reflective markers were determined for using a Prime 41 (OptiTrack, NaturalPoint Inc., USA) 3D accurate tracking of anatomical landmarks related to kine- motion capture system. The accuracy of this equipment is matic variables during gait [31–34]. submillimeter, with a latency of 5.5 ms [30]. The calibration During the experiment, the positional information of the was performed with errors less than 2 mm. As shown in markers on the subjects was recorded at a rate of 160 Hz Figure 4(a), eight cameras, marked in blue circles, were Applied Bionics and Biomechanics 5 Walking direction Walking direction T [m] rot Right hip Right hip Left hip Left hip (a) (b) Figure 9: Definition of hip rotation angle T : T in (a) equals the included angle θ of the right triangle ΔROH in (b). rot rot placed in a square with approximate dimensions of 10 m × constant) are considered as the identical functional sequence 10 m. The x-axis was defined as the direction of walking, with of gait cycle when m is an equal value for all cycles. Accord- the y-axis as the vertical direction. The direction of the right ingly, if m is the same in every dataset, the parameters asso- (negative value) and left sides (positive value) was defined as ciated with the sagittal and transverse planes, S and T, the z-axis. The experimental staircase was installed at the respectively, in Figure 1 are averaged in the final step of the center of the square. analysis protocol to generate a standard gait pattern. The datasets D = ½X Y Z  measured by the The dataset also needed to be normalized in space to ðrawÞ ðrawÞ ðrawÞ ðrawÞ standardize the trajectories of the joints because the length motion capture system consisted of the x, y, and z coordi- of each body segment is different from the other. Hence, nates for one cycle of stair walking. Each portion of the data- the positional trajectories of the joints were reconstructed sets, X , Y , and Z , denoted by time-series data for ðrawÞ ðrawÞ ðrawÞ 17×N by obtaining the equivalent lengths of each body segment. the attached 17 markers, was expressed by X ∈ R , ðrawÞ Figure 6 expresses the method for normalization of the body 17×N 17×N Y ∈ R , and Z ∈ R , where N is the number of ðrawÞ ðrawÞ segment length. data points recorded for each marker. The value of N A real segment length, L , from reference point P = Real 0 was different among the obtained datasets because of each ðx , y , z Þ to the other point P = ðx , y , z Þ was rearranged 0 0 0 1 1 1 1 participant’s walking speed. In this study, the datasets were to a new point P = ðx , y , z Þ with the desired ðnormÞ norm norm norm obtained for the six subjects who completed two stride length L .We decided L to be the average value of ðnormÞ ðnormÞ cycles of stair ascent and descent a total of five times. the length of the lower leg and thigh in Table 1. The relation Thus, a total 60 datasets of D (6 subjects × 5 times × ðrawÞ between normalized point P , the reference point P , ðnormÞ 0 2 cycles = 60 sets) were used for motion analysis of stair and the new point P is shown in (1) and the normalized data- ascent and stair descent. set D was computed through the equation given in [38]. ðnormÞ 2.2. Data Preprocessing for Normalization. Because of the norm participants’ own habits in walking, the walking velocity var- P = P − ðÞ P − P : ð1Þ ðÞ norm 0 0 1 Real ied per person or trial. The lengths of body segments and the gap between the joints were also different among the partic- ipants. Therefore, it was necessary to normalize the data for 2.3. Parameters for Motion Analysis. The hip, knee, and ankle joints were mainly characterized by large ranges of motion time and space to simplify various conditions. To unify the stride time condition, every D was (ROMs) in the sagittal plane rather than in the coronal or ðrawÞ transverse mobility [9, 18–20]. Despite the small actions on resampled to dataset D = ½X Y Z ðresmpÞ ðresmpÞ ðresmpÞ ðresmpÞ the transverse plane, it is important that hip movement with the same number (M) of components by applying the can contribute to the advancement of muscle strength and interpolation method of a cubic spline. The cubic spline is a effective balance training [39]. Thus, the parameters for anal- function constructed of piecewise third-order polynomials ysis of motion on the transverse plane, in particular the hip that are smoother and have smaller errors than some joint, as well as that on the sagittal plane were examined. other interpolating polynomials [35, 36]. Figure 5 shows an Four parameters were considered in this study: joint flexio- example of resampling the data D ½m (k = 1, 2, and 3 ðrawÞk n/extension angle and positional trajectory (on the sagittal and m =0,1, ⋯, M − 1, where k and M are constants), k k plane), tendency of hip translation, and hip rotation (on which is measured with the same sampling frequency but the transverse plane). These were determined by the relevant with a different length M . D is a modified dataset with k ðresmpÞk positions either to the sagittal plane ½Y Z  or to ðnormÞ ðnormÞ the same number of samples (M =10 in the example). To the transverse plane ½X Z . ðnormÞ ðnormÞ analyze the gait motion, the duration of a stride was divided The first parameter was angular trajectory S = ½θ , into several sequences by physical and functional properties, ang hip θ , θ , which signifies the trend of the hip, knee, and such as period, i.e., stance and swing. The temporal unit was knee ankle Stride cycle (%) for the analysis [20, 33, 37]. Therefore, the ankle during a stride on the stair. The angular trajectory components of D ½m (m =0, ⋯, M − 1, where M is a was obtained from the first law of cosines. The directions ðresmpÞ 70 6 Applied Bionics and Biomechanics −20 −10 −40 −20 −20 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Stride cycle (% cycle) Stride cycle (% cycle) Stride cycle (% cycle) (a) (b) (c) Figure 10: Mean angles of the (a) hip, (b) knee, and (c) ankle joint: the blue lines indicate the variation of the joint angle during stair ascent, and the red lines indicate the variation of the joint angle during stair descent. 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 0.5 0.5 −0.5 0 −0.5 0 x position (direction of progress) (m) x position (direction of progress) (m) (c) (d) Figure 11: Relative trajectories from the hip joint during stair ascent: (a) knee trajectories and (c) ankle trajectories of each subject. (b and d) Knee and ankle trajectories are shown as a result of normalization for the lengths of the body segments. Hip angle (degree) y position (direction of vertical) (m) y position (direction of vertical) (m) Knee angle (degree) y position (direction of vertical) (m) y position (direction of vertical) (m) Ankle angle (degree) Applied Bionics and Biomechanics 7 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 0 0.5 0 0.5 −0.5 −0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (c) (d) Figure 12: Relative trajectories from the hip joint during stair descent: (a) knee trajectories and (c) ankle trajectories of each subject. (b and d) Knee and ankle trajectories are shown as a result of normalization for the lengths of the body segments. 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) Figure 13: Standard trajectories of the (a) knee and (b) ankle during stair ascent. indicated in Figure 7 and the following conditions defined is an open curve. For this reason, the trajectories of the joints, these angles and their signs (positive/negative): as secondary parameters, were replaced with relative positions from a point for stair-gait patterns during a circular walk. The (i) If the hip joint poses on hip flexion, θ >0 reference point was set as the hip marker position. In other hip words, the position of the hip is considered as (0, 0) and the (ii) If the knee joint poses on knee flexion, θ >0 knee positions of the knee and ankle, which were secondary param- eters, moved relatively to the reference point. (iii) If the ankle joint poses on dorsiflexion, θ >0 ankle In general, most existing robotic locomotion rehabilita- tion systems address the kinematics on the sagittal plane The joints of the robot should be designed to move in a closed-loop pattern to generate a repetitive gait motion in because the lower limb is akin to working predominantly the fixed system even if the resulting data from the experiment for flexion/extension during locomotion. Such a movement y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) 8 Applied Bionics and Biomechanics 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) Figure 14: Standard trajectories of the (a) knee and (b) ankle during stair descent. 8 8 0 0 −2 −2 −4 −4 −6 −6 −8 −8 0 20 40 60 80 100 0 20 40 60 80 100 Stride cycle (% cycle) Stride cycle (% cycle) Figure 15: Variation of hip translation during stair ascent. Figure 17: Variation of hip translation during stair descent. 10 10 8 8 6 6 4 4 2 2 0 0 −2 −2 −4 −4 −6 −6 −8 −8 −10 −10 0 20 40 60 80 100 0 20 40 60 80 100 Stride cycle (% cycle) Stride cycle (% cycle) Figure 16: Variation of hip rotation during stair ascent. Figure 18: Variation of hip rotation during stair descent. constrained to only one anatomical plane can prevent mean- ingful training for more effective therapeutic impact. The hip Table 2: ROM on all subjects applying to the motion of the robotic joint, especially, has distinct movement on the transverse system. plane owing to weight bearing or weight shifting during walk- Stair ascent Stair descent ing. Among the features of relevance to the robotic gait- Min. Max. Min. Max. training system [39], the hip translational movement, T , trans ° ° ° ° in the mediolateral direction is considered as the third param- 56:10 Hip angle -14.87 -4.62 40.18 ° ° ° ° eter. Figure 8 shows the method used to calculate the variation Knee angle 0.051 104.11 0.0048 104.14 of hip movement on the transverse plane. The length between ° ° ° ° Ankle angle -36.93 24.13 -37.87 35.87 the left and right hip markers is considered a constant because Hip translation -2.68 cm 2.68 cm -3.17 cm 3.17 cm it is an intrinsic value as the length of a body segment. The var- ° ° ° ° Hip rotation -16.71 16.66 -10.60 10.29 iation of mediolateral hip movement can be measured in terms of displacement of the center of the hip segment. Rotation angle (degree) Direction of right and left (cm) y position (direction of vertical) (m) y position (direction of vertical) (m) Rotation angle (degree) Direction of right and left (cm) Applied Bionics and Biomechanics 9 Table 3: Principal standard deviation within each subject. Sub 1 Sub 2 Sub 3 Sub 4 Sub 5 Sub 6 Min. Max. Min. Max. Min. Max. Min. Max. Min. Max. Min. Max. Stair ascent Hip angle 1.16 5.02 1.62 8.12 0.64 6.89 1.17 6.89 1.17 6.50 1.04 5.60 Knee angle 1.18 11.83 0.86 16.41 1.12 15.85 0.89 10.16 1.44 7.69 0.79 4.99 Ankle angle 0.51 7.77 1.10 8.66 1.30 8.89 1.35 8.54 0.61 7.54 0.36 4.17 Hip trans. 0.15 0.39 0.10 0.49 0.15 0.46 0.14 0.68 0.21 0.69 0.17 0.32 Hip rotation 1.31 6.52 1.09 4.47 0.14 2.00 0.27 2.70 0.02 2.50 0.32 2.72 Stair descent Hip angle 0.63 3.26 0.91 5.29 0.68 4.92 1.19 5.09 1.26 3.45 0.53 2.79 Knee angle 0.81 8.03 1.59 10.42 1.05 15.27 1.51 11.79 0.93 5.84 0.61 6.81 Ankle angle 1.09 6.27 1.15 6.78 1.20 8.69 2.49 11.49 0.44 6.78 0.33 5.57 Hip trans. 0.21 0.28 0.13 0.87 0.29 0.91 0.16 0.90 0.07 0.68 0.14 0.61 Hip rotation 0.17 1.35 0.51 1.77 0.41 1.70 0.73 3.28 0.06 3.00 0.11 1.25 Although the participants performed stair walking in the Table 4: Principal standard deviation of all subjects. same coordinates and location, the planes on which their tra- jectories were described were not exactly coincident. In other Stair ascent Stair descent words, the walking directions for all the data sets were differ- Min. Max. Min. Max. ent. Therefore, the data sets were manipulated so that they Hip angle 2.12 6.28 2.30 4.86 were in the same sagittal plane using the rotational displace- Knee angle 2.96 12.22 2.55 11.18 ment formula [40]. Thus, the right and left hip markers made Ankle angle 4.57 8.70 3.73 11.10 a line, and the center point on the line drew a curve along Hip translation 0.32 0.53 0.38 0.69 weight shift. Then, trends of positional variation of the center point between the hip joints in the same walking direction Hip rotation 1.47 4.42 1.80 3.17 could be determined. sagittal plane to analyze stair-walk motion. Figure 10 shows The last parameter for the motion analysis is the angular variations in the hip, knee, and ankle joint angles during stair displacement associated with the hip rotation during gait. ascent (red line) and stair descent (blue line), and their stan- Figure 9 indicates the methods for calculating the variation dard deviations are given by the gray areas. In this study, the of hip rotation on the transverse plane. The hip rotation, average ROMs for the subjects’ hip joints in extension/flexion T , was defined as the angle between the line perpendicular rot ° ° during a stair ascent and descent cycle were (−6:75 ,48:69 ) to the walking direction and the line of hip markers. The ° ° and (6:41 ,31:67 ), respectively. The average ROM of the rotation angle was determined by making a right triangle ° ° knee joints in extension/flexion was (8:20 ,93:78 ) during and finding the included angle with the inverse tangent func- ° ° stair ascent and (7:38 ,91:93 ) during stair descent. Addi- tion as shown Figure 9(b). The parameter was defined as a tionally, the average ROMs of ankle joints in plantar-/dorsi- positive value where the right hip marker was placed in front ° ° ° ° flexion were ð−17:78 ,11:75 Þ and (−24:89 ,24:18 ) during of the left hip marker. stair ascent and descent, respectively. The result of the data processing such as normalization Figures 11 and 12 present the relative trajectories of and interpolation makes trajectories for a gait cycle, but it the knee and ankle joints for the hip joint on the sagittal might not be appropriate to be applied to a fixed type reha- plane during stair ascent and descent, respectively. The bilitation robot. If values in the beginning and end points of different colors of trajectories in Figures 11 and 12 present the trajectories are different, they make a discontinuity when different subjects. To reduce the individual variation in the the robot is working because the robot needs a cyclic gait lengths of the body segments, the data were normalized pattern. Therefore, the points of the beginning and the end with the algorithm described in Section 2.2. The red points points on all results should match to make a cyclic pattern. on these figures represent the hip marker at the reference To resolve this problem, the obtained datasets were proc- point (0, 0). essed by the cubic spline method using the points corre- After normalization, we attempted to find the standard sponding to the first 5% (0 to 5%) and the last 5% (96 to trajectories of the knee and ankle. As shown in Figures 13 100%) of the stride cycle. and 14, the averaged trajectories of the normalized datasets, the red lines, are considered the standard trajectories in this 3. Results experiment. 3.1. Angular and Positional Trajectories of Joints on the Sagittal Plane. As mentioned in the previous section, we cal- 3.2. Hip Movement on the Transverse Plane. Figures 15 and culated two parameters of joint angles and trajectories on the 16 present the variation in hip translation and rotation, 10 Applied Bionics and Biomechanics 10 20 −10 −20 −20 0 20 40 60 80 100 0 20 40 60 80 100 Cycle time (%) Cycle time (%) Applied data Applied data (ascent) (descent) Data from the Data from the robot (descent) robot (ascent) (a) (b) Figure 19: Comparison of the angular trajectories on (a) hip joint and (b) knee joint between robot movement and experimental data. respectively, during a stair-ascent cycle. The translation/rota- 4. Discussion tion is indicated by the red line. The standard deviation is indicated by gray lines. When ascending a stair, the averaged In this study, we attempted to create patterns of stair walking ROMs on the transverse plane were within ±1:57 cm for for application to a robotic lower-limb rehabilitation system. translation and ±2:52 for rotational movement. A subject’s legs moved in a cyclical pattern during stair nego- As with Figures 15 and 16, Figures 17 and 18 indicate tiation. The movement of the lower limb primarily appears as trends in the hip movement for a stair-gait cycle. The range a flexion/extension of each joint [20]. Therefore, initially, of translation movement was estimated to be within ±2:00 variations in the joint angles of the hips, knees, and ankles cm, and hip rotation was estimated to be within ±2:70 . were extracted on the anatomical sagittal plane such that Table 2 shows the maximum range in which subjects actually the robotic exoskeleton of the gait-training system can work moved in the experiment. with the most basic gait pattern. The calculated angular var- Table 2 shows the minimum and maximum values of iations of the hips, knees, and ankles, as shown in Figure 10, were used to establish the basic pattern in stair ascent and data, which consist of the resampled 120 datasets from the experiment. The values in Table 2 cover the range of all sub- stair descent. jects’ motion. As shown in Table 1, the subjects had different stride Because the gait cycle was divided into 200 phases to lengths and leg lengths in the stair-walk experiment. There- derive the pattern of stair walking, standard deviation values fore, we normalized the lengths of body segments before cal- were different for each point in Figure 10 and Figures 15–18. culating the knee and ankle trajectories relative to the hip. As Thus, the principal estimation of standard deviations for shown in Figures 11 and 12, it was easy to find the trend of each result for each motion is summarized in Tables 3 and the normalized knee and ankle joint trajectories. Addition- 4. Table 3 shows the maximal and minimal values of stan- ally, the normalization is supposed to establish criteria for dard deviations for each subject. Table 4 presents the princi- the gait pattern to drive a robotic gait trainer after standard- pal estimations of standard deviation on each result in ization of the relative trajectories. Figures 13 and 14 show the Figure 10 and Figures 13–18. desired tracks of the knee and ankle joints for a robotic sys- tem mimicking the experimental pattern in Figure 10. 3.3. Application of Derived Pattern to the Robotic System. In addition to the analysis on the sagittal plane, we tried If the trajectory is compared with the joint displacement to examine the hip joint on the transverse plane. The data of a robotic training system served by itself, it can ascer- medial-lateral movements of the hip during stair walking tain whether the system properly works within a normal seemed to be similar among the subjects, as shown in ROM, e.g., the height of a leg lift. Actual angular trajecto- Figures 15 and 17. However, the variation in hip rotation ries performed by the robotic system designed for stair angles had large standard deviations, as shown in Figures 16 walking during stair ascent and descent are displayed in and 18. This is due to differences in the gait patterns of each Figure 19. The trajectories generally follow the gait pattern individual, such as step length, body segment length, gender, obtained from this study (green and light blue line) even and other anatomical factors. Its effectiveness should be inves- though there is some delay or errors—average errors within tigated by a clinical test, which, however, is beyond the scope ±8% were calculated. of this work. Hip angle (degree) Knee angle (degree) Applied Bionics and Biomechanics 11 The exoskeleton of the robotic system was designed based Acknowledgments on the results shown in Table 2, and it could move within a This study was jointly supported by the Technology Innova- range that covered all subjects. As shown in Tables 3 and 4, tion Program (grant number: 20000843) funded by the Min- standard deviations on the sagittal plane in Table 3 are larger istry of Trade, Industry, and Energy (MOTIE, South Korea), than those in Table 4, and the results on the transverse plane a grant of the Asan Institute for Life Sciences intramural in Table 4 are larger than those in Table 3. It means that the research project funded by Asan Medical Center (grant num- standard patterns on the sagittal plane reflected the general ber: 2019-692), and a grant of the Korea Health Technology trend of stair walk, and the variation within an individual R&D Project through the Korea Health Industry Develop- on the transverse plane is larger than among subjects. There- ment Institute (KHIDI) funded by the Ministry of Health & fore, each joint of the exoskeleton was controlled by a stan- Welfare, Republic of Korea (grant number: HI17C2410). dard pattern in Figure 10 for reflecting general patterns on the robotic system. On the other hand, hip movements on the transverse plane were controlled within ranges of stan- References dard deviations depending on the individual difference as shown in Figures 15–18. [1] E. J. Benjamin, P. Muntner, A. Alonso et al., “Heart disease and As compared to the motion of a robot with the derived stroke statistics—2019 update: a report from the American Heart Association,” Circulation, vol. 139, no. 10, pp. e56– standard pattern shown in Figure 19, the trend of the motion e528, 2019. between the applied data and that measured from the robot is [2] United Nations, “Department of Economic and Social Affairs,” almost similar, but some inevitable errors occurred. 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Measurement and Analysis of Gait Pattern during Stair Walk for Improvement of Robotic Locomotion Rehabilitation System

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Copyright © 2019 Sang-Eun Park 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 1495289, 12 pages https://doi.org/10.1155/2019/1495289 Research Article Measurement and Analysis of Gait Pattern during Stair Walk for Improvement of Robotic Locomotion Rehabilitation System 1 1 2 1,3 1,4 Sang-Eun Park, Ye-Ji Ho, Min Ho Chun, Jaesoon Choi , and Youngjin Moon Biomedical Engineering Research Center, Asan Institute for Life Sciences, Asan Medical Center, Seoul, Republic of Korea Department of Rehabilitation Medicine, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Republic of Korea Department of Biomedical Engineering, College of Medicine, University of Ulsan, Seoul, Republic of Korea Department of Convergence Medicine, College of Medicine, University of Ulsan, Seoul, Republic of Korea Correspondence should be addressed to Youngjin Moon; jacobian@amc.seoul.kr Received 9 April 2019; Revised 26 June 2019; Accepted 13 August 2019; Published 13 October 2019 Academic Editor: Loredana Zollo Copyright © 2019 Sang-Eun Park 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. Background. Robotic locomotion rehabilitation systems have been used for gait training in patients who have had a stroke. Most commercialized systems allow patients to perform simple exercises such as balancing or level walking, but an additional function such as stair-walk training is required to provide a wide range of recovery cycle rehabilitation. In this study, we analyzed stair-gait patterns and applied the result to a robotic rehabilitation system that can provide a vertical motion of footplates. Methods. To obtain applicable data for the robotic system with vertically movable footplates, stair-walk action was measured using an optical marker-based motion capture system. The spatial position data of joints during stair walking was obtained from six healthy adults who participated in the experiment. The measured marker data were converted into joint kinematic data by using an algorithm that included resampling and normalization. The spatial position data are represented as angular trajectories and the relative displacement of each joint on the anatomical sagittal plane and movements of hip joints on ° ° the anatomical transverse plane. Results. The average range of motion (ROM) of each joint was estimated as (−6:75 ,48:69 )at ° ° ° ° ° ° ° ° the hip, ð8:20 ,93:78 Þ at the knee, and ð−17:78 ,11:75 Þ at the ankle during ascent and as ð6:41 ,31:67 Þ at the hip, ð7:38 ,91:93 Þ ° ° at the knee, and ð−24:89 ,24:18 Þ at the ankle during descent. Additionally, we attempted to create a more natural stair-gait pattern by analyzing the movement of the hip on the anatomical transverse plane. The hip movements were estimated to within ± ° ° 1:57 cm and ±2:00 cm for hip translation and to within ±2:52 and ±2:70 for hip rotation during stair ascent and stair descent, respectively. Conclusions. Based on the results, standard patterns of stair ascent and stair descent were derived and applied to a lower-limb rehabilitation robot with vertically movable footplates. The relative trajectory from the experiment ascertained that the function of stair walking in the robotic system properly worked within a normal ROM. 1. Background is one of the main goals for people who have had a stroke. Traditional therapies usually focus on treadmill training to According to a report by the United Nations, every year, restore the functional mobility of the affected limbs [3, 4]. During such rehabilitation training, a patient is made to more than 795,000 people in the United States have a stroke. Stroke patients 85 years of age and older make up 17% of all stand on a treadmill with his/her body supported by a sus- stroke patients. The worldwide percentage of the population pension system [5], and several physiotherapists make and/or 65 years of age or older is projected to grow from 9.1% to assist the walking movements of the patients’ legs by manual 15.9% between 2015 and 2050. Because of rapid aging, over handwork [6, 7]. However, the task is very difficult and labo- rious for therapists, and the procedure is complex to the the period from 2010 to 2050, the number of incident strokes is expected to more than double [1, 2]. Strokes are the most extent that their excessive burden can lead to inconsistent representative cause of serious long-term disabilities such as quality of the task or reduced duration of net training. For hemiplegia in adults. Therefore, rehabilitation of locomotion these reasons, various robotic locomotion therapy systems 2 Applied Bionics and Biomechanics Sagittal plane ang Joint angle [Y Z ] (norm) (norm) traj Joint trajectory ang Average of Motion Normalization Time traj each capture of body segment resampling trans D D parameter system D (resmp) length (norm) (raw) Transverse plane rot Hip translation trans [X Z ] (norm) (norm) rot Hip rotation (a) (b) (c) (d) Figure 1: Protocol for analyzing a stair-walk pattern: (a) experiment and data acquisition with a motion capture system, (b) normalization of time and body segment length, (c) calculation of each parameter to analyze motion during stair ascent/descent, and (d) averaging every dataset to unify stair-gait pattern. Table 1: Information about each subject. Length of Length of the Subject no. Gender the thigh (cm) lower leg (cm) 28 cm Sub 1 Male 36.67 38.09 Sub 2 Female 34.41 33.85 Sub 3 Male 40.04 41.69 17 cm Sub 4 Male 36.38 40.79 Sub 5 Female 36.19 35.08 Figure 2: The experimental staircase was designed to have five Sub 6 Male 40.81 39.90 steps. It had a 17 cm riser height and a 28 cm tread length Mean value of the length according to the Korean building standards law. 37.42 (2.47) 38.23 (3.18) (standard deviation) have been developed, and some of them have been used to train patients in the clinical field [8–11]. Usually, these systems are based on treadmill-type ASIS trainers in combination with exoskeletons and body weight Sacrum Hip support (BWS) systems. The Lokomat® (Hocoma AG, Thigh Switzerland) uses linear actuators that control the joint angles at the hip and knee. The system is synchronized with Knee the speed of the treadmill to assure precise matching between Shank the speed of the orthosis and the treadmill [12–14]. Similarly, Ankle the ReoAmbulator™ (Motorika, USA) employs powered leg Heel orthosis and robotic arms, which enable patients to contrib- Toe ute during walking on the treadmill. The robotic arms are (a) (b) attached laterally to the thigh and shank of the patient for control of the lower limbs [15, 16]. The LokoHelp (Lokohelp Figure 3: Markers were placed on a subject at the hip, thigh, knee, Group, Germany) aids the gait-training program on the shank, ankle, and toe on both the right and the left sides including treadmill without the use of exoskeletons on a patients’ legs. ASIS. (a) Front side. (b) Back side. It consists of an ankle orthosis for foot-drop prevention and a harness [17]. Such treadmill-type devices provide training programs exclusively for level walking owing to their exercises or level walking because the activities require more mechanical structure. muscle strength, balancing abilities, and complex movements In traditional rehabilitation, therapists allow patients to [9, 18–20]. However, such an additional function can be perform special gaits such as ascending or descending aided by just a few robotic systems of the footplate type. stairs. This training is more effective in improving the gait The G-EO System™ (Reha Technology AG, Switzerland) is ability of patients with low severity impairments than simple composed of robotic end-effector devices that allow Applied Bionics and Biomechanics 3 Camera (Right) Z (left) (Right) Z (left) (a) (b) Figure 4: (a) Experimental environment for a camera setup (blue circles). (b) Position of the staircase. Yellow, red, and white arrows on the figures define the axes in coordinate space. simulation of stair ascent and stair descent with a BWS sys- the anatomical sagittal and transverse planes. Finally, the tem [21]. The GaitMaster5 system by the University of average of each motion parameter was estimated as a stan- Tsukuba in Japan, is a lower-limb orthosis system; the patient dard stair-walk pattern. straps his/her feet into pads connected to motion platforms. These platforms can move the user’s foot forward (simulat- 2. Methods ing walking) or up and down, similar to climbing [22]. The footplates guide the feet, thereby reproducing the gait trajec- To make a patient train with a natural gait pattern, hip tory of the ankle joint. These technologies tend to focus on motion in the medial-lateral direction and hip rotation, as movements of the ankle joint; furthermore, the absence of well as the movement of each joint on the sagittal plane, need an exoskeleton or other structure that can control the hip to be applied to the robot. Figure 1 indicates the process of and knee does not allow support of the joints. As a result, it analyzing stair-gait motion. The protocol has four steps: (a) may become challenging for patients to train correctly and position data acquisition, (b) data rescaling on the time and effectively using systems where those joints are uncon- body segment length, (c) calculation of parameters for strained [10]. motion analysis, and (d) creation of a standard gait pattern. The robotic lower-limb rehabilitation system gait trainer, M181-1, was developed by Cyborg-Lab, Korea [23]. The 2.1. Experiment for Data Acquisition. For the test, a labora- system facilitates level walking using robotic linkages and tory staircase composed of five steps and having a riser height separate left and right footplates that track a patient’s foot and tread length of 17 cm and 28 cm, respectively, was pre- motion on the ground plane. As an improvement in the func- pared according to the Korean building standards law [24]. tionality of the system, the function of stair walking can be The prepared staircase is shown in Figure 2. Six healthy par- considered and a rehabilitation system that includes stair ticipants, four males and two females, participated in this walking is expected to actively train patients. This rehabilita- study. Table 1 summarizes information about the subjects. tion system is a hybrid of the footplate and treadmill types To generate a reference standard gait pattern, the because the system has footplates but the feet of a user do experiment was planned with subjects having no disorders not always touch the plates. If the footplates of the robot in their lower limbs. The subjects were asked to repeatedly are vertically and independently controlled, the patient can ascend and descend stairs at a self-selected velocity (normal train not only for level walking but also for stair walking. In pace) five times. The mean stride speeds were approximately other words, this robotic system can be designed to provide 0.88 m/s in stair ascent and 0.96 m/s in stair descent. The patients with various gait exercises by combining exoskeletal method of stair walking was step-to-step, and a stride cycle links with spatially movable footplates. was defined as the motion from the contact of the right foot In this study, a standard gait pattern of stair walking was of the first (third) step to the foot contact of the third (fifth) created and converted into applicable data that implemented step, as described in [25]. Briefly, two cycles of stair-gaits the stair-walking function in the M181-1 system. Thus, this were measured from the six subjects. study focused on the analysis of joint movement in stair The highly complicated structure of the human skeleton ascent and stair descent for the application to the joint actu- enables movement with high degrees of freedom. Each body ators of the robotic locomotion rehabilitation system. The part moves in an unpredictable and complex motion trajec- first step of the protocol involved an experiment to acquire tory. There are many types of systems for measuring body motion data using a motion capture system. The second movements, such as optical marker-based tracking systems, was processing the data and calculating the parameters on markerless visual systems, and inertial measurement unit- 4 Applied Bionics and Biomechanics d d d d r1[0] r1[9] n1[0] n1[9] (resmp)1 (raw)1 d d d r2[0] r2[8] n2[0] d n2[9] (resmp)2 (raw)2 d d r3[0] r3[11] d d n3[0] n3[9] (resmp)3 (raw)3 (a) (b) Figure 5: (a) Example of resampling datasets that have different lengths. (b) The vertical red lines are replaced using points by the cubic spline algorithm. (x ,y ,z ) (x ,y ,z ) (x ,y ,z ) (X ,Y ,Z ) 0 0 0 1 1 1 0 0 0 norm norm norm Origin Normalization Real norm Figure 6: Normalization of body segment length. Hip ° Knee hip Ankle ankle knee Toe Ground 0° (a) (b) (c) Figure 7: Definition of joint angles S : (a) flexion/extension of hip joint θ , (b) flexion/extension of the knee joint θ , and (c) ðangÞ hip knee dorsi-/plantar-flexion of ankle joint θ . The red points indicate joints, and the red/blue arrows denote the positive/negative sign of ankle angular direction. Left hip (IMU-) based systems, which can be used to capture irregular human motion [26]. Because the optical marker-based sys- tem is frequently used in medicine [27–29] owing to its rela- Center of hip tively high accuracy and minimal uncertainty of the subject’s movement, the optical marker-based system was used to T [m] trans Walking direction measure the normal stair-gait pattern in this study. To acquire the position data of each joint in three- dimensional (3D) space, 17 optical markers were placed, Right hip one on the subject’s sacrum, and two on the left and right anterior superior iliac spine (ASIS), hip, thigh, knee, shank, Figure 8: Definition of mediolateral movement, T . trans ankle, heel, and toe. Figure 3 presents the arrangement of the markers on the front and back sides of a subject. The placements of the reflective markers were determined for using a Prime 41 (OptiTrack, NaturalPoint Inc., USA) 3D accurate tracking of anatomical landmarks related to kine- motion capture system. The accuracy of this equipment is matic variables during gait [31–34]. submillimeter, with a latency of 5.5 ms [30]. The calibration During the experiment, the positional information of the was performed with errors less than 2 mm. As shown in markers on the subjects was recorded at a rate of 160 Hz Figure 4(a), eight cameras, marked in blue circles, were Applied Bionics and Biomechanics 5 Walking direction Walking direction T [m] rot Right hip Right hip Left hip Left hip (a) (b) Figure 9: Definition of hip rotation angle T : T in (a) equals the included angle θ of the right triangle ΔROH in (b). rot rot placed in a square with approximate dimensions of 10 m × constant) are considered as the identical functional sequence 10 m. The x-axis was defined as the direction of walking, with of gait cycle when m is an equal value for all cycles. Accord- the y-axis as the vertical direction. The direction of the right ingly, if m is the same in every dataset, the parameters asso- (negative value) and left sides (positive value) was defined as ciated with the sagittal and transverse planes, S and T, the z-axis. The experimental staircase was installed at the respectively, in Figure 1 are averaged in the final step of the center of the square. analysis protocol to generate a standard gait pattern. The datasets D = ½X Y Z  measured by the The dataset also needed to be normalized in space to ðrawÞ ðrawÞ ðrawÞ ðrawÞ standardize the trajectories of the joints because the length motion capture system consisted of the x, y, and z coordi- of each body segment is different from the other. Hence, nates for one cycle of stair walking. Each portion of the data- the positional trajectories of the joints were reconstructed sets, X , Y , and Z , denoted by time-series data for ðrawÞ ðrawÞ ðrawÞ 17×N by obtaining the equivalent lengths of each body segment. the attached 17 markers, was expressed by X ∈ R , ðrawÞ Figure 6 expresses the method for normalization of the body 17×N 17×N Y ∈ R , and Z ∈ R , where N is the number of ðrawÞ ðrawÞ segment length. data points recorded for each marker. The value of N A real segment length, L , from reference point P = Real 0 was different among the obtained datasets because of each ðx , y , z Þ to the other point P = ðx , y , z Þ was rearranged 0 0 0 1 1 1 1 participant’s walking speed. In this study, the datasets were to a new point P = ðx , y , z Þ with the desired ðnormÞ norm norm norm obtained for the six subjects who completed two stride length L .We decided L to be the average value of ðnormÞ ðnormÞ cycles of stair ascent and descent a total of five times. the length of the lower leg and thigh in Table 1. The relation Thus, a total 60 datasets of D (6 subjects × 5 times × ðrawÞ between normalized point P , the reference point P , ðnormÞ 0 2 cycles = 60 sets) were used for motion analysis of stair and the new point P is shown in (1) and the normalized data- ascent and stair descent. set D was computed through the equation given in [38]. ðnormÞ 2.2. Data Preprocessing for Normalization. Because of the norm participants’ own habits in walking, the walking velocity var- P = P − ðÞ P − P : ð1Þ ðÞ norm 0 0 1 Real ied per person or trial. The lengths of body segments and the gap between the joints were also different among the partic- ipants. Therefore, it was necessary to normalize the data for 2.3. Parameters for Motion Analysis. The hip, knee, and ankle joints were mainly characterized by large ranges of motion time and space to simplify various conditions. To unify the stride time condition, every D was (ROMs) in the sagittal plane rather than in the coronal or ðrawÞ transverse mobility [9, 18–20]. Despite the small actions on resampled to dataset D = ½X Y Z ðresmpÞ ðresmpÞ ðresmpÞ ðresmpÞ the transverse plane, it is important that hip movement with the same number (M) of components by applying the can contribute to the advancement of muscle strength and interpolation method of a cubic spline. The cubic spline is a effective balance training [39]. Thus, the parameters for anal- function constructed of piecewise third-order polynomials ysis of motion on the transverse plane, in particular the hip that are smoother and have smaller errors than some joint, as well as that on the sagittal plane were examined. other interpolating polynomials [35, 36]. Figure 5 shows an Four parameters were considered in this study: joint flexio- example of resampling the data D ½m (k = 1, 2, and 3 ðrawÞk n/extension angle and positional trajectory (on the sagittal and m =0,1, ⋯, M − 1, where k and M are constants), k k plane), tendency of hip translation, and hip rotation (on which is measured with the same sampling frequency but the transverse plane). These were determined by the relevant with a different length M . D is a modified dataset with k ðresmpÞk positions either to the sagittal plane ½Y Z  or to ðnormÞ ðnormÞ the same number of samples (M =10 in the example). To the transverse plane ½X Z . ðnormÞ ðnormÞ analyze the gait motion, the duration of a stride was divided The first parameter was angular trajectory S = ½θ , into several sequences by physical and functional properties, ang hip θ , θ , which signifies the trend of the hip, knee, and such as period, i.e., stance and swing. The temporal unit was knee ankle Stride cycle (%) for the analysis [20, 33, 37]. Therefore, the ankle during a stride on the stair. The angular trajectory components of D ½m (m =0, ⋯, M − 1, where M is a was obtained from the first law of cosines. The directions ðresmpÞ 70 6 Applied Bionics and Biomechanics −20 −10 −40 −20 −20 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Stride cycle (% cycle) Stride cycle (% cycle) Stride cycle (% cycle) (a) (b) (c) Figure 10: Mean angles of the (a) hip, (b) knee, and (c) ankle joint: the blue lines indicate the variation of the joint angle during stair ascent, and the red lines indicate the variation of the joint angle during stair descent. 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 0.5 0.5 −0.5 0 −0.5 0 x position (direction of progress) (m) x position (direction of progress) (m) (c) (d) Figure 11: Relative trajectories from the hip joint during stair ascent: (a) knee trajectories and (c) ankle trajectories of each subject. (b and d) Knee and ankle trajectories are shown as a result of normalization for the lengths of the body segments. Hip angle (degree) y position (direction of vertical) (m) y position (direction of vertical) (m) Knee angle (degree) y position (direction of vertical) (m) y position (direction of vertical) (m) Ankle angle (degree) Applied Bionics and Biomechanics 7 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 0 0.5 0 0.5 −0.5 −0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (c) (d) Figure 12: Relative trajectories from the hip joint during stair descent: (a) knee trajectories and (c) ankle trajectories of each subject. (b and d) Knee and ankle trajectories are shown as a result of normalization for the lengths of the body segments. 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) Figure 13: Standard trajectories of the (a) knee and (b) ankle during stair ascent. indicated in Figure 7 and the following conditions defined is an open curve. For this reason, the trajectories of the joints, these angles and their signs (positive/negative): as secondary parameters, were replaced with relative positions from a point for stair-gait patterns during a circular walk. The (i) If the hip joint poses on hip flexion, θ >0 reference point was set as the hip marker position. In other hip words, the position of the hip is considered as (0, 0) and the (ii) If the knee joint poses on knee flexion, θ >0 knee positions of the knee and ankle, which were secondary param- eters, moved relatively to the reference point. (iii) If the ankle joint poses on dorsiflexion, θ >0 ankle In general, most existing robotic locomotion rehabilita- tion systems address the kinematics on the sagittal plane The joints of the robot should be designed to move in a closed-loop pattern to generate a repetitive gait motion in because the lower limb is akin to working predominantly the fixed system even if the resulting data from the experiment for flexion/extension during locomotion. Such a movement y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) y position (direction of vertical) (m) 8 Applied Bionics and Biomechanics 0 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 −0.4 −0.4 −0.5 −0.5 −0.6 −0.6 −0.7 −0.7 −0.8 −0.8 −0.9 −0.9 −1 −1 −0.5 0 0.5 −0.5 0 0.5 x position (direction of progress) (m) x position (direction of progress) (m) (a) (b) Figure 14: Standard trajectories of the (a) knee and (b) ankle during stair descent. 8 8 0 0 −2 −2 −4 −4 −6 −6 −8 −8 0 20 40 60 80 100 0 20 40 60 80 100 Stride cycle (% cycle) Stride cycle (% cycle) Figure 15: Variation of hip translation during stair ascent. Figure 17: Variation of hip translation during stair descent. 10 10 8 8 6 6 4 4 2 2 0 0 −2 −2 −4 −4 −6 −6 −8 −8 −10 −10 0 20 40 60 80 100 0 20 40 60 80 100 Stride cycle (% cycle) Stride cycle (% cycle) Figure 16: Variation of hip rotation during stair ascent. Figure 18: Variation of hip rotation during stair descent. constrained to only one anatomical plane can prevent mean- ingful training for more effective therapeutic impact. The hip Table 2: ROM on all subjects applying to the motion of the robotic joint, especially, has distinct movement on the transverse system. plane owing to weight bearing or weight shifting during walk- Stair ascent Stair descent ing. Among the features of relevance to the robotic gait- Min. Max. Min. Max. training system [39], the hip translational movement, T , trans ° ° ° ° in the mediolateral direction is considered as the third param- 56:10 Hip angle -14.87 -4.62 40.18 ° ° ° ° eter. Figure 8 shows the method used to calculate the variation Knee angle 0.051 104.11 0.0048 104.14 of hip movement on the transverse plane. The length between ° ° ° ° Ankle angle -36.93 24.13 -37.87 35.87 the left and right hip markers is considered a constant because Hip translation -2.68 cm 2.68 cm -3.17 cm 3.17 cm it is an intrinsic value as the length of a body segment. The var- ° ° ° ° Hip rotation -16.71 16.66 -10.60 10.29 iation of mediolateral hip movement can be measured in terms of displacement of the center of the hip segment. Rotation angle (degree) Direction of right and left (cm) y position (direction of vertical) (m) y position (direction of vertical) (m) Rotation angle (degree) Direction of right and left (cm) Applied Bionics and Biomechanics 9 Table 3: Principal standard deviation within each subject. Sub 1 Sub 2 Sub 3 Sub 4 Sub 5 Sub 6 Min. Max. Min. Max. Min. Max. Min. Max. Min. Max. Min. Max. Stair ascent Hip angle 1.16 5.02 1.62 8.12 0.64 6.89 1.17 6.89 1.17 6.50 1.04 5.60 Knee angle 1.18 11.83 0.86 16.41 1.12 15.85 0.89 10.16 1.44 7.69 0.79 4.99 Ankle angle 0.51 7.77 1.10 8.66 1.30 8.89 1.35 8.54 0.61 7.54 0.36 4.17 Hip trans. 0.15 0.39 0.10 0.49 0.15 0.46 0.14 0.68 0.21 0.69 0.17 0.32 Hip rotation 1.31 6.52 1.09 4.47 0.14 2.00 0.27 2.70 0.02 2.50 0.32 2.72 Stair descent Hip angle 0.63 3.26 0.91 5.29 0.68 4.92 1.19 5.09 1.26 3.45 0.53 2.79 Knee angle 0.81 8.03 1.59 10.42 1.05 15.27 1.51 11.79 0.93 5.84 0.61 6.81 Ankle angle 1.09 6.27 1.15 6.78 1.20 8.69 2.49 11.49 0.44 6.78 0.33 5.57 Hip trans. 0.21 0.28 0.13 0.87 0.29 0.91 0.16 0.90 0.07 0.68 0.14 0.61 Hip rotation 0.17 1.35 0.51 1.77 0.41 1.70 0.73 3.28 0.06 3.00 0.11 1.25 Although the participants performed stair walking in the Table 4: Principal standard deviation of all subjects. same coordinates and location, the planes on which their tra- jectories were described were not exactly coincident. In other Stair ascent Stair descent words, the walking directions for all the data sets were differ- Min. Max. Min. Max. ent. Therefore, the data sets were manipulated so that they Hip angle 2.12 6.28 2.30 4.86 were in the same sagittal plane using the rotational displace- Knee angle 2.96 12.22 2.55 11.18 ment formula [40]. Thus, the right and left hip markers made Ankle angle 4.57 8.70 3.73 11.10 a line, and the center point on the line drew a curve along Hip translation 0.32 0.53 0.38 0.69 weight shift. Then, trends of positional variation of the center point between the hip joints in the same walking direction Hip rotation 1.47 4.42 1.80 3.17 could be determined. sagittal plane to analyze stair-walk motion. Figure 10 shows The last parameter for the motion analysis is the angular variations in the hip, knee, and ankle joint angles during stair displacement associated with the hip rotation during gait. ascent (red line) and stair descent (blue line), and their stan- Figure 9 indicates the methods for calculating the variation dard deviations are given by the gray areas. In this study, the of hip rotation on the transverse plane. The hip rotation, average ROMs for the subjects’ hip joints in extension/flexion T , was defined as the angle between the line perpendicular rot ° ° during a stair ascent and descent cycle were (−6:75 ,48:69 ) to the walking direction and the line of hip markers. The ° ° and (6:41 ,31:67 ), respectively. The average ROM of the rotation angle was determined by making a right triangle ° ° knee joints in extension/flexion was (8:20 ,93:78 ) during and finding the included angle with the inverse tangent func- ° ° stair ascent and (7:38 ,91:93 ) during stair descent. Addi- tion as shown Figure 9(b). The parameter was defined as a tionally, the average ROMs of ankle joints in plantar-/dorsi- positive value where the right hip marker was placed in front ° ° ° ° flexion were ð−17:78 ,11:75 Þ and (−24:89 ,24:18 ) during of the left hip marker. stair ascent and descent, respectively. The result of the data processing such as normalization Figures 11 and 12 present the relative trajectories of and interpolation makes trajectories for a gait cycle, but it the knee and ankle joints for the hip joint on the sagittal might not be appropriate to be applied to a fixed type reha- plane during stair ascent and descent, respectively. The bilitation robot. If values in the beginning and end points of different colors of trajectories in Figures 11 and 12 present the trajectories are different, they make a discontinuity when different subjects. To reduce the individual variation in the the robot is working because the robot needs a cyclic gait lengths of the body segments, the data were normalized pattern. Therefore, the points of the beginning and the end with the algorithm described in Section 2.2. The red points points on all results should match to make a cyclic pattern. on these figures represent the hip marker at the reference To resolve this problem, the obtained datasets were proc- point (0, 0). essed by the cubic spline method using the points corre- After normalization, we attempted to find the standard sponding to the first 5% (0 to 5%) and the last 5% (96 to trajectories of the knee and ankle. As shown in Figures 13 100%) of the stride cycle. and 14, the averaged trajectories of the normalized datasets, the red lines, are considered the standard trajectories in this 3. Results experiment. 3.1. Angular and Positional Trajectories of Joints on the Sagittal Plane. As mentioned in the previous section, we cal- 3.2. Hip Movement on the Transverse Plane. Figures 15 and culated two parameters of joint angles and trajectories on the 16 present the variation in hip translation and rotation, 10 Applied Bionics and Biomechanics 10 20 −10 −20 −20 0 20 40 60 80 100 0 20 40 60 80 100 Cycle time (%) Cycle time (%) Applied data Applied data (ascent) (descent) Data from the Data from the robot (descent) robot (ascent) (a) (b) Figure 19: Comparison of the angular trajectories on (a) hip joint and (b) knee joint between robot movement and experimental data. respectively, during a stair-ascent cycle. The translation/rota- 4. Discussion tion is indicated by the red line. The standard deviation is indicated by gray lines. When ascending a stair, the averaged In this study, we attempted to create patterns of stair walking ROMs on the transverse plane were within ±1:57 cm for for application to a robotic lower-limb rehabilitation system. translation and ±2:52 for rotational movement. A subject’s legs moved in a cyclical pattern during stair nego- As with Figures 15 and 16, Figures 17 and 18 indicate tiation. The movement of the lower limb primarily appears as trends in the hip movement for a stair-gait cycle. The range a flexion/extension of each joint [20]. Therefore, initially, of translation movement was estimated to be within ±2:00 variations in the joint angles of the hips, knees, and ankles cm, and hip rotation was estimated to be within ±2:70 . were extracted on the anatomical sagittal plane such that Table 2 shows the maximum range in which subjects actually the robotic exoskeleton of the gait-training system can work moved in the experiment. with the most basic gait pattern. The calculated angular var- Table 2 shows the minimum and maximum values of iations of the hips, knees, and ankles, as shown in Figure 10, were used to establish the basic pattern in stair ascent and data, which consist of the resampled 120 datasets from the experiment. The values in Table 2 cover the range of all sub- stair descent. jects’ motion. As shown in Table 1, the subjects had different stride Because the gait cycle was divided into 200 phases to lengths and leg lengths in the stair-walk experiment. There- derive the pattern of stair walking, standard deviation values fore, we normalized the lengths of body segments before cal- were different for each point in Figure 10 and Figures 15–18. culating the knee and ankle trajectories relative to the hip. As Thus, the principal estimation of standard deviations for shown in Figures 11 and 12, it was easy to find the trend of each result for each motion is summarized in Tables 3 and the normalized knee and ankle joint trajectories. Addition- 4. Table 3 shows the maximal and minimal values of stan- ally, the normalization is supposed to establish criteria for dard deviations for each subject. Table 4 presents the princi- the gait pattern to drive a robotic gait trainer after standard- pal estimations of standard deviation on each result in ization of the relative trajectories. Figures 13 and 14 show the Figure 10 and Figures 13–18. desired tracks of the knee and ankle joints for a robotic sys- tem mimicking the experimental pattern in Figure 10. 3.3. Application of Derived Pattern to the Robotic System. In addition to the analysis on the sagittal plane, we tried If the trajectory is compared with the joint displacement to examine the hip joint on the transverse plane. The data of a robotic training system served by itself, it can ascer- medial-lateral movements of the hip during stair walking tain whether the system properly works within a normal seemed to be similar among the subjects, as shown in ROM, e.g., the height of a leg lift. Actual angular trajecto- Figures 15 and 17. However, the variation in hip rotation ries performed by the robotic system designed for stair angles had large standard deviations, as shown in Figures 16 walking during stair ascent and descent are displayed in and 18. This is due to differences in the gait patterns of each Figure 19. The trajectories generally follow the gait pattern individual, such as step length, body segment length, gender, obtained from this study (green and light blue line) even and other anatomical factors. Its effectiveness should be inves- though there is some delay or errors—average errors within tigated by a clinical test, which, however, is beyond the scope ±8% were calculated. of this work. Hip angle (degree) Knee angle (degree) Applied Bionics and Biomechanics 11 The exoskeleton of the robotic system was designed based Acknowledgments on the results shown in Table 2, and it could move within a This study was jointly supported by the Technology Innova- range that covered all subjects. As shown in Tables 3 and 4, tion Program (grant number: 20000843) funded by the Min- standard deviations on the sagittal plane in Table 3 are larger istry of Trade, Industry, and Energy (MOTIE, South Korea), than those in Table 4, and the results on the transverse plane a grant of the Asan Institute for Life Sciences intramural in Table 4 are larger than those in Table 3. It means that the research project funded by Asan Medical Center (grant num- standard patterns on the sagittal plane reflected the general ber: 2019-692), and a grant of the Korea Health Technology trend of stair walk, and the variation within an individual R&D Project through the Korea Health Industry Develop- on the transverse plane is larger than among subjects. There- ment Institute (KHIDI) funded by the Ministry of Health & fore, each joint of the exoskeleton was controlled by a stan- Welfare, Republic of Korea (grant number: HI17C2410). dard pattern in Figure 10 for reflecting general patterns on the robotic system. On the other hand, hip movements on the transverse plane were controlled within ranges of stan- References dard deviations depending on the individual difference as shown in Figures 15–18. [1] E. J. Benjamin, P. Muntner, A. Alonso et al., “Heart disease and As compared to the motion of a robot with the derived stroke statistics—2019 update: a report from the American Heart Association,” Circulation, vol. 139, no. 10, pp. e56– standard pattern shown in Figure 19, the trend of the motion e528, 2019. between the applied data and that measured from the robot is [2] United Nations, “Department of Economic and Social Affairs,” almost similar, but some inevitable errors occurred. 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