# Prediction of Lower Limb Kinetics and Kinematics during Walking by a Single IMU on the Lower Back Using Machine Learning

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Finding the Location of a Single Measurement by the IMU

_{hs}, with the subscript hs denoting values at the onset of the stance phase (Figure 2), as follows:

**x**to the augmented state

**z**= [l, θ, lθ]

^{Τ}, which includes the state parameters, l and θ of the SLIP model, and its nonlinear term lθ as follows:

_{hs}− c

_{hs}+ d.

**z**and the augmented kinetics

**f**= [f

_{x}, f

_{y}, T

_{a}]

^{T}such as GRF and ankle torque are obtained as follows:

**z**and the augmented segment angles

**θ**= [θ

_{1}, θ

_{2}, θ

_{3}]

^{T}can be rewritten as follows:

**z**of the spring mechanics and the bias as follows:

**x**and the lower limb kinetics and kinematics [

**f**,

^{T}**θ**] as a form of weighted sum of x and bias, we tried to predict the unmeasured lower limb kinematics and kinetics using the sacrum motion profiles, the measurable approximation of the CoM. We may use the terms ‘CoM’ and ‘sacrum’ interchangeably throughout the manuscript (see also the Appendix A for the formulation of the lower limb kinematics and kinetics as an approximation of the weighted sum of the CoM states).

^{T}#### 2.2. Experimental Protocols and Data Collection

^{®}) and force plates (Bertec, FP 6012

^{®}), respectively. For the segment angle calculation, 12 markers were located at the toe, heel, ankle, knee, and anterior and posterior superior iliac spine (ASI and PSI) of both legs. The midpoint of the PSIs was used as the reference position for the IMU. Motion data and force data were collected at the sampling frequency of 100 Hz and 200 Hz, respectively, and filtered with a fifth-order low-pass Butterworth filter with a cutoff frequency of 10 Hz. The joint torque was calculated by the inverse dynamics of the seven-segmental rigid body model, which includes the hip, knee, and ankle. The mass distribution of the rigid body were based on the anatomical reports [31].

#### 2.3. Preprocessing of IMU Data for ANN Input

**v**(t) is the time integration of the acceleration data for time t over the duration of the stance phase T. To satisfy the steady walking assumption, the mean velocity change was set to zero so that position drift due to the random error was simultaneously removed.

_{0}was estimated as follows:

#### 2.4. Structure of the ANN and Its Training and Test Procedures

_{x}, v

_{y}, a

_{x}, a

_{y}), where x, y are horizontal and vertical position, respectively, and v and a are velocity and acceleration measured at a specific time, such as t = t

_{0}. The position of the CoM was reset to be zero at every HS, and we defined ‘displacement’ as the reset position. The eleven output nodes constitute an 11 × 1 column vector consisting of the GRFs and the joint kinetics and kinematics corresponding to t = t

_{0}, such as (GRF

_{x}, GRF

_{y}, T

_{ank}, T

_{knee}, T

_{hip}, θ

_{foot,stance}, θ

_{shank,stance}, θ

_{thigh,stance}, θ

_{foot,swing}, θ

_{shank,swing}, θ

_{thigh,swing}), where T, and θ are joint torque and segment angle, respectively, with subscripts showing the names of the lower limb segment. All kinematic data of the sacrum, such as the acceleration, velocity and displacement, were normalized by its maximum norm such that the values ranged from 0 to 1. The hidden layer has 20 nodes, and node weights are iteratively updated to best match the data. The sigmoid and linear activation transfer functions were used in the hidden and output layers. The loss function of the network was set as the mean square error of the predicted angles of both the stance and swing legs, the joint torque of the stance leg and the GRF with respect to the observed data. The network employed an Adam optimizer for the back-propagation process. To match the size of the training dataset collected at various gait speeds of many subjects, gait data of one stance phase were interpolated into 200 points. As a quantitative measure of prediction performance, we used the normalized root mean square error (NRMSE), which was normalized by the difference between the maximum and minimum values of the outputs of each subject at each speed. The NRMSE value of each subject represents the error of a total of 30 trials at one speed for one output. The neural network programming was conducted using PyTorch 0.4.1 [32].

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

_{hs}, with the subscript hs denoting values at the onset of the stance phase (Figure A1), as follows:

**Figure A1.**Compliant walking model with an off-centered, curvy foot combined with a springy foot-ankle segment [29]. (

**A**) The model parameters and state variables of the model, and (

**B**) the force and torque components. The position of the CoM in the sagittal plane; x and y are the positions of the horizontal and vertical axes, respectively, and the model state variables l and θ are the total spring length and angle, respectively, with a positive sign in the clockwise direction with respect to the vertical. The length and stiffness of the CoM–ankle are represented by l

_{a}and k

_{a}, respectively. The off-centered curvy foot parameters d and R are the offset of the ankle from the center of the foot and the radius of the curvy foot, respectively. The forces at the ground contact point are presented by f

_{x}and f

_{y}in the horizontal and vertical directions, respectively. The constraint force, f

_{a}, acts on the ankle in the vertical direction of the spring force, and the constraint ankle torque, T

_{a}, is generated to prevent foot rotation relative to the leg rotation, with a positive sign in the extension direction. With the kinematic constraint and the positions of the CoM and the ankle, (

**C**) multibody segment angles are determined by inverse kinematics. Segment lengths and angles are represented by l and θ, respectively, with subscripts 1~3, and angles are positive in the clockwise direction.

**x**to the augmented state

**z**= [l, θ, lθ]

^{Τ}, which includes the state parameters, l and θ of the SLIP model, and its nonlinear term lθ as follows:

_{hs}+ d − c

_{hs}.

**z**and the GRF and ankle torque are obtained from the CoM of the SLIP model as follows [29]:

_{0}are the stiffness and the rest length of the spring, respectively, and the geometric parameters of R and d are the radius of the curvy foot and the offset of the ankle joint from the center of the curved foot, respectively. l

_{a}and k

_{a}are the length and stiffness of the CoM–ankle, as shown in Figure A1. The constants c

_{l}and c

_{k}are the ratio of the rest length of l

_{a}to the rest length of l and the ratio of the total leg stiffness k to the CoM–ankle stiffness k

_{a}, respectively (Figure A1). The ankle torque T

_{a}is expressed as f

_{a}and l

_{a}, which are the constraint force applied to the ankle joint and the distance from the ankle to the CoM, respectively. By applying a small angle approximation, a small offset d approximation compared to the foot length R, such as d/R << 1, and the small length deviation approximation of the leg length l, such as l = l

_{0}(1 + δ), with δ being assumed to be small, then f

_{a}is approximated as follows:

^{2}≈ 0, then the augmented kinetics

**f**= [f

_{x}, f

_{y}, T

_{a}]

^{T}can finally be obtained as follows:

_{1}is the same as l

_{2}.

_{a}< 2l

_{1}, the segment angles

**θ**= [θ

_{1}, θ

_{2}, θ

_{3}]

^{T}can be rewritten as follows:

**z**of the spring mechanics and the bias as follows:

**x**and the joint kinematics and kinetics [

**f**,

^{T}**θ**], we tried to predict the 11 unmeasured joint kinetics during walking from a single IMU measurement near the CoM.

^{T}Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Segment angles of stance leg | |||||||

Slow | |||||||

Thigh | 8.81 | 9.38 | 8.34 | 5.27 | 8.58 | 9.32 | 8.03 |

Shank | 3.17 | 4.06 | 3.01 | 2.12 | 3.25 | 3.98 | 6.24 |

Foot | 3.49 | 3.84 | 3.48 | 4.03 | 3.02 | 4.24 | 6.31 |

Moderate | |||||||

Thigh | 5.45 | 10.04 | 8.19 | 5.26 | 9.48 | 7.64 | 7.86 |

Shank | 2.58 | 4.25 | 2.94 | 3.16 | 3.10 | 2.12 | 7.48 |

Foot | 4.06 | 3.82 | 4.21 | 3.80 | 3.31 | 3.47 | 7.04 |

Fast | |||||||

Thigh | 3.81 | 7.27 | 5.82 | 6.87 | 11.96 | 7.47 | 9.87 |

Shank | 2.42 | 3.71 | 2.76 | 3.70 | 3.60 | 3.61 | 4.40 |

Foot | 2.94 | 3.65 | 3.59 | 5.25 | 4.46 | 5.31 | 4.43 |

Segment angles of swing leg | |||||||

Slow | |||||||

Thigh | 9.91 | 8.99 | 10.55 | 5.57 | 8.24 | 10.36 | 12.33 |

Shank | 7.92 | 5.25 | 5.97 | 4.43 | 3.85 | 6.78 | 6.51 |

Foot | 5.99 | 5.07 | 5.29 | 5.58 | 4.71 | 8.85 | 9.53 |

Moderate | |||||||

Thigh | 6.41 | 10.39 | 10.31 | 6.17 | 8.38 | 7.48 | 13.13 |

Shank | 5.39 | 5.05 | 6.50 | 4.12 | 6.00 | 3.90 | 6.83 |

Foot | 5.02 | 5.41 | 5.63 | 4.83 | 5.97 | 5.93 | 8.43 |

Fast | |||||||

Thigh | 4.21 | 8.00 | 8.31 | 7.55 | 9.53 | 6.45 | 11.53 |

Shank | 4.15 | 4.94 | 7.89 | 3.72 | 4.64 | 3.99 | 5.63 |

Foot | 4.23 | 5.20 | 5.65 | 5.56 | 7.46 | 6.16 | 5.22 |

Joint torques of stance leg | |||||||

Slow | |||||||

Hip | 11.27 | 8.45 | 13.55 | 12.65 | 9.44 | 13.46 | 12.85 |

Knee | 10.81 | 11.34 | 8.70 | 9.51 | 10.47 | 13.43 | 9.78 |

Ankle | 8.58 | 8.90 | 7.65 | 8.33 | 6.44 | 15.62 | 11.88 |

Moderate | |||||||

Hip | 11.67 | 8.28 | 12.12 | 11.39 | 11.00 | 10.30 | 10.44 |

Knee | 11.48 | 9.44 | 8.41 | 8.10 | 11.43 | 8.59 | 10.00 |

Ankle | 7.96 | 8.99 | 8.33 | 8.11 | 7.41 | 11.94 | 11.97 |

Fast | |||||||

Hip | 11.67 | 9.79 | 10.75 | 11.80 | 11.59 | 9.52 | 9.44 |

Knee | 7.67 | 8.28 | 10.04 | 7.36 | 16.50 | 6.06 | 9.39 |

Ankle | 9.51 | 8.53 | 7.35 | 8.32 | 11.81 | 8.58 | 11.49 |

Ground reaction forces | |||||||

Slow | |||||||

Vertical | 8.02 | 6.02 | 7.66 | 4.49 | 5.30 | 12.24 | 3.87 |

A–P | 11.00 | 4.57 | 4.95 | 5.14 | 6.56 | 8.79 | 4.38 |

Moderate | |||||||

Vertical | 7.65 | 6.63 | 7.29 | 4.22 | 6.82 | 6.21 | 5.01 |

A–P | 8.95 | 4.92 | 4.98 | 5.38 | 8.41 | 5.78 | 4.70 |

Fast | |||||||

Vertical | 6.10 | 6.75 | 8.55 | 5.19 | 15.77 | 5.91 | 9.21 |

A–P | 5.22 | 5.80 | 5.90 | 5.93 | 13.43 | 4.95 | 5.64 |

Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Angles of stance leg | |||||||

Slow | |||||||

Thigh | 0.92 | 0.89 | 0.93 | 0.97 | 0.92 | 0.91 | 0.94 |

Shank | 0.98 | 0.97 | 0.98 | 0.99 | 0.98 | 0.97 | 0.91 |

Foot | 0.96 | 0.96 | 0.96 | 0.95 | 0.98 | 0.93 | 0.88 |

Moderate | |||||||

Thigh | 0.97 | 0.88 | 0.93 | 0.94 | 0.91 | 0.94 | 0.94 |

Shank | 0.99 | 0.97 | 0.98 | 0.98 | 0.98 | 0.99 | 0.88 |

Foot | 0.95 | 0.96 | 0.95 | 0.96 | 0.97 | 0.96 | 0.86 |

Fast | |||||||

Thigh | 0.99 | 0.95 | 0.97 | 0.96 | 0.85 | 0.95 | 0.91 |

Shank | 0.99 | 0.98 | 0.99 | 0.98 | 0.98 | 0.97 | 0.96 |

Foot | 0.98 | 0.97 | 0.97 | 0.94 | 0.96 | 0.94 | 0.95 |

Angles of swing leg | |||||||

Slow | |||||||

Thigh | 0.90 | 0.91 | 0.90 | 0.97 | 0.93 | 0.90 | 0.87 |

Shank | 0.95 | 0.98 | 0.97 | 0.98 | 0.99 | 0.96 | 0.96 |

Foot | 0.96 | 0.97 | 0.97 | 0.97 | 0.98 | 0.91 | 0.91 |

Moderate | |||||||

Thigh | 0.96 | 0.88 | 0.89 | 0.97 | 0.93 | 0.95 | 0.85 |

Shank | 0.98 | 0.98 | 0.96 | 0.99 | 0.97 | 0.99 | 0.96 |

Foot | 0.97 | 0.97 | 0.97 | 0.98 | 0.97 | 0.96 | 0.93 |

Fast | |||||||

Thigh | 0.98 | 0.94 | 0.93 | 0.95 | 0.89 | 0.96 | 0.87 |

Shank | 0.99 | 0.98 | 0.95 | 0.99 | 0.98 | 0.99 | 0.97 |

Foot | 0.98 | 0.98 | 0.97 | 0.97 | 0.95 | 0.97 | 0.98 |

Joint torques of stance leg | |||||||

Slow | |||||||

Hip | 0.42 | 0.76 | 0.31 | 0.45 | 0.69 | 0.22 | 0.42 |

Knee | 0.80 | 0.73 | 0.85 | 0.84 | 0.79 | 0.70 | 0.81 |

Ankle | 0.91 | 0.90 | 0.93 | 0.91 | 0.96 | 0.71 | 0.78 |

Moderate | |||||||

Hip | 0.41 | 0.75 | 0.37 | 0.56 | 0.56 | 0.54 | 0.58 |

Knee | 0.78 | 0.72 | 0.86 | 0.88 | 0.71 | 0.87 | 0.75 |

Ankle | 0.92 | 0.88 | 0.92 | 0.90 | 0.93 | 0.85 | 0.72 |

Fast | |||||||

Hip | 0.50 | 0.72 | 0.67 | 0.56 | 0.68 | 0.68 | 0.71 |

Knee | 0.91 | 0.87 | 0.82 | 0.92 | 0.48 | 0.94 | 0.81 |

Ankle | 0.87 | 0.90 | 0.92 | 0.88 | 0.83 | 0.90 | 0.76 |

Ground reaction forces | |||||||

Slow | |||||||

Vertical | 0.88 | 0.82 | 0.87 | 0.95 | 0.94 | 0.70 | 0.96 |

A–P | 0.79 | 0.96 | 0.95 | 0.95 | 0.92 | 0.84 | 0.96 |

Moderate | |||||||

Vertical | 0.87 | 0.90 | 0.88 | 0.95 | 0.90 | 0.82 | 0.93 |

A–P | 0.86 | 0.95 | 0.96 | 0.95 | 0.87 | 0.94 | 0.96 |

Fast | |||||||

Vertical | 0.91 | 0.91 | 0.83 | 0.93 | 0.49 | 0.91 | 0.82 |

A–P | 0.95 | 0.94 | 0.94 | 0.93 | 0.68 | 0.96 | 0.93 |

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**Figure 1.**Schematics of the procedures of lower limb kinetics prediction from a single inertial measurement unit (IMU) using machine learning. Processed IMU signals, such as velocity, position and time, were fed into input nodes of the network. The network has seven input nodes followed by one hidden layer of 20 nodes and 11 output nodes. The output predictions are the angle of the thigh, shank, and foot of the stance and swing leg and the joint torques of the hip, knee, and ankle and the vertical and horizontal ground reaction forces.

**Figure 2.**Compliant walking model with an off-centered, curvy foot combined with a springy foot-ankle segment [29]. (

**A**) The model parameters and state variables of the model, and (

**B**) the force and torque components. The position of the CoM in the sagittal plane; x and y are the positions of the horizontal and vertical axes, respectively, and the model state variables l and θ are the total spring length and angle, respectively, with a positive sign in the clockwise direction with respect to the vertical. The length and stiffness of the CoM–ankle are represented by l

_{a}and k

_{a}, respectively. The off-centered curvy foot parameters d and R are the offset from the ankle from the center of the foot and the radius of the curvy foot, respectively. The forces at the ground contact point are presented by f

_{x}and f

_{y}in the horizontal and vertical directions, respectively. The constraint force, f

_{a}, acts on the ankle in the vertical direction of the spring force, and the constraint ankle torque, T

_{a}, is generated to prevent foot rotation relative to the leg rotation, with a positive sign in the extension direction. With the kinematic constraint and the positions of the CoM and the ankle, (

**C**) multibody segment angles are determined by inverse kinematics. Segment lengths and angles are represented by l and θ, respectively, with subscripts 1–3, and angles are positive in the clockwise direction.

**Figure 3.**Schematics of the gait event detection and IMU data segmentation algorithm. To detect the gait events of heel strike (HS) and toe off (TO), the acceleration measurement in the (

**B**) vertical and (

**D**) anteroposterior (AP) directions is compared with the (

**A**) vertical and (

**C**) eranteroposterior GRF measurement. Timings of specific gait events, such as the CoM apex, HS, and TO, are marked with reversed triangle. Data filtered by 10 Hz and 40 Hz cutoff frequencies are presented by black and gray solid lines, respectively. (

**E**) Gait event detection algorithm. From the local and global minimum points of the vertical and A–P accelerations (see Methods section), the apex, HS and TO events are detected.

**Figure 4.**The average trajectories of (

**A**) displacement and (

**B**) speed of the CoM over 90 trials of seven subjects at gait speeds ranging from 1.0 to 2.3 m/s. Vertical and horizontal components are presented in the left and right columns, respectively. The experimental mean and standard deviation are depicted as gray shaded and white solid lines, respectively, whereas the estimated values are depicted as thick and thin black solid lines, respectively.

**Figure 5.**The prediction results and experimental data of (

**A**) the segment angles of the stance leg, (

**B**) swing leg, (

**C**) the joint torques of the stance leg, and (

**D**) the ground reaction forces, averaged for all seven subjects. The mean and standard deviations of the experimental data are depicted as white solid lines with a gray shadow, and those of the prediction results are shown as thick and thin black solid lines, respectively.

**Figure 6.**The prediction results and experimental data of (

**A**) the segment angles of the stance leg, (

**B**) swing leg, (

**C**) the joint torques of the stance leg, and (

**D**) the ground reaction forces. The mean and standard deviations of the experimental data are depicted as a white solid line with a gray shadow, and those of the prediction results are shown as thick and thin black solid lines, respectively. The data correspond to three subjects with different levels of estimation errors of the minimum (NRMSE: 6.15 ± 2.52%), median (NRMSE: 7.11 ± 2.70%), and maximum errors (NRMSE: 8.21 ± 2.81%), shown from left to right. The graph shows the average trajectories of 90 trials per subject collected at various (slow, moderate, and fast) gait speeds.

**Figure 7.**Normalized root mean square errors (NRMSEs) of the estimation of (

**A**) the segment angles of the stance leg, (

**B**) the segment angles of the swing leg, (

**C**) the joint torques of the stance leg, and (

**D**) the ground reaction forces as a function of the input variables fed into the neural network. Prediction errors in response to the ANN input data with and without displacement (x) of the sacrum are shown as black and gray bar graphs, respectively. Asterisk shows statistical significance (p < 0.05).

**Figure 8.**Prediction errors (NRMSEs) of (

**A**) the segment angles of the stance leg, (

**B**) the segment angles of the swing leg, (

**C**) the joint torques of the stance leg, and (

**D**) the GRFs at various (slow, moderate, and fast) gait speeds. The ANN was trained with data collected at slow, moderate and fast speeds (dark gray bars), slow and moderate speeds (light gray bars), and moderate speed only (white bar). There was no statistically significant difference.

**Figure 9.**The experimental data and the prediction data of the (

**A**) joint torques and (

**B**) GRFs at various gait speed obtained from the ANN trained by trials of moderate speed only. The average and standard deviations of the experimental data are represented by a white line and gray shaded area, respectively, and those of the estimation are represented by thick and thin black lines, respectively.

Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Average |
---|---|---|---|---|---|---|---|---|

Slow (m/s) | 1.07 | 1.71 | 1.38 | 1.22 | 1.29 | 1.00 | 1.20 | 1.27 ± 0.23 |

Moderate (m/s) | 1.21 | 1.87 | 1.49 | 1.37 | 1.51 | 1.14 | 1.36 | 1.42 ± 0.24 |

Fast (m/s) | 1.54 | 2.26 | 1.78 | 1.76 | 2.07 | 1.49 | 1.76 | 1.81 ± 0.27 |

MAE (s) | Slow | Moderate | Fast | Total |
---|---|---|---|---|

HS | 0.030 ± 0.022 | 0.025 ± 0.016 | 0.021 ± 0.017 | 0.025 ± 0.019 |

TO | 0.016 ± 0.010 | 0.016 ± 0.011 | 0.010 ± 0.009 | 0.014 ± 0.010 |

**Table 3.**Mean absolute error and normalized root mean square error (NRMSE) of displacement and velocity of sacrum.

Error | Slow | Moderate | Fast | Total | |
---|---|---|---|---|---|

Vertical displacement | MAE (m) | 0.006 ± 0.003 | 0.005 ± 0.002 | 0.006 ± 0.003 | 0.006 ± 0.003 |

NRMSE (%) | 20.12 ± 10.67 | 16.83 ± 7.14 | 16.82 ± 7.48 | 17.93 ± 8.71 | |

A–P displacement | MAE (m) | 0.06 ± 0.03 | 0.04 ± 0.02 | 0.04 ± 0.02 | 0.04 ± 0.03 |

NRMSE (%) | 8.76 ± 4.72 | 5.96 ± 3.75 | 4.69 ± 2.90 | 6.47 ± 4.21 | |

Vertical velocity | MAE (m/s) | 0.06 ± 0.02 | 0.06 ± 0.02 | 0.06 ± 0.03 | 0.06 ± 0.02 |

NRMSE (%) | 15.89 ± 5.82 | 14.21 ± 4.84 | 12.77 ± 4.43 | 14.29 ± 5.22 | |

A–P velocity | MAE (m/s) | 0.14 ± 0.079 | 0.12 ± 0.07 | 0.16 ± 0.08 | 0.14 ± 0.08 |

NRMSE (%) | 43.98 ± 24.94 | 34.87 ± 20.82 | 43.96 ± 23.40 | 40.94 ± 23.48 |

Speed | Slow | Moderate | Fast | |
---|---|---|---|---|

Segment angles of stance leg | Thigh | 8.25 ± 1.40 | 7.70 ± 1.82 | 7.58 ± 2.66 |

Shank | 3.69 ± 1.30 | 3.66 ± 1.81 | 3.46 ± 0.66 | |

Foot | 4.06 ± 1.07 | 4.24 ± 1.27 | 4.23 ± 0.89 | |

Segment angles of swing leg | Thigh | 9.42 ± 2.13 | 8.89 ± 2.52 | 7.94 ± 2.31 |

Shank | 5.82 ± 1.41 | 5.40 ± 1.13 | 4.99 ± 1.43 | |

Foot | 6.43 ± 1.93 | 5.89 ± 1.20 | 5.64 ± 1.00 | |

Joint torques of stance leg | Hip | 11.67 ± 2.03 | 10.74 ± 1.26 | 10.65 ± 1.06 |

Knee | 10.58 ± 1.53 | 9.63 ± 1.40 | 9.33 ± 3.42 | |

Ankle | 9.63 ± 3.12 | 9.24 ± 1.91 | 9.37 ± 1.68 | |

Ground reaction forces | Vertical | 6.80 ± 2.85 | 6.26 ± 1.24 | 8.21 ± 3.63 |

A–P | 6.49 ± 2.51 | 6.16 ± 1.76 | 6.70 ± 2.99 |

Error | Minimum | Median | Maximum | |
---|---|---|---|---|

Segment angles of stance leg | Thigh | 5.80 ± 0.93 | 7.45 ± 1.41 | 8.59 ± 1.11 |

Shank | 2.99 ± 0.80 | 2.90 ± 0.13 | 6.04 ± 1.55 | |

Foot | 4.36 ± 0.78 | 3.76 ± 0.39 | 5.93 ± 1.35 | |

Segment angles of swing leg | Thigh | 6.43 ± 1.02 | 9.72 ± 1.23 | 12.33 ± 0.80 |

Shank | 4.09 ± 0.36 | 6.79 ± 0.99 | 6.32 ± 0.62 | |

Foot | 5.33 ± 0.43 | 5.53 ± 0.20 | 7.73 ± 2.24 | |

Joint torques of stance leg | Hip | 11.95 ± 0.64 | 12.14 ± 1.40 | 10.91 ± 1.75 |

Knee | 8.32 ± 1.09 | 9.05 ± 0.87 | 9.72 ± 0.31 | |

Ankle | 8.25 ± 0.12 | 7.78 ± 0.50 | 11.78 ± 0.25 | |

Ground reaction forces | Vertical | 4.63 ± 0.50 | 7.84 ± 0.65 | 6.03 ± 2.82 |

A–P | 5.49 ± 0.41 | 5.28 ± 0.54 | 4.91 ± 0.65 |

Inputs | x, t | x, v, t | v, t | x, v, a, t | v, a, t |
---|---|---|---|---|---|

Segment angles of stance leg | 5.20 ± 2.42 | 5.23 ± 2.69 | 7.62 ± 2.71 | 5.21 ± 2.38 | 6.34 ± 2.71 |

Segment angles of swing leg | 7.22 ± 2.19 | 6.76 ± 2.30 | 8.44 ± 2.81 | 6.71 ± 2.25 | 8.37 ± 2.88 |

Joint torques of stance leg | 10.04 ± 2.64 | 10.44 ± 2.63 | 12.25 ± 3.57 | 10.09 ± 2.10 | 11.56 ± 3.91 |

GRF | 6.95 ± 2.58 | 6.76 ± 2.31 | 10.18 ± 3.17 | 6.77 ± 2.55 | 8.06 ± 2.34 |

Total | 7.39 ± 3.04 | 7.35 ± 3.19 | 9.57 ± 3.57 | 7.24 ± 2.95 | 8.63 ± 3.63 |

Speed | Slow | Moderate | Fast | |
---|---|---|---|---|

Joint torques of stance leg | Hip | 13.41 ± 2.91 | 11.42 ± 0.65 | 11.07 ± 1.41 |

Knee | 11.35 ± 2.64 | 10.11 ± 2.23 | 9.92 ± 2.94 | |

Ankle | 10.38 ± 3.94 | 9.30 ± 2.29 | 9.41 ± 1.95 | |

Ground reaction forces | Vertical | 6.64 ± 2.00 | 6.84 ± 1.30 | 7.93 ± 1.61 |

A–P | 6.24 ± 2.05 | 5.93 ± 0.85 | 7.09 ± 2.83 |

S. E. Oh et al. (2013) | G. Leporace et al. (2018) | Proposed Method | ||||
---|---|---|---|---|---|---|

Number of subjects | 48 | 17 | 7 | |||

Measurement | 11 Optical markers | 2 IMUs at each shank | 1 IMU at sacrum | |||

Prediction method | GRNN | FFNN | FFNN | |||

Prediction parameters | rRMSE (%) | ρ | MAD (%) | ρ | NRMSE (%) | ρ |

Vertical GRF | 5.8 ± 1.0 | 0.98 | 4.6 ± 0.7 | 0.97 | 6.26 ± 1.24 | 0.96 ± 0.03 |

A–P GRF | 7.3 ± 0.8 | 0.97 | 4.0 ± 0.8 | 0.98 | 6.16 ± 1.76 | 0.98 ± 0.01 |

ML GRF | 19.8 ± 2.2 | 0.92 | 10.5 ± 3.3 | 0.80 | - | - |

A Findlow et al. (2008) | T.P. Luu et al. (2014) | Proposed Method | ||||
---|---|---|---|---|---|---|

Number of subjects | 8 | 17 | 7 | |||

Measurement | 4 IMUs at each shank and feet | 2 Gait parameters + 4 Anthropometric data | 1 IMU at sacrum | |||

Prediction method | GRNN | GRNN | FFNN | |||

Prediction parameters (proposed) | MAD (degree) | ρ | MAD (degree) | ρ | RMSE (degree) | ρ |

Hip (thigh) | 8.64 ± 1.45 | 0.80 ± 0.05 | 3.73 ± 1.64 | 0.98 ± 0.03 | 3.14 ± 1.49 | 0.99 ± 0.03 |

Knee (shank) | 7.14 ± 1.33 | 0.89 ± 0.05 | 5.41 ± 2.01 | 0.97 ± 0.04 | 2.17 ± 1.23 | 0.99 ± 0.00 |

Ankle (foot) | 4.91 ± 0.76 | 0.75 ± 0.06 | 3.58 ± 1.44 | 0.92 ± 0.07 | 3.35 ± 1.58 | 0.99 ± 0.01 |

M. M. Ardestani et al. (2014) | M. Mundt et al. (2018) | Proposed Method | ||||
---|---|---|---|---|---|---|

Number of subjects | 4 | 12 | 7 | |||

Measurement | 14 sEMGs | 3D joint angles | 1 IMU at sacrum | |||

Prediction method | WNN | LSTM | FFNN | |||

Prediction parameters | rRMSE (%) | ρ | MAD (%) | ρ | NRMSE (%) | ρ |

Hip | 6.42 | 0.93 | 18.15 | 0.97 | 10.74 ± 1.26 | 0.90 ± 0.04 |

Knee | 4.30 | 0.98 | 13.50 | 0.93 | 9.63 ± 1.40 | 0.96 ± 0.03 |

Ankle | 4.20 | 0.98 | 6.41 | 0.98 | 9.24 ± 1.91 | 0.98 ± 0.01 |

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## Share and Cite

**MDPI and ACS Style**

Lim, H.; Kim, B.; Park, S.
Prediction of Lower Limb Kinetics and Kinematics during Walking by a Single IMU on the Lower Back Using Machine Learning. *Sensors* **2020**, *20*, 130.
https://doi.org/10.3390/s20010130

**AMA Style**

Lim H, Kim B, Park S.
Prediction of Lower Limb Kinetics and Kinematics during Walking by a Single IMU on the Lower Back Using Machine Learning. *Sensors*. 2020; 20(1):130.
https://doi.org/10.3390/s20010130

**Chicago/Turabian Style**

Lim, Hyerim, Bumjoon Kim, and Sukyung Park.
2020. "Prediction of Lower Limb Kinetics and Kinematics during Walking by a Single IMU on the Lower Back Using Machine Learning" *Sensors* 20, no. 1: 130.
https://doi.org/10.3390/s20010130