# Indirect Measurement of Ground Reaction Forces and Moments by Means of Wearable Inertial Sensors: A Systematic Review

^{*}

## Abstract

**:**

## 1. Introduction

- It is inherently cumbersome and requires dedicated spaces and controlled environment, i.e., a motion analysis laboratory.
- It does not allow the measurement of tasks in open-field or requiring large spaces.
- It is expensive.
- It requires highly skilled operators.

- Methods based on matrix and/or pressure sensors used as insoles.
- Methods based on wearable load cells that directly measure three-dimensional GRF.
- Methods based on the kinematic data obtained by OS.
- Methods based on IMUs that measure motion of body segments and estimate GRF by means of a biomechanical model and/or machine learning methods.

## 2. Data Analysis

#### 2.1. Search Strategy

#### 2.2. Inclusion/Exclusion Criteria

## 3. Discussion

#### 3.1. Methods Based on Biomechanical Modelling

#### 3.1.1. Walking and Running

_{i}and a

_{i}are the mass and acceleration of the i-th segment of the model. T is the stance time. The acceleration was computed at the centre of mass of each segment by rotating and translating the acceleration measured.

_{x,y,z}are the components of measured acceleration and c

_{1,2,3}, are empirical coefficients.

#### 3.1.2. Jumping and Other Tasks

^{2}= 0.812, p ≤ 0.01), thus the authors concluded that the peak GRF may be computed from Newton’s second law by knowing subject’s mass. This study helped identifying several inaccuracies in the procedure such as: (i) the relative movement of the accelerometer with respect to the body; (ii) noise and non-removable instrumental errors; (iii) unmeasured angle between tibia and ground during impact; (iv) possible non-linearity in the relationship between acceleration and GRF [65]. Moreover, a clear correlation was not identified between the height of the jump and peak impact forces while it was demonstrated by other studies [7]. Interestingly, the authors were able to compute the flying time for the jump and hence the vertical height from the temporal profile of vertical acceleration by using a previously validated algorithm [66].

^{®}IMUs in combination with the built-in X-Sens

^{®}full body segment model [74,75]. The model used 17 IMUs composed of tri-axial accelerometers, gyroscopes and magnetometers, remotely controlled and triggered. Sampling frequency was 120 Hz. The full body configuration allowed the estimation of the three dimensional GRF acting on the feet segments. The protocol needed a calibration obtained by recording an upright posture and then the acceleration of each body segment during the bending exercise was measured. The moments and the GRF were estimated by means of a top-down approach, using Newton’s second law. The results were compared to the GRF simultaneously measured by a FP and to the internal forces/moments computed taking advantage of the information from the FP and an OS. As observed in previous studies [72], a good agreement between the FP and the IMUs was observed for the profile of vertical component of GRF with a RMS error below 20 N corresponding to the 2% of maximum vertical force [73]. A good agreement was also observed between the peak values of GRF. Instead, the forces on antero-posterior and medio-lateral directions were overestimated by the IMU method. Regarding the internal moments on L5/C1, the maximum RMS error was below 10 Nm corresponding to the 5% of the peak extension moment [73]. The main inaccuracies observed were attributed to the rigid body assumption and to the mass of each body segment that was assigned according to a statistical model based on percentages of the total body mass [73]. Thus, the masses used for computation at may not well represent the masses of the actual body segments of each subject. In agreement with previous studies, the authors concluded that inertial motion capture is a good candidate for GRF and internal moment estimation in ambulatory settings but its validity is limited to the task analysed, i.e., the trunk bending. Further study is required for the analysis of other tasks.

#### 3.2. Methods Based on Machine Learning

## 4. Summary

## 5. Conclusions and Final Remarks

- (1)
- The number of sensors/body segments required for the biomechanical modelling
- (2)
- Knowledge of the inertial properties of each body segment
- (3)
- Determining the antero-posterior and medio-lateral components of GRF
- (4)
- Determining the GRF acting on each foot in double support conditions and evaluating loading asymmetry
- (5)
- Even if a correlation between predicted and directly measured GRF exists, it is difficult to estimate the absolute value of peak force.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Study selection through the different phases using PRISMA framework [25].

**Figure 2.**Accelerometer positioning and biomechanical model as designed by [26].

**Figure 3.**Detection of walking phases from the radial acceleration of the shank according to the algorithm proposed by [26]. A: heel strike, B: beginning of mid stance, C: rising of heel, D: toe off.

**Figure 4.**Identification of gait phases from the angular position of the feet, according to [44].

**Figure 5.**Biomechanical model as defined by [44] and the respective free body diagrams of: (

**a**) trunk, (

**b**) foot, (

**c**) lower leg, (

**d**) upper leg.

**Figure 6.**Forces on heel and phalange estimated by the method proposed by [44] and compared to the output of load cells placed under the shoe.

**Figure 7.**Biomechanical model and landmarks for IMUs as proposed by [45].

**Figure 9.**Graphical representation of the GRF vector estimated by the IMU (red) and by the force platform (blue) as found by [56]. (

**A**) sprint start task, (

**B**,

**C**) change of direction tasks. Angular error between the vectors is represented.

**Figure 10.**Graphical representation of the GRF curves along the gait cycle for IMU (red) and FP (blue) as found by [56]. (SS) sprint start task, (COD) change of direction tasks. F

_{z}is the vertical component.

**Figure 11.**Musculoskeletal model designed by [60]. The coordinate frame within the hip represents the reference system for the IMUs.

**Figure 12.**Components of Ground Reaction Forces estimated from the model designed by [60]. On the first row: forces estimated by the OS, on the second row: forces estimated by IMUs.

**Figure 13.**The vertical GRF measured by the force plate (red) compared to the one predicted by the IMUs (blue) for one subject, according to the method by [62].

**Figure 14.**IMU placement landmarks and sensor design according to the protocol proposed by [72].

**Figure 15.**Free body diagram for each segment according to the model proposed by [72].

**Figure 16.**Comparison of the vertical GRF calculated by the IMUs and the one directly measured by the force platform [72].

**Figure 17.**Five-links biomechanical model (

**a**) and free body diagram (

**b**) of the method proposed by [76]. The inclination angle of each segment is defined on the sagittal plane and the internal forces and moments are represented on the free body diagram.

**Figure 18.**The experimental setup proposed by [76]. (

**a**) Representation of body segments and sensors, (

**b**) Landmarks and sensors worn by the subject.

**Figure 19.**Membership function for the distribution of vertical GRF among the two feet as determined by [87]. The upper line is the left membership function, representing the left single support phases. The bottom line represents the right membership function. The transients represent the double support.

**Figure 20.**Vertical GRF profile predicted by the method proposed by [87] and the one directly measured by pressure insoles.

**Figure 21.**Model based on the two artificial neural networks (ANN) and its training from IMU data. The two ANNs sequentially estimated kinematics and kinetics [89].

**Figure 22.**Accuracy of the estimated GRF and knee flexion/extension for different running speeds using single-subject training [89].

**Figure 23.**The estimated GRF profiles are compared to the respective reference profiles. Reference profiles were classified according to the respective reference kinematics (IMU and Plug In Gait joint angle output) [89]. These estimates were obtained using training datasets from different subjects. Left forces are depicted on the first row, while right stances are on the bottom row. At the top of each graph it is reported the comparison between the curves in terms of: the Pearson correlation coefficient, the RMSE and its standard deviation [89].

Reference | Year | Task | No. of Segments | Sensor Type/IMU | Sensor Positioning | Subjects Studied | Method | Reported RMSE or Other Inaccuracy Measures (Worst Case) | Outcomes and Remarks |
---|---|---|---|---|---|---|---|---|---|

Ohtaki et al. [26] | 2001 | Gait | 5 | 1D Acc, 1D Gyro | Distal shank and thigh | Healthy adults | Newton’s Law of motion | Vertical: 0.31 ± 0.012 N/BW Horizontal: 0.076 ± 0.031 N/BW | Gait phase identification. Spectral analysis of acceleration. |

Elvin et al. [65] | 2007 | Vertical jump | 2 | 1D Acc. | Shank | Male athletes | Correlation | Correlation R^{2} = 0.748 | Correlation between peak GRF and peak tibial acceleration. Computation of the flying time. |

Neugebauer et al. [28] | 2012 | Walking, running | 1 | 2D Acc. | Iliac crest of the right hip | Healthy teenagers | Statistical Model. | 9.0 ± 4.2% | Estimation of peak ground reaction force |

Neugebauer et al. [30] | 2014 | Walking, running | 1 | 3D Acc. | Iliac crest of the right hip | Healthy adults | Statistical model | Vertical: 8.3 ± 3.7% Braking: 17.8 ± 4.0% | Estimation of peak vertical and peak braking ground reaction forces. Acceleration of hip does not estimate correctly GRF. Worst case: running. |

Howard et al. [67] | 2014 | Counter and drop jump | 1 | 3D Acc. | Pelvis | Healthy adults | Newton’s Law of motion | Counter jump: 35.8% Drop jump: 53.6% | Estimated GRF did not match the measured GRF. |

Wundersitz et al. [31] | 2013 | Running, direction change | 1 | 3D Acc. | Upper back, T2 | Healthy adults | Newton’s Law of motion | ~24% | Acceleration signal needed to be smoothed. |

Charry et al. [37] | 2013 | Running | 2 | 3D Acc. | Medial tibia | Healthy adults | Correlation | 8.28% | Implemented gait events identification. Logarithmic correlation observed between acceleration and peak GRF. |

Pouliot-Laforte et al. [68] | 2014 | Vertical jump | 1 | 3D Acc. | Right Hip | Children and teenagers with “osteogenesis imperfect” | Newton’s Law of motion | 31% | Good correlation between the GRF estimated and the one directly measured. |

Min et al. [71] | 2015 | Squat | 3 | 3D Acc, 3D Gyro, 3D Mag. | Lumbar spine, thigh, shank | Healthy adults | Inverse dynamics/Newton’s Law of motion | R = 0.93 0.02 BW | High accuracy of estimated GRF. High correlation between acceleration and GRF. |

Logar and Munih [72]. | 2015 | Ski Jumping | 10 | 3D Acc, 3D Gyro, 3D Mag. | Total body tracking | Athletes–ski-jumpers | Biomechanical model and inverse dynamics. | 12 ± 13% | Required calibration procedure. Good similarity between measured and calculated GRF. |

Meyer et al. [39] | 2015 | Walking, jogging, running, landing and other tasks | 1 | 3D Acc. | Right hip | Healthy Children | Newton’s Law of motion | R = 0.89 | Good correlation between acceleration and measured GRF although GRF were overestimated by accelerometer method. |

Yang et al. [44] | 2015 | Walking | 7 | 3D Acc, 3D Gyro | Trunk, thigh, shank, foot. | Healthy adults | Biomechanical model 3D | R = 0.95 66 N | Estimation of the Intersegmental forces and GRF. Identification of walking cycle. |

Leporace et al. [86] | 2015 | Walking | 1 | 3D Acc. | Shank | Healthy adults | Machine learning | Vertical: 5.2 ± 1.7% BW Antero-Posterior: 5.4 ± 1.8% BW Medio-Lateral: 13.0 ± 6.1% BW | Good prediction of all the components of GRF. |

Faber et al. [73]. | 2016 | Bending | 17 | 3D Acc, 3D Gyro, 3D Mag. | Full body | Healthy adults | Biomechanical model/Newton’s law. | 20 N | Calibration needed. The full body configuration allowed to estimate the three dimensional GRF. Good agreement observed between estimated and measured forces. |

Kodama and Watanabe [76] | 2016 | Sit to stand, squat | 7 | 3D Acc. | Trunk, Pelvis, thigh, shank | Healthy adults | Biomechanical model/Newton’s law. | Vertical: 15 N Horizontal: 10 N | Estimated internal forces/moments, GRF and CoP. Good estimation of GRF. Main limitation due to statistics used to determine inertial properties of body segments. |

Setuain et al. [80] | 2016 | Vertical jump | 1 | 3D Acc, 3D Gyro, 3D Mag. | Lumbar spine | Healthy adults | Newton’s Law of motion | 19% R = 0.93 | Identification of jump phases from velocity profile. Good correlation between acceleration and force platform, but disagreement between values. |

Karatsidis et al. [45] | 2017 | walking | 17 | 3D Acc, 3D Gyro, 3D Mag. | Full Body | Healthy adults | Biomechanical model | 29.6% | Use of smooth transition function to determine GRF in double support. |

Gurchiek et al. [56] | 2017 | Acceleration and change of direction | 1 | 3D Acc, 3D Gyro, 3D Mag. | Sacrum | Healthy adults | Newton’s law. | 182.92 N R = 0.53 | 3D GRF. Static calibration needed. Poor results for the lateral components of force. |

Raper et al. [59] | 2018 | Running | 1 | 3D Acc. | Medial tibia | Professional Athletes | Newton’s law. | 16.04% | IMU underestimates the force, but good correlation with the direct measurement. |

Aurbach et al. [60] | 2017 | Gait | 15 | 3D Acc, 3D Gyro, 3D Mag. | Full body | Healthy adults | AnyBody™ musculoskeletal model. | 15.60 ± 12.54% | GRF and ankle internal forces. |

Guo et al. [87] | 2017 | Gait | 1 | 3D Acc. | L5, C7, Forehead | Healthy adults | Machine learning. | 5.0% | Membership function to identify GRF during double support. Good estimation of GRF. Gait phase identification was dependent on pressure insoles. L5 is the best placement. |

Wouda et al. [89] | 2018 | Running | 3 | 3D Acc, 3D Gyro, 3D Mag. | Pelvis, shank. | Athletes/runners | Multi stage machine learning. | 0.27 BW | Minimal sensor setup. Only vertical GRF was estimated. Excellent results when using training data from the same subject. |

Thiel et al. [62] | 2018 | Sprint running | 2 | 3D Acc, 3D Gyro, 3D Mag. | Shank | Athletes/sprinters | Linear modelling. Empirical parameter estimation. | 33.32% | Estimation of peak GRF by linear modelling. Method was not reliable for every participant. |

Kiernan et al. [63] | 2018 | Running | 1 | 3D Acc. | Thigh | Athletes/runners | Statistical model/linear regression equation | N.A. | Estimation of peak GRF. Relation between peak GRF and potential injury. Evaluation of the training level. Use of the lateral component of acceleration to determine which foot is in contact with the ground. |

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**MDPI and ACS Style**

Ancillao, A.; Tedesco, S.; Barton, J.; O’Flynn, B. Indirect Measurement of Ground Reaction Forces and Moments by Means of Wearable Inertial Sensors: A Systematic Review. *Sensors* **2018**, *18*, 2564.
https://doi.org/10.3390/s18082564

**AMA Style**

Ancillao A, Tedesco S, Barton J, O’Flynn B. Indirect Measurement of Ground Reaction Forces and Moments by Means of Wearable Inertial Sensors: A Systematic Review. *Sensors*. 2018; 18(8):2564.
https://doi.org/10.3390/s18082564

**Chicago/Turabian Style**

Ancillao, Andrea, Salvatore Tedesco, John Barton, and Brendan O’Flynn. 2018. "Indirect Measurement of Ground Reaction Forces and Moments by Means of Wearable Inertial Sensors: A Systematic Review" *Sensors* 18, no. 8: 2564.
https://doi.org/10.3390/s18082564