# Towards Accurate Gait Instability Assessment:
Identifying a Fixed Pelvis Point that Best Matches the
Whole-Body Center of Mass

Laurine Tirel, Ariane P. Lallès, Bruno Watier, Hélène Pillet

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Laurine Tirel, Ariane P. Lallès, Bruno Watier, Hélène Pillet. Towards Accurate Gait Instability Assessment: Identifying a Fixed Pelvis Point that Best Matches the Whole-Body Center of Mass. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the.., 10.46298/mbj.16222. hal-05191776v2

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# Towards Accurate Gait Instability Assessment: Identifying a Fixed Pelvis Point that Best Matches the Whole-Body Center of Mass

Laurine Tirelª, Ariane P. Lallèsª, b*, Bruno Watierª, Hélène Pilletᵇ

a LAAS-CNRS, Université de Toulouse, Toulouse, France

b Arts et Métiers Institute of Technology, EPF Engineering School, Université Sorbonne Paris Nord, IBHGC-Institut de Biomécanique Humaine Georges Charpak, F-75013 Paris, France

* Corresponding author: ariane.lalles@ensam.eu

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** gait, center of mass, optimization

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Falls can be an economic burden for the society. While many devices focus on fall detection, monitoring gait degradation offers better insight into risk identification and tailored interventions.

Wearable sensors, like Inertial Measurement Units (IMUs) can be used in near-falls detection, thanks to their cost and lightweight design. Most recent studies use accelerometer data to train machine learning models (Pang et al., 2019), which, while sensitive, offer limited insight into underlying mechanisms. Alternatively, bio-mechanical parameters such as the distance between the body center of mass (BCoM) and the minimal moment axis ($d_{BCoM-MMA}$) (Bailly et al., 2018) — have shown effectiveness in assessing locomotion instability in laboratory settings.

Current wearable methods do not directly estimate BCoM position. Estimations from a single IMU, such as one on the sacrum, are affected by integration drift and positional offset errors (Floor-Westerdijk et al., 2012).

This study aimed to identify a fixed point in the pelvis that minimizes BCoM estimation error during gait (i.e., optimized position). Using this optimized point, we evaluate its impact on $d_{BCoM-MMA}$ estimation. We hypothesize that this approach would better approximate $d_{BCoM-MMA}$ obtained with full-body kinematics.

## 2. Methods

### 2.1 Protocol

This study used data from a previously approved protocol (Lallès et al., 2024) (RCB 2020-A01357-32). Fourteen healthy adults (5 F/9 M, 26.0 ± 2.2 years old, 71.4 ± 6.3 kg) walked on an instrumented dual-belt treadmill (1000 Hz, Treadmetrix, Park City, UT, USA) while 50 markers were tracked by a 9-camera Vicon system (100 Hz, MX-T10, MX-T20S) (Dumas et al., 2007). Participants wore their own flat-soled shoes and a safety harness. Only normal walking trials (1.2 m/s) were analyzed.

### 2.2 Data processing

Kinematic and dynamic data were pre-processed in Nexus (Vicon Motion Systems Ltd, Oxford, UK), and analyzed in MATLAB (MathWorks, Natick, MA, USA) using custom scripts. Data were filtered using a fifth-order low-pass Butterworth filter (5 Hz cut-off).

BCoM position was computed in four ways, all relative to a pelvis frame defined per (Dumas et al., 2007), with the lumbar joint centre as origin. The reference (BCoM_fullbody) was obtained by the weighted sum of segmental centres of mass, based on anthropometric tables (Dumas et al., 2007).

BCoM was then estimated as i/ the midpoint of the posterosuperior iliac spines (BCoM_sacrum) ii/ a fixed point in the pelvis frame obtained from the
initial position of the BCoM_fullbody during the static acquisition (BCoM_pelvis). Static acquisition was performed in the anatomical position: standing upright, feet at pelvis width, palms facing forward.

In addition, a last estimation called BCoM_optimized was computed using the Broyden-Fletcher-Goldfarb-Shanno algorithm (Python software foundation, scipy. optimize.minimize). This function allows to find the best point in the pelvis frame that minimizes the mean squared error with BCoM_fullbody.

To assess the impact of BCoM optimization on instability metrics, we evaluated its effect on the distance between the BCoM and the minimal moment axis ($d_{BCoM-MMA}$), calculated as the norm of the corresponding vector (Bailly et al., 2018):

$$d_{BCoM-MMA} = \frac{F_{ext} \times M_{BCoM}}{\|F_{ext}\|^2}$$

where $\times$ denotes the cross-product, $F_{ext}$ the resultant of the external force, and $M_{BCoM}$ the total external moment expressed at BCoM. We then computed the norm of this vector. Note that for this outcome, BCoM was expressed in the global frame.

Root mean square error (RMSE) was computed between the reference (fullbody) and main outcomes (sacrum, pelvis, optimized) over the entire recording

(14.36 ± 1.55 cycles). Mean and standard deviation are presented.

## 2.4 Statistical analyses

Statistical analysis was conducted in Python. Normality was tested using the Shapiro-Wilk test. The Friedman test assessed differences between methods ($\alpha$ = 0.05), with Wilcoxon post hoc for pairwise comparisons.

## 3. Results and discussion

Optimization significantly reduced BCoM RMSE (Table 1). Mean translation from the sacrum to the optimized point was 13.5 ± 2.6 cm anteroposteriorly (AP), -0.2 ± 0.8 cm mediolaterally and 0.7 ± 1.1 cm vertically. As expected, this was particularly efficient along the AP axis. However, as BCoM_optimized was fixed within the pelvis frame, it did not account for internal pelvic BCoM motion, particularly along the AP axis.

Using BCoM_optimized notably impacted $d_{BCoM-MMA}$: its evolution closely matched the reference (Fig. 1), with RMSEs under the centimetre (Table 1). This suggests that an optimized point provides accurate $d_{BCoM-MMA}$ estimates during gait, especially compared to BCoM_pelvis, which is affected by pelvis anteflexion. Application of this optimized point is yet to be demonstrated during perturbed situations.

<table><caption>**Table 1.** Root mean square errors (RMSE) obtained for the BCoM position (in the pelvis frame), the distance between the body centre of mass and the minimal moment axis ($d_{BCoM-MMA}$), and the norm of $d_{BCoM-MMA}$.</caption><thead><tr><th>RMSE [cm]</th><th>AP</th><th>ML</th><th>V</th><th>Norm</th></tr></thead><tbody><tr><td colspan="5"><strong>BCoM position in the pelvis frame</strong></td></tr><tr><td>Fullbody vs. sacrum</td><td>13.5*** ± 2.6</td><td>1.0*** ± 0.6</td><td>1.0*** ± 0.4</td><td>-</td></tr><tr><td>Fullbody vs. optimized</td><td>1.1 ± 0.4</td><td>0.3 ± 0.1</td><td>0.7 ± 0.2</td><td>-</td></tr><tr><td>Fullbody vs. pelvis</td><td>4.4*** ± 2.1</td><td>1.5*** ± 0.6</td><td>0.9*** ± 0.4</td><td>-</td></tr><tr><td colspan="5"><strong>d<sub>BCoM-MMA</sub> in the global frame</strong></td></tr><tr><td>Fullbody vs. sacrum</td><td>11.5*** ± 2.3</td><td>1.1*** ± 0.3</td><td>1.1*** ± 0.2</td><td>10.5*** ± 0.2</td></tr><tr><td>Fullbody vs. optimized</td><td>1.0 ± 0.4</td><td>0.6 ± 0.2</td><td>0.1 ± 0.0</td><td>0.9 ± 0.2</td></tr><tr><td>Fullbody vs pelvis</td><td>3.8*** ± 1.7</td><td>0.8*** ± 0.3</td><td>0.4*** ± 0.2</td><td>3.3*** ± 1.6</td></tr></tbody></table>

AP: anteroposterior, ML: mediolateral, V: vertical,

*: significant difference with optimized (*: p≤0.05, **: p≤0.01, ***: p≤0.001).

Credit: Laurine Tirel.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Evolution of the *d*<sub>BCOM-MMA</sub> for all subjects (mean and standard error) during a normalized gait cycle. *d*<sub>BCOM-MMA</sub> was computed in four different ways: using BCOM fullbody, sacrum, pelvis, and optimized.</figcaption></figure>

Credit: Laurine Tirel

## 4. Conclusions

The optimization method significantly reduced discrepancies across BCOM estimates and enabled accurate computation of a mechanical instability parameter, supporting the development of a fully wearable, single-IMU system. In the future, identifying a population-specific, individually adaptable optimized point could eliminate the need for a full-body reference.

## Acknowledgements

This research was funded in whole or in part by the National Research Agency (ANR) under project BAC2WALK (ANR-22-CE19-0003-01).
Projet réalisé avec le soutien de la Fondation de l'Avenir, Paris, France.

## Conflict of Interest Statement

None.

## Contributor Roles

LT: Formal analysis, methodology, software, visualization, writing - original draft; AL: Conceptualization, data curation, investigation, methodology, software, writing - original draft; BW: Conceptualization, funding acquisition, project administration, software, supervision, validation, writing - review & editing; HP:

Conceptualization, funding acquisition, investigation, project administration, resources, software, supervision, writing - review & editing.

## Funding

This research was funded in whole or in part by the National Research Agency (ANR) under project ANR-22-CE19-0003-01.

## References

Bailly, F., Carpentier, J., Pinet, B., Soueres, P., & Watier, B. (2018). A mechanical descriptor of human locomotion and its application to multi-contact walking in humanoids. *2018 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (Biorob)*, 350–356. https://doi.org/10.1109/BIOROB.2018.8488125

Dumas, R., Chèze, L., & Verriest, J.-P. (2007). Adjustments to McConville et al. and Young et al. body segment inertial parameters. *Journal of Biomechanics*, *40*(3), 543–553. https://doi.org/10.1016/j.jbiomech.2006.02.013

Floor-Westerdijk, M. J., Schepers, H. M., Veltink, P. H., van Asseldonk, E. H. F., & Buurke, J. H. (2012). Use of inertial sensors for ambulatory assessment of center-of-mass displacements during walking. *IEEE Transactions on Bio-Medical Engineering*, *59*(7), 2080–2084. https://doi.org/10.1109/TBME.2012.2197211

Lallès, A., Watier, B., & Pillet, H. (2024). Dynamic criterion to quantify instability during locomotion. *2024 International Symposium on 3D Analysis of Human Movement (3DAHM)*, 1–5. https://doi.org/10.1109/3DAHM62677.2024.10920803

Pang, I., Okubo, Y., Sturnieks, D., Lord, S. R., & Brodie, M. A. (2019). Detection of near falls using wearable devices: A systematic review. *Journal of Geriatric Physical Therapy*, *42*(1), 48. https://doi.org/10.1519/JPT.0000000000000181