# Dynamic criterion to quantify instability during locomotion

Ariane Lallès, Bruno Watier, Hélène Pillet

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Ariane Lallès, Bruno Watier, Hélène Pillet. Dynamic criterion to quantify instability during locomotion. 18th International Symposium of 3DAHM, Dec 2024, Montevideo, Uruguay. 10.1109/3DAHM62677.2024.10920803. hal-04919418

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# Dynamic criterion to quantify instability during locomotion

Ariane Lallès
IBHGC / LAAS-CNRS
ENSAM Paris / CNRS
Paris, France / Toulouse, France
ariane.lalles@ensam.eu

Bruno Watier
LAAS-CNRS
Université de Toulouse, CNRS, UPS
Toulouse, France
bruno.watier@univ-tlse3.fr

Hélène Pillet
IBHGC
ENSAM Paris
Paris, France
helene.pillet@ensam.eu

**Abstract**— Despite numerous teams attempted to quantify fall risks during gait, few used dynamic criteria to assess instability. While most studies focused on kinematic criteria (e.g., extrapolated center of mass, virtual pivot point, inverted pendulum model.), this study proposes, based on a theoretical approach, to use a dynamic criterion by measuring the distance between the body center of mass (BCoM) and the minimal moment axis of the external mechanical action applied to the body. This can easily be linked to the variation of the whole-body angular momentum. So far, in this preliminary study, eight asymptomatic volunteers walked on dual-belt instrumented treadmill equipped with two force platforms (Treadmetrix©). This protocol was approved by an ethical committee (RCB 2020-A01357-32). All participants provided their informed consent. A motion capture system (Vicon©) was used to obtain three-dimensional kinematics. After walking at a stable speed (1.2m/s), volunteers were subjected to acceleration and deceleration perturbations (3m/s2 and 10 m/s2 up to 2.04 and 0.36m/s) causing trips and slips. While participants were informed about the disruptions, no information was given regarding the type and the timing occurrence. Results showed significant variations of the mean and maximal distance during pre-perturbation phases and perturbation phases during both slips (p<0.001) and trips (p<0.001) (10m/s2). Future validation is needed with high-risk individuals to establish thresholds for inevitable falls. In the long run, this could be used to detect in real time with embedded systems people at risk of falls, or in rehabilitation protocols. The results of this study could also benefit to the control of humanoid robots during gait.

**Keywords**— biomechanics, gait, risk-of-falls, treadmill, acceleration, deceleration

## I. INTRODUCTION

Maintaining balance is a key factor in performing activities of daily living (e.g., standing, walking, walking while talking). This requires a complex synergy of the vestibular, visual, somatosensory, musculoskeletal systems, and the central nervous system [1]. Balance can be assessed in static (maintaining a standing position) or dynamic (ability to maintain stability during movement) conditions [2]. A stable gait is a gait that prevents falls despite disturbances [3] and requires controlling the position of the center of mass relatively to the base of support (BoS) [4].

The ability to maintain locomotion is essential for preserving the autonomy of individuals whose locomotor system is impaired due to aging, disability, or pathology. If a

fall is the final consequence of the loss of balance, monitoring the degradation of gait is far more interesting, as it offers perspectives on prevention through specific training for at-risk population. However, quantifying instability in real life is currently not feasible. One way to reproduce unstable walking conditions is to expose individuals to unexpected disturbances, which are known to account for about 60% of unintentional falls in young adults and older individuals [5]. This can be done in the laboratory, offering a safe environment to the participants and controlled conditions. Several setups have been proposed in the literature to reproduce both trips (using obstacles [6], [7], [8], [9] or cables [8], [10]) and slips (sliding plates [6]). Other perturbations can be generated by hidden holes [8] or irregular surfaces [11], [12], [13]. Instrumented treadmill offers the possibility to continuously collect data over long periods of time. They can also deliver standardized perturbations [14].

Laboratory-based dynamic stability measurements resulted in various parameters. Nevertheless there is still no consensus on the quantitative method [3]. Hof et al. [15] introduced the concept of extrapolated center of mass and margin of stability as an extension of the inverted pendulum model [16] to describe both static and dynamic balance. This parameter evaluates both body center of mass (BCoM) position and velocity, in relation to the BoS [17]. While this outcome was evaluated in several perturbation setups and within pathological populations, it is only valid under strict conditions. In fact, the pendulum must be non-deformable, there should be no external forces (e.g., cane, ramp), and counter-rotation movements beyond the model's scope must not be included [18], [19]. Whole body angular momentum (WBAM) and time rate of change of WBAM (dWBAM/dt) could be a good approach as they both provide a continuous measurement and account for counter-rotation movements. Several authors evaluated its ability to detect perturbations [20], [21], [22], [23]. Nevertheless, their translational use (i.e., in the clinic) is still limited by their interpretability.

In this context, we propose to take advantage of the equivalence between the derivative of the whole body angular momentum at the center of mass and the external contact wrench to propose an alternative parameter which should enhance the clinical interpretability. This parameter is expressed as a distance between the BCoM and the minimal moment axis of the external mechanical action applied to the body (dBCoM-MMA). The minimal moment axis corresponds to the sets of points where the overall moment induced by external forces is minimal for the Euclidian norm [24]. This parameter is linked to the variation of the angular momentum of the whole body. The greater the distance, the greater the angular acceleration of the body around BCoM [25]. Our

<footnote>This research was funded in whole or in part by the National Research Agency (ANR) under project ANR-22-CE19-0003-01. To facilitate its publication in open access, the author holding the rights applies a CC-BY Open Access license to any article accepted for publication resulting from this submission applicable funding agency here.</footnote>
approach is particularly interesting as it enables computation for uneven surfaces or multi contacts [24]. It also has the advantage of taking into account both whole body dynamics and contact forces. This parameter has already been calculated on healthy and pathological populations [24], [25], [26], [27]. However, its sensitivity to external destabilizing perturbations is yet to be determined.

Therefore, the goal of the present study is to determine how this parameter evolves under external perturbations while walking on an instrumented treadmill. The hypothesis is that after a perturbation, the pattern of the parameter would deviate from the one under normal walking conditions, and that its maximum value would be higher.

## II. MATERIALS AND METHODS

### A. Participants

We included all healthy participants who provided their informed consent. Pregnant women and individuals unable to walk without experiencing discomfort, pain, or excessive fatigue were excluded from this study. We also excluded any participants presenting pain, injuries, or joint instabilities at the time of inclusion and data acquisition, as well as those with known histories of balance disorders. This protocol was approved by an ethical committee (RCB 2020-A01357-32). During the measurements, each participant was equipped with a safety harness attached above the treadmill to prevent potential falls (Fig. 1). Each participant also wore their own flat-soled sneakers (Fig. 1). So far, eight participants were included in this study (3 F/5 M, 25.6 ± 1.3 years old, 73 ± 5 kg). A total of 143 perturbation trials were analyzed. One trial was removed because of an incorrect identification of the timing of the perturbation.

### B. Experimental procedures

Participants walked on a dual-belt instrumented treadmill (1000 Hz, Treadmetrix, Park City, UT, USA) equipped with 50 markers tracked by 9 optoelectronic cameras (100 Hz, MX-T10, MX-T20S, Vicon Motion Systems Ltd, Oxford, UK)[28], [29]. Protocol starts with a familiarization phase at a constant speed of 1.2 m s⁻¹ (Vi) for 5 minutes. Each participant was then submitted to two types of perturbations: slip and trip randomly sent on the right and left foot. Participants were informed of the presence of perturbations during the walking session. However, no information was provided about the occurrence or type of perturbation. Perturbations were triggered via a LabView interface (National Instruments Corp., Austin, TX, USA) allowing to modify the belt speed at a given instant of the gait cycle. Occurrence was defined at the instant the perturbed foot made contact with the ground. At that point, a target speed signal of ± 70% of the initial speed [30] was sent to the treadmill (i.e., tripping = 0.36 m s⁻¹, slipping = 2.04 m s⁻¹). Acceleration rates were set in the treadmill's control software at 3 and 10 m s⁻². Perturbation duration was set at 500 ms. On total, each participant encountered eight perturbations.

### C. Data processing

Preprocessing of the kinematic and dynamic data was carried out using Nexus (Vicon Motion Systems Ltd, Oxford, UK). Data were then processed in MATLAB (MathWorks, Natick, MA, USA) using custom-made software. Kinematic and kinetic data were filtered using a fifth-order low-pass Butterworth filter with a cutoff frequency of 5 Hz.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Participant equipment and treadmill environment. Security harness (red circle), rigid clusters equipped with markers (green circle), flat-soled sneakers (white circle).</figcaption></figure>

The actual belt speed was calculated following the method presented by [31]. Markers were placed on each belt so that 10 markers (5 per belt) were visible. Perturbation was considered active as soon as the actual treadmill speed was ± 10% of the initial speed (i.e., Vi = 1.2 m s⁻¹) [32]. This enabled the computation of perturbation duration, defined as the time during which the perturbation was considered active. Perturbation occurrence was calculated as the time (s) and percentage of the gait cycle (% GC) between the heel strike of the perturbed cycle and the instant the perturbation became active.

BCoM position was obtained by the weighted sum of segmental centers of mass. Their respective position was obtained through anthropometric tables [28], [29].

The main outcome, the distance between the BCoM and an axis where the moment is minimal (dBCoM-MMA) was formulated and calculated as the norm of the following vector [24]:

$$ \mathbf{d}_{BCoM-MMA} = \frac{F_{ext} \times \mathbf{M}_{BCoM}}{\|F_{ext}\|^2} = \frac{F_{ext} \times \dot{\mathbf{h}}_{BCoM}}{\|F_{ext}\|^2} \quad (1) $$

where × denotes the cross-product, Fext the resultant of the external force, and MBCoM the total external moment expressed at BCoM. This parameter can be related to conventional mechanical quantities. According to the dynamic wrench relationship to Newton's laws, MBCoM is equal to the rate of change of the angular momentum (hBCoM). Therefore, the norm of dBCoM-MMA can also be expressed as follows:

$$ \| \mathbf{d}_{BCoM-MMA} \| = \frac{\| \dot{\mathbf{h}}_{BCoM} \| |\sin \theta|}{\| F_{ext} \|} \quad (2) $$

where the angle sin θ corresponds to the angle between external forces, and rate of change of the angular momentum at BCoM.

Discrete parameters, such as mean and maximum values of the norm of dBCoM-MMA, were computed for all situations.

### D. Statistical analyses

Data normality and homogeneity of variances were respectively verified using the Shapiro and Levene tests in R Studio (Posit Software, PBC, Boston, MA, USA). Discrete variables were compared using a paired t-tests between
normal and perturbed trials. Effect sizes were calculated using Cohen's d. A sample size was then estimated (significance level = 0.05, power = 0.8). Due to a small sample size, continuous data were compared using statistical non-parametric mapping analysis in MATLAB (spm1d) [33], [34]. A paired t-test was used to compare perturbed situations versus normal gait.

### III. RESULTS

#### A. Perturbation characterization

Perturbation occurrence and duration are provided Table 1. For all situations, perturbation occurred before 10% GC. Regardless of the perturbation type, perturbation duration was 0.70 ± 0.03 s (acceleration = 3 m.s⁻²) and 0.55 ± 0.02 s (acceleration = 10 m.s⁻²).

<table><caption>TABLE I. PERTURBATION CHARACTERIZATION (MEAN ± SD)</caption><thead><tr><th>Type</th><th>Acceleration [m.s<sup>-2</sup>]</th><th>Perturbation duration [s]</th><th>Perturbation occurrence [s]</th><th>Perturbation occurrence [%GC]</th></tr></thead><tbody><tr><td rowspan="2">Slip</td><td>10</td><td>0.56 (0.02)</td><td>0.06 (0.04)</td><td>6 (5)</td></tr><tr><td>3</td><td>0.71 (0.03)</td><td>0.08 (0.05)</td><td>9 (5)</td></tr><tr><td rowspan="2">Trip</td><td>10</td><td>0.55 (0.01)</td><td>0.06 (0.05)</td><td>6 (5)</td></tr><tr><td>3</td><td>0.68 (0.01)</td><td>0.09 (0.04)</td><td>9 (6)</td></tr></tbody></table>

#### B. Distance between the BCoM and the minimal moment axis ($d_{BCoM-MMA}$)

Mean and maximum values of the norm of $d_{BCoM-MMA}$ are provided in Table II. Paired t-test revealed significant differences between normal and slip trials for the mean $d_{BCoM-MMA}$ (10 m.s⁻¹: $p<0.001$, Cohen's d: -2.03, sample size: 5). It also showed significant differences for the maximum $d_{BCoM-MMA}$ (10 m.s⁻¹: $p<0.001$, Cohen's d: -2.31, sample size: 4). Paired t-test also showed significant differences between normal and trip trials for the mean $d_{BCoM-MMA}$ (10 m.s⁻¹: $p<0.001$, Cohen's d: -2.06, sample size: 5). Significant differences were also observed for the maximum $d_{BCoM-MMA}$ (10 m.s⁻¹: $p<0.001$, Cohen's d: -2.06, sample size: 5; 3 m.s⁻¹: $p<0.001$, Cohen's d: -2.00, sample size: 7).

The evolution of the norm of $d_{BCoM-MMA}$ is presented in Fig. 2. A difference of pattern is visible between the perturbed and normal situations, especially for higher accelerations (Fig. 2., top and bottom right). No statistical differences have been observed during the perturbation.

<table><caption>TABLE II. DISCRETE VALUES OF THE NORM OF $D_{BCoM-MMA}$ (MEAN ± SD)</caption><thead><tr><th>Type</th><th>Acceleration [m.s<sup>-2</sup>]</th><th>Mean $d_{BCoM-MMA}$ [mm]</th><th>Max $d_{BCoM-MMA}$ [mm]</th></tr></thead><tbody><tr><td rowspan="2">Normal</td><td>N/A</td><td>43.9 (4.7)</td><td>79.8 (6.2)</td></tr><tr><td>10</td><td>50.9 (5.8)***</td><td>320.0 (106.1)***</td></tr><tr><td rowspan="2">Slip</td><td>3</td><td>46.1 (6.2)</td><td>205.9 (204.3)</td></tr><tr><td>10</td><td>49.9 (6.3)***</td><td>160.8 (34.8)***</td></tr><tr><td rowspan="2">Trip</td><td>3</td><td>45.2 (5.6)</td><td>99.5 (11.6)***</td></tr></tbody></table>

### IV. DISCUSSION

This study aimed to validate the sensitivity of a mechanical parameter for quantifying walking stability in response to external disturbances induced by an instrumented treadmill.

The present protocol enabled to generate a disturbance with minimal delay between the command sent by the LabView interface and the actual response of the treadmill. The actual duration of the disturbance perceived by each participant aligns with other reported in the literature [21], [32], [35], [36], even though our duration falls within the higher range.

The $d_{BCoM-MMA}$ had not yet been used in situations involving perturbed walking. A few articles have estimated it in different situations, such as walking in a straight line, step initiation, and walking on inclined blocks [24], [25], [26], [27]. Our average values during the normal walk are consistent with those obtained in a non-pathological population (i.e., 55.1 ± 6.2 mm [24]; 37 ± 4.5 mm [26]). However, they remain lower than those reported by [27] (i.e., 70 ± 9 mm). These differences cannot be attributed to the calculation of the BCoM position since all these studies use the same model (i.e., [28]) and a full-body marker set. The differences may then be related to the various methods of measuring ground reaction forces and moments. Indeed, in the published studies, these were assessed using force platforms anchored to the ground, while in the present study, they are integrated into a treadmill. These differences could also be explained by age and the number of participants. Studying this parameter in a larger cohort would establish reference values for both non-perturbed and perturbed walking.

To date, only one study has investigated the effect of perturbed walking on this parameter. Bailly et al. [24] asked subjects to walk on inclined blocks at spontaneous and fast speeds. Just like our results, the index increases with the integration of a more complex and unstable situation. No significant differences were found on the curves using statistical parametric mapping. This could particularly be due to the small sample size, or outliers. This method presents the main drawback regarding sensitivity (i.e., ability to detect a true effect) [37]. A central assumption in statistical parametric mapping is the assumption that trajectories have both been smoothed and normalized (e.g., temporally) [34]. This was not the case in our study, since we centered data at a heel strike, and looked at the evolution of the parameter over time. We did not normalize gait cycles as the perturbed one was usually shorter than non-perturbed ones. We also faced specific responses that were different from traditional gait cycles (i.e., HS was not always followed by a HS on the opposite side).

The proposed parameter seems to be sensitive to external disturbances, to a certain extent, during walking. However, thresholds which can be used as an abnormal instability signature are still needed. To identify such thresholds, it could be relevant to have experimental assessment of the parameter during actual falls. As ethical considerations must be taken into account, we could not simulate this in the laboratory with real participants. An approach could be to use humanoid robots, that are also prone to falls. This parameter could also be interesting in robotics to better optimize motion generation and control.

While the perturbation characterization method enabled us to obtain an *a posteriori* estimation, this lacks of precision. A direct evaluation of belt velocity would provide a more accurate belt speed estimation. This work present other limitations, such as a low number of individuals. As this is an

<footnote>a. GC: gait cycle. Perturbation occurrence describes the timing after heel strike.</footnote>

<footnote>b. Significant differences with the normal walk (*: $p<0.05$, **: $p<0.01$, ***: $p<0.001$).</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 2. Evolution of the norm of the distance between the body center of mass and the minimal moment axis ($d_{BCOM-MMA}$) for slip (top) and trips (bottom). $d_{BCOM-MMA}$ computed during normal situation (black) is displayed along with perturbed situations (red = 10 m.s⁻², blue = 3 m.s⁻²). Vertical green lines represent the average start and end of the perturbation for the group. Significant differences between $d_{BCOM-MMA}$ under normal and perturbed conditions are highlighted in yellow. Trials are centered at a heel strike. For perturbation trials, 0 corresponds to the heel strike preceding the perturbed cycle.</figcaption></figure>

ongoing work, we aim at increasing the number of participants to determine baseline values of unperturbed gait. While treadmill enables to record longer bouts of walking, it is known to modify gait in comparison to overground walking [38]. Spatiotemporal parameters (i.e., stride length, step length) are shorter on the treadmill, while peak vertical ground reaction forces are altered (i.e., lower during push-off, higher minimum value) [38]. Our participants had a familiarization phase on the treadmill, but their gait patterns may have been altered as an attempt to increase gait stability [38]. Overground walking in laboratories is also different from real life settings. Developing systems that could measure this parameter in daily-living conditions is necessary. This would also enable to record perturbations that are closer to reality. For example, in our study, trips were delivered at heel strike, while they usually occur when the foot is in the swing phase.

## V. CONCLUSION

The norm of $d_{BCOM-MMA}$ showed a sensitivity in detecting external disturbances during treadmill walking. We are currently validating the use of this metric in biped robots. This could ease the determination of thresholds above which the fall would be inevitable. In the short term, the goal will be to (1) determine basal values for a healthy population, (2) identify the sensitivity delay of this parameter, defined as the time between the actual disturbance and when $d_{BCOM-MMA}$ values differ from baseline. On the long run, the objective

will be to develop a portable system to estimate this parameter.

## ACKNOWLEDGMENT

We thank volunteers who took part in this experiment. We also would like to thank Sylvain Persohn who helped us to build the LabView interface.

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