## Materials and Methods
### Minimum Moment Axis Computation  
Ground reaction forces and moments were measured by force plates and filtered using a 4 th order, zero phase-shift, low-pass Butterworth with a 15 Hz cut-off frequency.  
At any point \(A\), external mechanical actions applied on the foot can be represented by a force \(\mathbf{F}\) and a moment \(\mathbf{M_{A}}\). \(\mathbf{F}\) and \(\mathbf{M_{A}}\) define a moment field that can be expressed at any point \(B\) as:  
\[\mathbf{M_{B}}=\mathbf{M_{A}}+\mathbf{F}\mathbf{\times}\mathbf{P_{(A,B)}} \tag{1}\]  
where \(\mathbf{P_{(A,B)}}\) is the position of \(B\) with respect to \(A\).  
There exists one axis \(\Delta\) such that, at each point of this axis, the moment is collinear to \(\mathbf{F}\)[18]. This axis is called the central axis of the external contact wrench. We can demonstrate that the moment in space is minimum along this axis. Assume that point \(Q\in\Delta\). \(\Delta\) is computed as in [5]:  
\[\forall B\text{ in space, }\forall Q\in\Delta,\mathbf{P_{(B,Q)}}=\frac{\mathbf{F} \mathbf{\times}\mathbf{M_{B}}}{\left\|\mathbf{F}\right\|^{2}}+\lambda\mathbf{F},\quad\lambda \epsilon\mathbb{R} \tag{2}\]  
If we now assume that \(B\) is the COM:  
\[\forall Q\in\Delta,\quad\mathbf{P_{(COM,Q)}}=\frac{\mathbf{F}\mathbf{\times}\mathbf{M_{COM}} }{\left\|\mathbf{F}\right\|^{2}}+\lambda\mathbf{F},\quad\lambda\epsilon\mathbb{R} \tag{3}\]  
When \(\lambda=0\), Q is the orthogonal projection of the COM onto \(\Delta\) and the distance \(\left\|\mathbf{P_{(COM,Q)}}\right\|\) is the minimal distance between \(\Delta\) and the COM. The vector \(\mathbf{P_{(COM,Q)}}\) will be called \(\mathbf{d_{COM-\Delta}}\) hereafter:  
\[\mathbf{d_{COM-\Delta}}=\frac{\mathbf{F}\mathbf{\times}\mathbf{M_{COM}}}{\left\|\mathbf{F}\right\| ^{2}} \tag{4}\]  
From Equation (4), we compute the Euclidian norm of the distance from COM position and force platform data:  
\[\left\|\mathbf{d_{COM-\Delta}}\right\|=\frac{\left\|\mathbf{F}\mathbf{\times}\mathbf{M_{COM}} \right\|}{\left\|\mathbf{F}\right\|^{2}} \tag{5}\]Interestingly, it can be noted that this distance can also be linked to the angular momentum at the COM by considering the relation: \(\dot{\mathbf{h}}_{\mathbf{COM}}=\mathbf{M}_{\mathbf{COM}}\) where \(\dot{\mathbf{h}}_{\mathbf{COM}}\) is the derivative of the angular momentum. Thus:  
\[\mathbf{d}_{\mathbf{COM}-\Delta}=\frac{\left\|\dot{\mathbf{h}}_{\mathbf{COM}}\right\|\cdot\left\| \dot{\mathbf{s}}\mathbf{\theta}\right\|}{\left\|\mathbf{F}\right\|} \tag{6}\]  
With \(\theta\) is the angle between \(\mathbf{F}\) and \(\dot{\mathbf{h}}_{\mathbf{COM}}\).  
We project \(\mathbf{d}_{\mathbf{COM}-\Delta}\) in Equation (4) on the subject's anterior-posterior axis, medial-lateral axis, and vertical axis:  
\[\left[\begin{array}{c}d_{ML}\\ d_{AP}\\ d_{V}\end{array}\right]=\frac{1}{\left\|\mathbf{F}\right\|^{2}}\left[\begin{array}[ ]{c}F_{AP}\times M_{V}-F_{V}\times M_{AP}\\ F_{V}\times M_{ML}-F_{ML}\times M_{V}\\ F_{ML}\times M_{AP}-F_{AP}\times M_{ML}\end{array}\right] \tag{7}\]  
where \(d_{ML},\ d_{AP},\ d_{V}\) respectively refer to the medio-lateral, anterior-posterior and vertical component of \(\mathbf{d}_{\mathbf{COM}-\Delta}\).