## 2 Materials and Methods
### UCM Implementation  
The UCM approach aims at testing the hypothesis that available DoFs, also referred to as _elemental variables_, covary across repetitions to minimize the variability of the controlled variable, namely _task performance_[10, 11, 16]. In the framework of this study, we used segmental angles rather than joint angles as _elemental variables_ according to the evidence that segmental angles covary during numerous walking-related tasks [17, 18, 19, 20, 21] while joint angles  
Figure 2: On the left panel, half (right side) body marker set is reported as follows: 1. middle point between posterior iliac spines; 2. anterior iliac spine; 3. prominence of the greater trochanter external surface; 4. lateral epicondyl of the femur; 5. medial epicondyl of the femur; 6. head of the fibula; 7. lateral malleolus; 8. and medial malleolus; 9. 5 th metatarsal head; 10. 1 st metatarsal head; 11. calcaneus; 12. marker rigidly attached to a wand over midfemur; 13. marker rigidly attached to a wand over midshaft of the tibia. On the right side, the 7-segments kinematical model is reported. Axes \(\mathrm{x_{lab}}\), \(\mathrm{y_{lab}}\), and \(\mathrm{z_{lab}}\) refer to the lab-related reference frame. do not [22], under the assumption of planar approximation of locomotion. To test the hypothesis that the redundant DoFs represent an adaptable source of solutions to ensure a stable MTC (i.e., _task performance_) across strides, the inter-stride variability of _elemental variables_ is split in two components: i. the former defines a domain of segmental orientations leading to the same MTC value across strides; ii. the latter defines an orthogonal domain accounting for all solutions that do modify the MTC across strides. When the variability of _elemental variables_ is mostly confined to the former domain, namely the uncontrolled manifold, it is possible to conclude that the orientation of lower limb segments is functionally organized across strides to minimize the MTC inter-stride variability (i.e., MTCSD). Noticeably, the average number of strides collected across subjects and trials was 25 \(\pm\) 2 in accordance with earlier findings [23]. The algorithm adopted to implement the UCM analysis resembles that reported in our previous works [12; 24]. Briefly, a 3D kinematics model of lower limbs, accounting for seven body segments (feet, shanks, thighs, and pelvis) and six spherical joints (hips, knees, and ankles) was developed, as shown in Figure 2. The location of each joint was estimated as follows: the ankle joint coincided with the middle point between medial and lateral malleolus; the knee joint coincided with the middle point between medial and lateral epicondyle of the femur; the hip joint coincided with the acetabulum whose location was computed as described elsewhere [25], based on the markers on anterior iliac spines and middle point between posterior iliac spines. The orientation of each body segment was estimated in terms of azimuth and elevation angles (spherical coordinates) from the \(x\)-axis of the lab-related reference frame. The trigonometric model relating _elemental variables_ (elevation and azimuth angles of lower limb body segments) and _task performance_, i.e., the MTC of the right foot, was developed according to the Equation (1):  
\[MTC=AH_{z}=\sum_{m=1}^{7}L_{m}\cdot cos(\varepsilon_{m})\cdot sin(\alpha_{m}) \tag{1}\]  
where:  
* \(AH_{z}\) coincides with the MTC;
* \(L_{m}\), \(\varepsilon_{m}\), and \(\alpha_{m}\) refer to length, elevation, and azimuth angles of the \(m\) body segment;
* \(m=1,2,\ldots,7\) refers to the ordered series of body segments, from the left foot to the right one. The Jacobian matrix (J) of the function in Equation (1), relating small changes in the elemental variables (i.e., \(\varepsilon_{1}\), \(\alpha_{1}\),..., \(\varepsilon_{m}\), and \(\alpha_{m}\)) to task performance (i.e., MTC), was hence computed.