## 3 Results
### Muscle Synergies  
Four synergies were required to reconstruct muscle activations during walking without the Ekso: (3.6 _mean_\(\pm\) 1.2 std). When walking with the Ekso, the number of synergies was (_mean_\(\pm\) std): B-NA = 3.87 \(\pm\) 0.99; B-FA = 3.75 \(\pm\) 1.75; B-AA = 3.13 \(\pm\) 1.24; U-AA = 3.00 \(\pm\) 0.00; U-NA = 3.37 \(\pm\) 0.74. Notice that the total variability accounted for (Figure 7) based on the number of modules extracted by NNMF was lower for the first synergies when walking with the Ekso than when walking without the Ekso (\(p<0.01\)). Figure 7: Total variability accounted for (mean \(\pm\) se) based on the number of modules extracted by non-negative matrix factorization (NNMF) for all the investigated walking conditions (normal walking without the Ekso: NW; Ekso-assisted walking: B-NA, B-FA, B-AA, U-AA, U-NA). Colors indicate the different walking modalities: black for normal walking without the Ekso (NW); the other colors refer to walking with the Ekso with bilateral no assistance (B-NA, dark green), bilateral full assistance (B-FA, red), bilateral adaptive assistance (B-AA, dark blue), unilateral adaptive assistance (U-AA, light blue), and unilateral no assistance (U-NA, light green). To characterize and compare the synergies' composition and timing, we extracted four independent modules for all the subjects and walking conditions (Figure 8). _Synergy 1_ was due to the simultaneous activations of the ankle plantar flexors GM and SOL, and in all the walking conditions, it was mainly active between 20-60% of the gait cycle, in the late stance providing support to the body for the forward propulsion and for initiating the gait [34; 42]. _Synergy 2_ was dominated by TA, the ankle dorsiflexor. During normal walking without the Ekso, Synergy 2 was active at \(<\)20% and more in the second half (\(>\)50%) of the gait cycle, with a peak between 60-90%. These activations correspond to the muscle activity for ankle dorsiflexion during and immediately after the heel strike and during the early swing for supporting the ground clearance of the foot [34; 42]. When walking with the Ekso, the main peak of activation in all the conditions appeared delayed at about 10% of the gait cycle with respect to walking without the Ekso (\(p<0.001\), Figure 9). _Synergy 3_ was dominated by the knee extensors VM and RF, with the latter also being the knee abductor, and by the GLM, which determines the hip extension and abduction. This synergy was active mainly at the beginning and at the end of the gait cycle, contributing to weight acceptance in the early stance [34; 42]. Synergy 3 was quite similar across all the conditions, with and without the Ekso, with the main peak of activity at the end of the gait cycle that in most subjects was anticipated in about 10% in the conditions where participants were wearing the Ekso with respect to when they were not. This behavior reached the threshold for significance for the B-FA modality (\(p<0.001\), Figure 9). _Synergy 4_ was mainly characterized by the ST and BF activity. The activation of this synergy was completely different between walking with and without Ekso. Indeed, in the normal walking without the Ekso, synergy 4 was active at the beginning (\(<\)20% of the gait cycle) and at the end (\(>\)80%) of the gait cycle, i.e., during stance, contributing to stabilizing the body and flexing the knee, and during the middle/late swing, contributing at decelerating the leg [34; 42]. Instead, in all the Ekso walking modalities, synergy 4 was active only between 60-80% of the gait cycle (\(p<0.001\) in all intervals). Figure 8: Weights (**left panel**) and activation coefficients (**right panel**) of the four muscle synergies when normal walking without the Ekso and when walking with the Ekso: B-NA, B-FA, B-AA, U-AA, and U-NA.