## 3 Results  
All subjects walked on the treadmill at three different walking speeds, receiving a variety of perturbations while EMG signals were recorded (Figure 2). Four synergies were sufficient to satisfy the requirement for the overall reconstruction quality (\(\text{VAF}_{\text{overall}}\geq 85\%\)) for all left-inward-directed perturbation conditions (Figure 3). This requirement was satisfied for four synergies for all subjects for all conditions, apart from three exceptions in which \(\text{VAF}_{\text{overall}}\) was \(83.9\pm 4\%\). Four synergies were also sufficient to satisfy the requirement for \(\text{VAF}_{\text{muscle }k}\geq 75\%\), apart from 1% of the cases where \(\text{VAF}_{\text{muscle }k}\) was \(69.3\pm 6\%\). All four bilateral muscle synergies were typically composed of one unilateral muscle synergy for each leg (Figure 4). Unilateral muscle synergies were interchanged within the bilateral muscle synergies. Bilateral muscle synergy \(\text{W}_{1}\) was composed of unilateral muscle synergy \(\text{U}_{1}\) of the left leg and unilateral muscle synergy \(\text{U}_{3}\) of the right leg. Contrarily, bilateral muscle synergy \(\text{W}_{3}\) was composed of unilateral muscle synergy \(\text{U}_{3}\) and \(\text{U}_{1}\) of  
Figure 3: Overall Variation Accounted For (\(\text{VAF}_{\text{overall}}\)) with respect to the number of synergies extracted. The graph represents the VAF values for both unperturbed and left-inward perturbed walking for all combinations of walking speed and perturbation onset for all subjects. Figure 2: EMG signals for a selection of muscles of a representative subject for inward-directed perturbed (orange) and unperturbed (grey) (**a**) slow and (**b**) fast walking. Perturbation onset was 0% of the stance phase of the gait cycle. EMG signals are shown as the mean (solid line) \(\pm\) standard deviation (shaded area) of three trials. LSOL, left soleus; LTA, left tibialis anterior; LHAM, left hamstring; LADD, left hip adductor. the left and right leg, respectively. Bilateral muscle synergies \(W_{2}\) and \(W_{4}\) were composed similarly. Unilateral muscle synergy \(U_{1}\) was named the _push-off_ synergy, since its main contributors, the soleus, gastrocnemius medialis, and gastrocnemius lateralis, provide push-off in the terminal stance phase [5; 14]. Unilateral muscle synergy \(U_{2}\)was named the _initial swing_ synergy, since its main contributors, the tibialis anterior and rectus femoris, provide hip flexion to propel the leg forward, and knee extension to stop the knee flexion resulting from the earlier push-off during the initial swing. Unilateral muscle synergy \(U_{3}\) was named the _terminal swing_ synergy, since its major contributors, the tibialis anterior and hamstrings, slow down the swinging leg to prepare the leg for the next stance phase during the terminal swing phase. Unilateral muscle synergy \(U_{4}\) was named the _loading response_ synergy, since it was mostly active during early stance, where its main contributors, the rectus femoris, gluteus medius, and gluteus maximus provide stability. For a single representative subject, four muscle synergies for inward and outward perturbed fast walking were similar to those for unperturbed fast walking at 0.8 m/s, regardless of perturbation onset \(r_{p}\geq 0.623\) (see Figure 5 for outward-directed perturbations and Figure 6 for inward-directed perturbations). Furthermore, all four weighting curves for perturbed fast walking were similar to those for unperturbed fast walking as well. Contradictorily, only one or two muscle synergies per condition for perturbed slow walking were similar to those for unperturbed slow walking at 0.4 m/s. Additionally, even fewer weighting curves were similar for perturbed and unperturbed walking at the lowest walking speed. Figure 4: Muscle synergies and weighting curves for unperturbed walking at the highest walking speed for a representative subject. (**a**) Bilateral muscle synergies (\(\textbf{W}_{i}\)) were composed of two unilateral muscle synergies (\(U_{i}\)).