## 3 Results
### Actuation Type 1  
In the case of Type 1, the state tracking results closely tracked the target state variables regardless of the mesh density used in the simulation. The state variables that were included in the objective function, which are the generalized coordinates (Figure 3a-c), generalized speeds (Figure 3d-f), and muscle activation (Figure 4a-i), showed good tracking results for the gait cycle. The experimental EMG patterns during a natural walking speed of adults [39; 40] were added to (Figure 4) for comparison with the target muscle activations obtained from CMC. The EMG patterns were scaled to match the CMC results. All of the muscle activations had similar patterns with EMG, except for the bifemsh andilioposas muscles. The fiber length and muscle excitation, which were not included in the objective function in (Equation (1)), showed practically identical results to the target values (Figure 5).  
The assistive torques and forces were obtained as shown in (Figure 6). For comparison, GRF, which occurs during 1 g normal gait, are also shown (red dashed lines in Figure 6). Due to the periodicity constraints assigned to the actuators, the actuator inputs showed the same values at both ends (Figure 6). \(F_{x}\) showed peak force of 400 N around 55% and showed about 2 times magnitude difference from GRFx data. Except for that point, the entire curves are located in the range \(-\)100 N to 100 N (Figure 6a). The maximum force of \(F_{y}\) was about 1 BW and 1.3 BW at 13% and 50% of the walking cycle, which is similar to the peak force of GRFy (Figure 6b). The slopes in the 0-10% and 50-60% of the gait cycle were in good agreement with the GRF. The magnitude of the GRFy was positive in all sections, whereas \(F_{y}\) showed negative direction assistance at 90%. The assistive torque in the z-direction was significantly different from the ground reaction moment in the same direction (Figure 6c). The smoother control input curves were obtained as the mesh density increased. We can see that when using the smallest number of 25 nodes, the results are not smooth (Figure 6). Therefore, it is expected that the reliability of the results would be decreased significantly for node mesh smaller than 25.  
Figure 4: Tracking results of the muscle activation (Type 1). Tracking results of the muscle activation ((**(a–i)**, solid lines) are shown for the right limb compared to the objective tracking data (red dashed lines). The difference between the mesh densities is small. The shaded areas are surface EMG patterns obtained from natural speed walking in healthy adults [39, 40]. It is scaled to match the simulation data for comparison. See Supplementary Materials for results on the left limb (Figure S2).  
Figure 3: Tracking results of the generalized coordinates and generalized speeds (Type 1). Tracking results of the generalized coordinates ((**(a–c)**, solid lines) and generalized speeds ((**(d–f)**, solid lines) are shown for the right limb compared to the objective tracking data (red dashed lines). The difference between the mesh densities is small, and the results closely match the objective data for all the mesh densities. Hip flexion, knee extension, and ankle dorsiflexion are positive. See Supplementary Materials for the results of the left limb (Figure S1).