## 4 Discussion  
We obtained the actuator inputs needed to generate the load of walking motion during resistance training in a microgravity environment and the tracking results of state variables using the direct collocation optimization method. The state variables showed good tracking results, and the net joint moments calculated from the obtained results were similar to those of inverse dynamics at 1 g normal walking. Fiber length and muscle excitation were not included in the objective function but results equivalent to the target data were obtained. In addition, periodic inputs were obtained due to the periodicity constraint included in the actuator input. In the case of Type 1 assistance (Figure 2a), the actuation system was designed with the underlying intention to compensate for the external torque term, which is a decreasing term in the governing equation in reduced gravity condition. Therefore, the result was expected to be similar to that from GRF data for 1 g normal walking. As expected, the simulation results showed similar results to 1 g GRF data. The negative values observed in the \(F_{y}\) input corresponding to the swing phase (gait cycle during 80-95% in Figure 6b) may be to generate a force by the weight of the leg at 1 g walking under a microgravity condition. The torque in the z-direction (red dashed line in Figure 6c) is the torque produced by the GRF on the feet and is calculated using \(COP_{x}\times GRF_{y}\). Type 1 has two linear actuators and one torque actuator acting on the center of the soles. However, during normal walking, the center of pressure (CoP) of a sole moves towards the toes from the heel, and the resulting effect is compensated by the external torque input at a fixed position in the center of the sole. In Figure 6c, the results of the simulations and the calculated torque results have been similarly obtained, so it is possible to confirm that the effect produced by the movement of the COP, the point at which the GRF is applied, has been compensated by the \(\tau_{z}\) actuator. Figure 10 shows the torque input of the external actuators required to follow the state variables in 1 g normal walking using Type 2. Because Type 2 has actuators at the hip, knee, and ankle joints, it can be presumed that the external torque input will appear as the difference between the net joint torques obtained by performing inverse dynamics at 0 g and 1 g. Therefore, for comparison, the \"ID difference\" (red dashed lines) is shown as the difference in the net joint torques obtained by the inverse dynamics using the same kinematics data for the 1 g normal gait (1 g with GRF) and microgravity (0 g without the GRF). The knee and ankle assist (Figure 10b,c) show similar results as expected, but the hip shows relatively different tendency (Figure 10a). The potential reason for this discrepancy may be due to differences between the original and modified model. The original model was originally capable of tilt, \(x\) and \(y\) motions in pelvis and lumbar flexion/extension. Thus, in inverse dynamics, \begin{table}
\begin{tabular}{c c c c c c} \hline  & & **25 Nodes** & **51 Nodes** & **75 Nodes** & **101 Nodes** \\ \hline \multirow{4}{*}{TYPE 1} & Total number of variables & 1800 & 3672 & 5400 & 7272 \\  & Number of iterations & 105 & 42 & 58 & 39 \\  & CPU time (s) & 6659 & 6600 & 14,138 & 14,277 \\  & Minimum objective & 0.013936 & 0.011556 & 0.0043457 & 0.002848 \\  & function value & & & & \\ \hline \multirow{4}{*}{TYPE 2} & Total number of variables & 1800 & 3672 & 5400 & 7272 \\  & Number of iterations & 45 & 44 & 32 & 24 \\  & CPU time (s) & 3172 & 6855 & 8171 & 10,725 \\  & Minimum objective & 0.012737 & 0.0068445 & 0.0031853 & 0.0032639 \\ \cline{1-1}  & function value & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Total number of variables, number of iterations, CPU time, minimum objective function value for the Type 1 and Type 2 simulations. there were forces or moments in the pelvis and lumbar acting in those directions.