## 4 Discussion
Resistance training in microgravity requires the body to be fixed, so the pelvis is fixed in the modified model to reflect it. As a result, the forces and moments mentioned above can no longer act on the corresponding body segment. However, the goal of the simulation was to track the kinematics data and muscle related state variables obtained from the original model at 1 g normal walking in the modified model. To achieve this, the forces and moments that existed in the original model must be compensated by the external actuators in the modified model, which is why this difference appears to have occurred. Figure 11 shows the net joint torques by the muscles calculated from the state variables, as obtained from the Type 1 simulation, and the joint torques acquired by inverse dynamics using the 1 g gait data. The movement of the ankle joint (solid lines in Figure 11c) shows a tendency opposite to that of the Type 1 torque actuator (solid lines in Figure 6c). Therefore, it can be regarded that the torque actuator is mainly used for generating a resistance torque against the ankle torque. Figure 12 displays the net joint torques of the HKA joints calculated from the state variables obtained by the Type 2 simulation. For comparison, the net joint torques of the 1 g normal gait are shown as red dashed lines, and the results are in good agreement. Figure 11: Net joint torques by the muscles (Type 1). Using the state variables obtained by the optimization for Type 1, the net joint torques caused by the muscles acting on the right lower limb joints are shown for the gait cycle ((**a–c**), solid lines). In addition, the joint torque data obtained with inverse dynamics at 1 g normal walking are also shown (red dashed lines). The results of the optimization and inverse dynamics are well matched during the gait cycle. Hip flexion, knee extension, and ankle dorsiflexion are positive. See Supplementary Materials for results on the left limb (Figure S9). The direct collocation method divides state and control variables by the number of node meshes. In Table 1, it can be seen that the total number of variables ranges from 1800 to 7272 depending on the number of node meshes used. In addition, the number of iterations can be seen to decrease gradually. This may be because the grid refinement method allowed the simulation to start closer to the optimal solution as the node mesh increased. The most computationally expensive process during simulation is the numerical computation of constraint Jacobian. Therefore, as the mesh density increases, more CPU time was required (CPU time (s), Table 1). The minimum objective function value means the sum of the integral of the squared error between the target tracking data and the optimal solution (Equation (1)). This value tends to get smaller as a large number of node meshes are used. For the 101 nodes in TYPE 2 (Table 1), this value increased slightly, which will be reduced by setting small convergence criteria. In this study, the actuator position and corresponding control input, which can be used in the design of a LEAD for resistance training in microgravity, were obtained by an optimization method using OpenSim and MATLAB. We calculated all the state variables from the 1 g normal gait data and obtained the position and control input of the external actuator to track the state variables. We did not perform the muscle force predictions from the experimental data similar to the previously performed data tracking methods. Comparing the existing data tracking method [13] with the method used in this study, there is a similarity in that it tracks data obtained during movement. However, there is a difference in that the objective is not to conduct muscle force prediction based on the human walking strategy such as metabolic cost minimization. One of the main goals is to obtain the actuator input for tracking.