## 1 Introduction
The dynamic optimization is a method that finds the optimal solution for the entire motion cycle by considering muscle contraction dynamics. Static optimization solves the optimization problem for each divided moment of the entire motion cycle without considering muscle contraction dynamics [18]. Data tracking simulation aims to predict muscle force, for which static optimization is used with inverse dynamics [19]. In addition, the computed muscle control (CMC) method that uses both static optimization and forward dynamics is used to obtain muscle excitation [20]. In predictive simulation (or optimal control), optimization and forward dynamics are used to obtain muscle excitations and corresponding actions to maximize or minimize the objective function, and integration is required over time [19]. As a method for solving the optimal control problem numerically, direct shooting, which uses the control variables as the design variables [21; 22], and direct collocation, which optimizes the state and control variables [14; 23; 24], are widely used [25]. With a good initial guess, it is known that direct collocation is superior to the shooting method in terms of computational performance, which is approximately 100 to 250 times better when reaching the same solution [14]. Direct collocation can be used not only for predictive simulation but also for solving data tracking problems [13]. The human musculoskeletal system, which consists of muscles and bones, can be represented by a system that is driven by the governing equations of the muscle excitation--contraction dynamics, musculotendon dynamics, musculoskeletal dynamics, and skeletal dynamics [26]. It is possible to model the musculoskeletal system and perform simulations considering these governing equations by using software such as OpenSim [27], Anybody, and SIMM. OpenSim, which is free software, providesan interface with other software via the OpenSim application programming interface (API). It allows the human models provided by OpenSim to be accessed from external programs, which adopt other programming languages such as MATLAB and Python. This feature can be exploited, not only in data tracking simulation that relies on experimental data, but also for dynamic optimization, which enables predictive simulation that incorporates muscle contraction dynamics. Related simulation studies that feature a combined use of MATLAB and OpenSim include predictive simulation using a dynamic optimization method [14; 28] and data tracking simulation of a 3-D walking motion [13]. Studies on the control inputs required when external actuator forces or torques are applied to a human body include CMC-based simulation, which yields the optimal locations of the external actuators and their assistive torques to minimize the metabolic cost of a human body. This is done while tracking the kinematics data of running under loading conditions [29]. A similar study was also performed using a unidirectional actuator under the load gait condition [30]. In the present study, the objective of the simulation is to obtain the control input of an external actuator to allow the musculoskeletal model to track the state variables generated during a 1 g normal gait in a microgravity environment. The reason for selecting walking motion as the target motion is that it is not only one of the motions included in the exercise routine during long-term space flight, but is also advantageous to verify the results as it is relatively easy to access experimental data compared to other movements. In order to achieve our research goals, we propose two actuating methods to compensate for the changes in the governing equation of the human musculoskeletal system due to the reduction in gravitational force. Second, for the proposed actuating methods, the control input required to track the state variables generated in a 1 g normal gait is obtained. We used OpenSim (version 3.3) and MATLAB with OPTI Toolbox, which provides the IPOPT solver for solving large-scale optimization problems [31].