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Static Optimization is a method for estimating muscle activations and muscle forces that satisfy the positions, velocities, accelerations, and external forces (e.g., ground reaction forces) of a motion. The technique is called  "static" since calculations are performed at each time frame, without integrating the equations of motion between time steps. Because there is no integration, Static Optimization can be very fast and efficient, but it does ignore activation dynamics and tendon compliance. (See Hicks et al., (2015) for more details regarding this and similar modeling and simulation choices and their pros and cons.)  

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In Study 1 we added actuators to assist each coordinate of the model. However, we saw that the these reserve actuators contributed a significant amount of the total joint torque that we would prefer the muscles to provide. In this Study, you will reduce the strength of the reserve actuators and observe the resulting changes in reserve actuator torques and Gastrocnemius muscle activation and forces. 

The current actuators file has optimal forces of 100 N for each force actuator (i.e., residuals FX and FY) and optimal torques of 100 N-m for each coordinate actuatortorque actuator (i.e., residual MZ, and reserve coordinate actuators). When trying to minimize the sum of activations squared, the optimizer can use small activation values to these force and torque actuators generate large forces . In this case (optimal force = 100)or torques. For example, with an optimal torque of 100 N-m, an activation of 0.5 will generate a force torque of 50 N-m. If we change , instead, the optimal force to 1torque were 1 N-m, the optimizer must now use very high activations to produce any meaningful forcestorques. In this latter case (optimal force torque = 1) , an activation of 0.5 would only generate 0.5N. So 5 N-m, and an activation of 50 is necessary to generate 50 N-m of torque. Thus, when the optimal force is very low (~1 N or 1 N-m) the optimizer can still choose to use the reserve actuators when needed, but the cost is so high that it will only use them when neededrelative to the muscles that the optimizer will preferentially use muscles to generate joint torques and only use the reserve actuators when the muscles cannot generate sufficient torque.

<optimal_force>100</optimal_force>

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