![]() ![]() While the characteristic curves that define muscle forces are non-linear, muscle activations are the only design variables in the problem and appear linearly in the muscle-generated joint moment equations. One important property of static optimization is that the problem is linear in its design variables. In this lab, we will use the moment-matching approach, but think about how you would solve the acceleration-matching problem as you work on your code. Lastly, rather than matching muscle-generated moments to net joint moments from inverse dynamics, OpenSim's StaticOptimizationTool requires that joint accelerations generated from muscle forces match joint accelerations computed from motion data. However, OpenSim's implementation does not include passive muscle contributions when computing total muscle force, f^m. Typically, an activations-squared cost function ( p = 2) is used for most research applications. OpenSim uses a similar cost function where activation raised to a user-defined power is minimized. OpenSim's Static Optimization Tool is similar to the problem definition above (see How Static Optimization Works). Net joint moments are typically computed from inverse dynamics, and inverse kinematics is used to compute all muscle kinematic states. The muscle activations are the only problem "design variables", or the values that the optimizer can change to minimize the cost and satisfy the constraints. The labels "minimize" and "subject to" denote the problem cost function and constraints, respectively. We often describe this as the "muscle redundancy problem". We use the term "static" since no dynamics appear in the optimization problem: activation dynamics are ignored, tendons are assumed rigid, and multibody dynamics are prescribed via motion data. Most static optimization problems take the following form: Since there are more muscles than degrees-of-freedom in the human body, this problem is "non-unique" (i.e., many possible solutions exist), hence the need for optimization. The goal of static optimization is to solve for muscle activations that produce the dynamics of an observed motion. Learn how to write your own static optimization code.Become familiar with using the OpenSim API through MATLAB. ![]() Learn the basics of the static optimization problem, including OpenSim's implementation and alternative implementations.In this lab, you will write your own code to better understand the elements required to solve the static optimization problem, draw comparisons to OpenSim's implementation, and learn how extend the basic tool to fit new research applications. Despite its popularity, OpenSim's implementation of this method only permits one type of cost function and a fixed set of constraints, and therefore is only applicable to research questions that can accept these limitations. Static optimization is a widely used tool for estimating muscle activity due to its speed and ease-of-use, and many OpenSim users rely on the Static Optimization Tool as a key part of their simulation research pipelines. Methods for estimating muscle forces from experimental data are an essential part of the biomechanist's simulation toolkit. The tutorial below is designed for use with OpenSim version 4.0 and later. ![]()
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