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Here are the figures of sample simulation models. I modified the RRA-adjusted model to create several different types of models for comparison.
Loaded gait models
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The path actuator supporting plantarflexion is attached to the heel and tibia, and the path actuator supporting hip extension is attached to the backpack and femur. For simplicity, the loaded mass was added directly to the torso.
Unloaded gait models
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In this project, I make different use of the optimization process in CMC in order to optimize the control input force for active actuators.
CMC procedure is static optimization process, and it minimizes the cost function J which can be
represented asrepresented as
Mathblock J = \sum_{i=1}^{n_x} x_i^2 + \sum_{j=1}^{n_q} w_j \left( \ddot{q}_j\,^* - \ddot{q}_j \right)^2
When we add active actuators to an OpenSim model, the activation term in the cost function
becomesbecomes
Mathblock x = \begin{bmatrix} x_{\mathrm{muscle}} \\ x_{\mathrm{actuator}} \end{bmatrix}
where Xmuscle is muscle control and Xactuator is actuator control. As Xactuator is part of activation states, it is also adjusted after the optimization process.
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| Loaded walking | Unloaded walking | ||||||||
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- Metabolic cost reduction when active actuators are added to the loaded gait model:
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| Loaded walking | Unloaded walking | |
|---|---|---|
| Ankle actuator |   |   |
| Hip actuator |   |   |
Optimal input force for the ankle actuator:
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We can explain how the optimal actuation input for the ankle actuator helps loaded gait by investigating the change of plantarflexor muscle forces.
- The gastrocnemius muscle forces barely change.
- Other plantarflexor muscle forces, including soleus muscle forces, are significantly decreased.
- If we compare the active actuator input force with the sum of the baseline uniarticular forces, we can see that the active actuator force follows the sum of the baseline uniarticular muscle forces.
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- My initial guess was to saturate the optimal input force that I found earlier at 400 N. I generated an new input force which is identical to the optimal input force up to 400 N, and saturated once the optimal input force exceeded 400 N.
- The second input force I tried was a new result from my CMC simulations. The new CMC result was acquired by assigning 4000 N to the maximum actuation force and bounding the control input between 0 and 0.1. In other words,
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- by assigning 4000 N to the maximum actuation force and bounding the control input between 0 and 0.1. In other words,
| Mathblock |
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F_{\mathrm{actuator}}^{\mathrm{max}} = 400 N, \quad 0 \leq x_{\mathrm{actuator}} \leq 0.1 |
According to the formula Factuator = Factuatormax * Xactuator, the new CMC result also has a maximum force of 400 N. As Xactuator is bounded between 0 and 0.1 and Xmuscle is chosen between 0 and 1, the influence of Xactuator to the objective function of the CMC procedure is relatively lower than that of Xmuscle, so we can use this idea to create an optimal input for the ankle actuator when the maximum actuation force is limited.
When we compare the saturated optimal input and the result from the new CMC procedure, we find similarity. Now, let's compare the metabolic cost reduction when each control input is applied to ankle actuators.
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| Loaded walking | Unloaded walking |
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- Metabolic cost reduction when active actuators are added to loaded gait model:
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Now that we know both the ankle actuator and the hip actuator can reduce metabolic cost during loaded walking, a natural progression is to test actuators which can affect both ankle plantarflexion and hip extension. To reduce the number of actuators, I added single-degree-of-freedom biarticular actuators affecting ankle plantarflexion and hip extension to legs on both sides, and investigate the metabolic cost. The main idea in creating a biarticular actuator is to let the path actuator go through the axis of ankle joint rotation. I chose the attachment points of the ankle and hip actuators as the via points and end points of the biarticular actuator line, and also set the origin of the ankle joint rotation as one of the via points. By doing so, I created a biarticular actuator which combines the effects of the ankle and hip actuators.
Simulation result
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| Optimal input | Metabolic cost reduction |
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- Metabolic cost reduction when biarticular actuators are added to loaded gait is 3.12% from baseline. It is much lower than the reduction observed using either the ankle or hip actuator.
- Control input is complex, which makes it hard to realize.
- The biarticular actuator is not as effective as the uniarticular actuators in terms of metabolic cost reduction.
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