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In this project, I make use of different use of the objective function in CMC in order to find optimal input force.
- CMC procedure contains static optimization process, and it tries to minimize the cost function J which can be represented as
- When we add active actuators on OpenSim Model, the activation term in cost function becomes
- Where X_muscle is muscle control and X_actuator is actuator control. X_actuator is part of activation state, and it is also adjusted after the optimization process.
- Now, if we diminish the influnece of X_actuator on J, and run CMC, the optimizer tries to find X_actuator in order to minimize muscle activation.
- We know that minimizing muscle activation correponds to minimizing metabolic cost, so we can we can say that the actuator input force resulted from CMC after diminishing the influence of X_actuator is the optimal actuator input for most efficient metabolic reduction.
- Muscle force is constructed by the equation
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- And if we assign large value of maximum force to each actuator, then actuator control x_actuator decreases, so that the influence of actuator to J is decreases.
- Using this methodology, I could find an optimal input for each actuator, and also see the metabolic cost reduction after active actuators are added to a model.
Result & Discussion
Metabolic cost change when active actuators are added to model
First, I investigated how much metabolic cost is reduced when active actuators are added to a model, and optimal input force is applied to actuators. I did simulation for both loaded and unloaded walking cases, and I compared the influence of hip actuator and ankle actuator to metabolic cost reduction.
I assigned 10,000N to maximum active actuator force in order to find optimal control input force through CMC.
| Loaded walking | Unloaded walking | ||||||||
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Loaded walking
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- Metabolic cost reduction when active actuators are added to loaded gait model
- Ankle actuator: 10.35%
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- Hip actuator: 6.62%
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- Metabolic cost reduction when active actuators are added to unloaded gait model
- Ankle actuator: 10.62%
- Hip actuator: 1.04%
I put together the metabolic cost changes in loaded gait case and unloaded walking case
The first thing to notice is that the- Things to notice
- The metabolic cost is much lower during unloaded walking than loaded walking. Loaded walking costs only 75% metabolic energy
In loaded walking case, ankle actuator reduces metabolic cost by 10%, while hip actuator reduces it by about 7%.
On the other hand, in unloaded walking case, ankle actuator reduces metabolic cost by 10%, while hip actuator reduces it by 1%.
- compared to loaded walking.
- Ankle actuator works better to reduce metabolic cost than hip actuator when we can apply optimal input force.
- Hip actuator is not assistive to unloaded gait.
Therefore, we can say that ankle actuator helps metabolic cost reduction better than hip actuator if we have an optimal actuator which has no maximum force limitation.
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Optimal actuator input
| Loaded walking | Unloaded walking | |
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| Ankle actuator |  |  |
| Hip actuator |  |  |
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