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The next question we investigated is if we are given a single actuator, how should we allocate assistive moments across the exosuit to cause the greatest reduction in metabolic cost? We introduced a tradeoff parameter, alpha, to allow us to weight the assistance between multiple joints. 

Hip and Ankle

The first case we investigated is similar to the Quinlivan study in that we only assist at the ankle and hip. In this case, positive values of alpha means the hip flexion moment would be assisted more than the ankle plantar-flexion moment and vice-versa for negative values of alpha. In this problem we are optimizing for alpha and the exosuit activation over a range of maximum actuator forces. 

We found that instead of getting a bowl shaped curve for change in metabolic rate, the values plateau at larger peak assistive forces. This can be seen in the exosuit moment plots because all of the curves collapse on top of each other at the higher forces. 

Interestingly, we find that the optimized assistive hip moment exceeds the inverse dynamics moment. This means there were more benefits to assisting the ankle with this profile than there were costs associated with exceeding the hip moment .

Hip, Knee and Ankle

The next case we explored included adding an assistive moment at the knee. In the current device, the load path passes through the knee center. If we shifted the attachment point of the device at the ankle to increase the moment arm and assist more in ankle plantar-flexion, the load path would pass behind the knee and we would assist in knee flexion.  If we shifted the moment arm of the device at the hip to assist in more hip flexion the load path would pass in front of the knee center and we would assist in knee extension. This tradeoff is again captured with alpha.

We again see the metabolic reductions plateau at higher force values. The changes are overall larger because we are now assisting an extra joint. Looking at the assistive moments across the joints we now find that the optimizer is favoring the ankle over the hip. The knee and ankle moment are close to each other in timing so great metabolic savings could be achieved even though the profile no longer aligns well with the hip. This shows the importance of the timing between the assistive moments and joint moments from inverse dynamics. 

Limitations

One limitation is that the kinematics data was fixed for this study. The Quinlivan paper showed that ankle angle changed significantly with assistance level and this is not something we captured. The change in ankle angle observed in the study is shown below. Grey is the powered-off condition and purple, blue, green, and orange are the low, medium, high, and maximum conditions respectively.

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