## 3 Experimental Results
### Evaluation of Reflex Control Model  
The VAF values of all five subjects vary with the change of time-increasing point, as displayed in Figure 7. The overall tendency can be broken into three parts. In the first part (from before 450 to 1000 ms), the values of VAF are above 90%. At the end of this part, values of VAF decrease. In the second part (from 500 ms to 1200 ms), the VAF values are within the range from 70% to 90%. In the third part (after 1200 ms), the values of VAF decrease continuously as the time increases. A one-way ANOVA test was performed on the three parts. The VAF values were collected from the six trials. As time points were different among trials, the following rule was used: the first part is collected from 200 ms before the time point at which angular velocity changes the direction; the second part is collected from 200 ms after the angular velocity direction change; the third part is collected from 200 ms before the end. Each part collects 20 points of VAF values for each trial. The results are depicted in Figure 8. For all five subjects, since \(p\) values are smaller than 0.01, it can be inferred that the aforementioned three parts are significantly different. Given the root mean square error (RMSE) between prediction and measured activations, the changing trend between the three parts shows that the reflex model fits the change in the first 450 to 1000 ms of calf muscle activation level well (RMSE around 0.03), as well as obtaining a fair result over a longer time period (RMSE from 0.03 to 0.08) and an unpromising result for the overall period (RMSE above 0.10). These experimental results may  
Figure 6: Activation ratio of SOL to GAS in calf control part. Red line is the mean value. Gray area is the standard deviation (SD). Subgraph (**A**) to (**E**) represents the results of subject A to E, respectively. indicate that reflex dominates the first 400 to 1000 ms, while more complicated control mechanisms may be involved as time increases. The variations of \(p_{a}\) and \(d_{a}\) of subject A in one trial are shown in Figure 9. At the early stage of this trial, values of \(p_{a}\) and \(d_{a}\) change rapidly at first, and subsequently remain stable when a sufficient amount of recorded data is applied. On the other hand, VAF decreases with the increase of time or the amount of recorded data (as shown in Figure 6). There is a tradeoff between VAF and stable reflex parameters. The time point at which VAF is above 90% and the reflex parameters are within a stable range is selected. In this paper, the period from the beginning of muscle activation to the selected time point is called the forepart of muscle activation. For four of the subjects, the time point is close to the time point at which the direction of joint angular velocity changes. For the left one, it is about 200-300 ms ahead of direction change. If we assume that calf muscle fiber length changes with the variation of ankle joint angle, this result will be consistent with the mechanism of stretch reflex. Muscle spindle senses the stretch motion of muscle fibers. When ankle joint angular velocity changing its direction or muscle fibers starting contraction, the spindle is not under a stretch condition, and the stretch reflex model is no longer suitable. Figure 8: Boxplot of the three parts from five subjects. All the \(p\) values (ANOVA) are much smaller than 0.01. Figure 7: VAF values of reflex prediction results. Each column represents one subject. The red lines are the mean values of six trials. The gray areas represent maximum and minimum values. The reflex control model fitting results of forepart of subject A are shown in Figure 10, where the blue, red and yellow lines, respectively, are the recorded muscle activations, the prediction results with gains calculated from each trial, and the prediction results using the mean values of the gains. The VAF values of SOL and GAS between the red lines and the blue lines are \(94.8\pm 1.3\%\) and \(95.7\pm 1.8\%\), respectively.