# Towards Online Estimation of Human Joint Muscular Torque with a Lower Limb Exoskeleton Robot
## 3 Experimental Results and Discussion
### Comparison Experiments  
We carried out comparison experiments with an independent motion analysis system (MAS) developed by Motion Analysis Corporation (Santa Rosa, CA, USA) to verify the overall accuracy and adaptability of the proposed method with different users in different motion. Five subjects were employed to wear the APAL exoskeleton, and 22 markers were attached to each subject. The subject performed squatting, running in place and jumping motions on the force plates of the MAS 30 times each. The hip, knee, and ankle joint torques of the human body were calculated by both the exoskeleton and the MAS independently. The performance of the proposed method was quantitatively evaluated by inspecting the root-mean-square error (RMSE) and the correlation coefficient (CC) of the torque from the exoskeleton and the MAS. Note that differences existed in the output JMT between the exoskeleton and the MAS due to the fact that the weight of the exoskeleton influences the actual JMT of the human body, but the MAS does not incorporate the existence and influence of the exoskeleton. The influence should be eliminated to make the outputs from the MAS and the exoskeleton comparable. The force (\(\mathbf{F}_{Exo}\)) is caused by the weight that the exoskeleton exerts onto the human trunk and transfers to the force plate of the MAS. We calculated this force using the inverse dynamics of the exoskeleton and subtracted it from the force plates' signals to avoid influencing the output of the MAS. We exerted a virtual inverted \(\mathbf{F}_{Exo}\) to the human trunk while calculating the JMT with our method. By doing this, the theoretical output of the two systems should be the same. Figure 13 demonstrates the difference in joint torques of subject 1 calculated by the exoskeleton and the MAS. Three kinds of motion were measured. The gait cycles of squatting and jumping motions start when the trunk begins moving downward, and end at stand straight. The gait cycles of each leg during running in place start and end at stance-to-swing shifting. The average torque curve of each joint under the three different types of motion appear to have preferable accordance. The error bands of the knee and ankle torques from the exoskeleton are slightly smaller than the MAS, which means our method obtains more stable torque values for the knee and ankle than the MAS. According to the RMES shown in Table 2, we can see three phenomenon: (1) The error of ankle torque is very small for all subjects in each motion, which means the FCF from contact force measurement shoe is quite accurate, and the neglect of inertial torque caused by ankle movement did not lead to a large error of ankle joints; (2) in general, the further the joint is from the foot plate, the larger the error appears, because of the cumulative error of the limb length and joint angle. The RMSE of the hip joint is larger than that of the knee joint, even though the maximal torque of hip is smaller, as shown in Figure 13, and the RMSE of the knee is also larger than that of the ankle. (3) Comparing the individual RMSE to the average RMSE of the five subjects, differences between individuals truly exist but are not significant--these differences are mainly caused by individual parameter error. If a more accurate result is required, individual parameters, such as limb length, mass, inertial, and the mass center of each limb, should be further investigated, like [PERSON]. [PERSON] et al. did in Ref. [PERSON] et al. (2018). Table 3 shows the CC of the torque from the exoskeleton and the MAS. The CC reveals the similarity between the torque curves. There are several phenomenon: (1) Most average CC values are larger than 0.81. The average CC values of the knees and ankles are all larger than 0.96; only the hip joint during running in place drops to 0.81. This means that the overall similarity is not too bad. (2) The standard deviation (SD) of CC of the five subjects are smaller than 0.091; in particular, those of knee and ankle joints are smaller than 0.04.