# Towards Online Estimation of Human Joint Muscular Torque with a Lower Limb Exoskeleton Robot
## 3 Experimental Results and Discussion
### Motion Data Sampling and JMT Estimation
It can measure the human FCF in both the stance and the swing phases. 5 JMT estimation  
After all required parameters and variables for solving the human inverse dynamics equation were obtained, the mass-induced torques at the hip and knee joints \(\tau_{T1}\) and \(\tau_{S1}\) were derived via Equation (7), as shown in Figure 12a. The FCF-induced torques (\(\tau_{T2}\) and \(\tau_{S2}\)) were derived via Equation (8), as shown in Figure 12b. The resultant JMT (\(\tau_{T}\)) was calculated via Equation (9), as shown in Figure 12c. In Figure 12c, LST means the left leg is in stance phase, LSW means the left leg is in swing phase, R means the right leg, and DST means both the left and the right legs are in the stance phase. As shown in Figure 12a, the left hip torque drops to \(-7.3\) Nm in the stance phase and rises up to about \(40\) Nm just after the DST. It again drops to \(-12.3\) Nm in the middle of swing phase, and rises up to about \(51\) Nm before the left leg enters the stance phase. The trend of the right hip torque is similar to the left one. The knee torques are significantly smaller than the hip torque, because the knee only drives the shank and foot, but the hip takes the entire mass of the leg. The amplitudes of mass-induced JMT show no significant difference between the swing and the stance phase. The FCF-induced torque shown in Figure 12b is significantly larger than the mass-induced torque. All FCF-induced JMT in swing phase are very small. However, in the stance phase, the peak of the hip torques reach up to \(90\) Nm, while the peak of the knee torques rise up to about \(270\) Nm. Unlike the mass-induced torques, the knee torques are larger than the hip torques. Most of the time, FCF-induced hip and knee torques during running in place are positive because the knees usually bend during stance phase and the upper body leans forward. The total torques are combinations of the mass-induced torques and the FCF-induced torques. Their amplitudes and curves are close to the FCF-induced torques, which indicates that the FCF-induced torques are the major parts. The trend of  
Figure 11: (**a**) Force signals from each sensor on the left foot; (**b**) resultant force signals on the left foot; (**c**) force signals from each sensor on the right foot; (**d**) resultant force signals on the right foot. the right leg is similar to the left leg, but some local differences still exist due to the asymmetric nature of the two legs. From the results, we can declare that the proposed method successfully acquired the joint torque of the human body without any auxiliary devices. The integrated sensor system ensures its portability. Besides, there is no need to mount sensors on the human body. This makes it easier to wear and take off. The newly designed IDA process is also beneficial to the accuracy of torque estimation. The mass-induced joint torque is far smaller than the FCF-induced one. According to Equation (8), FCF and the joint angles are major factors that influence the FCF-induced torque. Since the FCF is directly measured by force sensors, and the joint angles are derived from the signals of the displacement sensors, errors caused by the differentiation and inaccuracy of the human model do not influence the major part of the final results. As shown in Figure 11, even though large impacts existed in the angular accelerations of the hip and knee joints, they did not cause noticeable mutations in the total torque curves. The torque curves were smooth and continuous, which allows an exoskeleton robot to  
Figure 12: Human joint muscular torque (JMT) calculated from running in place: (**a**) mass-induced JMT; (**b**) FCF-induced JMT; (**c**) total torque of the hip and knee JMT. provide compliant man-machine coordination, because whatever the foot contact status changes into, no switching of dynamic equations is required; thus, there is no sudden change in the output.