# 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  
In this experiment, the user wearing the exoskeleton did ran in place with a stride frequency of approximately 2.8 Hz. The power unit of the exoskeleton was switched off and all joints were set free to avoid interference. The weight of the exoskeleton was assumed to be carried by the subject. The motion information of the human body was acquired by the embedded sensing system.The hip and knee JMTs were calculated by the controller of the exoskeleton and sent to a PC in real-time for recording and graphing. We had five subjects. Their parameters were calculated according to previous research [31; 32] and are listed in Table 1. Only subject 1 participated in this experiment. 1. The Posture of the Trunk Since we only studied the motion in the sagittal plane, just the pitch angle was required. The maximal sample frequency of the IMU is 100 Hz. For smoother IDA, a higher sample frequency, e.g., 1 kHz is required. So, a first-order-sample-and-hold, a linear interpolation, and a low-pass filter were adopted to deal with the original signal from the IMU. As shown in Figure 7, in each step of running in place, the trunk inclines forward and pitches slightly in the range of \((-20^{\circ},-16^{\circ})\). The original signal (\(\omega_{0}\)) looks like a step wave with steep edges after each sampling. This can cause mutation on the on pitch angular acceleration. After linear interpolation and filtering, a smooth and high sample frequency pitch angle (\(\omega_{2}\)) was acquired. 2. The Acceleration of the Hip Joints Figure 8 shows the acceleration on hip and knee joints in the sagittal plane. Both \(a_{LHx}\) and \(a_{RHx}\) vary around the zero axis in the range of \((-5\) m/s\({}^{2}\), \(5\) m/s\({}^{2})\), and \(a_{LHz}\) and \(a_{RHz}\) have a \(-\) 9.8 m/s\({}^{2}\) bias caused by gravity. \begin{table} \  
3. The Joint Kinematics Information Figure 9 shows the displacement of hydraulic cylinders and the angles of the hip and knee joints of the exoskeleton robot. The stroke range of the linear displacement sensor is (0 mm, 73 mm), corresponding to the knee joint angle range of (\(0^{\circ}\), \(135^{\circ}\)), and that of the hip joint of (\(-15^{\circ}\), \(150^{\circ}\)). During running in place, the hip and knee joint angles varied from \(38^{\circ}\) to \(65^{\circ}\) and from \(60^{\circ}\) to \(100^{\circ}\), respectively. The four joints did not reach the stroke limit. The lengths of the thighs and shanks of the exoskeleton were manually adjusted to be slightly larger than those of the user. This helps to avoid a dead point when the knee joint approaches \(0^{\circ}\). Doing this does not affect the motion mapping. Figure 10 shows the motion information of the human body. It can be seen that the joint angular velocity is relatively smooth, but sharp variations appear in the angular acceleration which are caused by the touchdown impact. Figure 8: Acceleration of hip joints: (**a**) left hip joint; (**b**) right hip joint. Figure 10: Joint information of the human lower limbs. Figure 9: Joint information of the exoskeleton robot. (4) The Foot Contact Forces  
The signals from the sensor and the resultant force are shown in Figure 11. During running in place, the toe touches the ground first, so a force (\(F_{z3}\)) below the toe is generated. The appearance of \(F_{z1}\) from the heel indicates that the entire foot is on the ground. The following is the push-off process. The resultant force in the vertical direction is significantly higher than the user's gravity, pushing the body to accelerate upwards and leap. Until the overall toe force drops to zero, the foot leaves the ground and switches to the swing phase. At this stage, FCF should be zero, but since the power system of the exoskeleton is not switched on, the gravity of the exoskeleton leg poses a negative vertical force on the human foot. This demonstrates that the force measurement shoe is adaptable to different foot contact states.