# Wireless Epidermal Six-Axis Inertial Measurement Units for Real-Time Joint Angle Estimation
## 3 Results
### Performance Evaluation  
Performance evaluation was performed in order to estimate the joint angle using the fabricated device, and the specific signal processing procedure was as follows. First, using the six-axis inertial sensor, raw signals of the three-axis acceleration and the three-axis gyroscope were obtained. Then, the obtained three-axis acceleration signals were normalized and converted into the measured inertial direction. Next, it was necessary to account for any error in the value derived from the transformed measured inertial direction and the estimate of the gravitational direction. Since the error value of each data must be compensated using the acceleration and gyroscope data, the Mahony AHRS (Attitude and Heading Reference System) algorithm [23] was applied. The error value was reduced using the proportional and integral gains. The derived value was reduced through the proportional and integral gains, and then the quaternion was defined by calculating the value with the angular velocities from the three-axis gyroscope. As mentioned previously, the gold standard for position estimation is to use an optoelectronic system. However, in this paper, the implemented epidermal 6-axis IMU was evaluated through a comparison experiment with Wearn notch (Notch Interfaces, Inc., New York City, NY, USA), a commercial wearable IMU that has previously been used to estimate the position in the ambulatory environment. According to the data-sheet [24], Wearn notch is generally known to have an error value of about 1-2\({}^{\circ}\) of angular estimation, and is thus a device that meets the maximum 5\({}^{\circ}\) estimation accuracy proposed by the American Medical Association for motion analysis in clinical situations [25]. First, the Euler angle measurement results received from the Wearn notch and epidermal IMU were measured using the rotation plate as shown in Figure 5. Both the implemented epidermal IMU and Wearn notch were positioned at the center of the rotation plate, which was placed horizontally, and the Euler angles were compared according to the rotation which ranged from 0 to 90\({}^{\circ}\). Both devices were assessed by rotating them along the roll, pitch, and yaw axes, and each plot was plotted against the rotating and non-rotating axes. The two devices were measured separately, resulting in an offset in the time step. However, very similar waveforms were measured for the rotation axis, as shown in Figure 5a. The root-mean-square (RMS) errors of the epidermal IMU with respect to the Euler angle received from the Wearn notch were measured to be 1.41\({}^{\circ}\), 1.60\({}^{\circ}\), and 1.84\({}^{\circ}\) for the rotating roll, pitch, and yaw axes, respectively. In Figure 5b, the rotation angle estimation experiment was performed at the end of the rotation plate, approximately 30 cm from the center, using each device. This was a preliminary experiment for estimating the actual elbow joint angle, and the experiment was performed with the rotation plate set vertically. Similarly, the RMS error of the epidermal IMU for the Wearn notch was measured, with this experiment performed by setting up the devices in three different axial directions. As a result, the RMS error of the implemented device when rotating in the X-, Y-, and Z-axis directions were measured to be 1.94\({}^{\circ}\), 3.31\({}^{\circ}\), and 2.91\({}^{\circ}\), respectively. The results for the above experiments are summarized in Table 1. As shown in Table 1, the maximum angle difference for the non-rotation axis was measured for each experiment to verify the operation of the error compensation algorithm. As shown in Figure 6, the implemented wireless epidermal six-axis IMU was attached in order to estimate the precise joint angle of the forearm. The experiments were carried out using Wearnotch