Estimating Relative Angle between two 6-axis Inertial Measurement Units (IMUs)

Inertial measurement units (IMUs) are used in biomechanical and clinical applications for quantifying joint kinematics. This study aimed to assist researchers who are new to IMUs and want to develop inexpensive IMU system to estimate the relative angle between IMUs, while understanding the effect of different computational algorithms for estimating angular kinematics. Thus, there were three sub-goals: 1) to present a low-cost and convenient IMU system utilizing two 6-axis IMUs for computing the relative angle between the two IMUs, 2) to examine seven methods for estimating the absolute angle of an IMU, and 3) to provide open-source code and working principles of these methods. The raw gyroscopic and accelereomter data were pre-processed. The seven methods included gyroscopic integration (GI), accelerometer inclination (AC), Complementary filter (CF), Kalman filter (KF), Digital Motion Processor (DMP, a proprietary algorithm)), Madgwick filter (MW), and Mahony filter (MH). An apparatus was designed to test nine conditions that computed angles for rotation about three axes (roll, pitch, yaw) and three movement speeds (20˚/s, 100˚/s, 200˚/s). Each trial lasted 25 minutes. The root mean squared error (RMSE) between the gold-standard value measured from the apparatus’ encoder and the value calculated from the computational method was determined for each of the seven methods. For roll and pitch, all methods accurately quantified angles (RMSE < 6˚) at all speeds. For yaw, all methods except AC and DMP displayed drift-free and RMSE < 6˚ at all speeds. Researchers can utilize appropriate methods based on their study’s duration, rotation axis, and speeds.