Sensor fusion for estimating joint kinematics and kinetics of biomechanical systems

Abstract

The study of human motion consists of the analysis of kinematics, dealing with joint angles, velocities and accelerations, and kinetics, which deals with joint torques and interaction forces. Traditionally, kinematics and kinetics are estimated from optical marker data and sometimes measured interaction forces. Inertial measurement units (IMUs) were introduced as a low cost alternative that makes measurements outside the laboratory possible. Measurements are often used in a loosely coupled combination of marker-based inverse kinematics (IK) or orientation-based inverse kinematics (OBIK) and inverse dynamics (ID). The orientations for OBIK are first estimated from IMU data. Recently, tightly coupled estimation methods based on nonlinear state space models have been introduced for both sensor modalities to improve accuracy. Sensor fusion of marker and IMU data is a relatively unexplored area of research. Markers provide a measurement on the position level whereas IMUs measure on the velocity and acceleration levels. Fusing the two sensor modalities is hypothesized to result in the most accurate estimation of kinematics and kinetics. The objective of this thesis is to investigate the effects of the sensor modality and the estimation method on the accuracy of estimated kinematics and kinetics. An iterated extended Kalman filter (IEKF) was developed which estimates joint angles, velocities and torques using any combination of marker data, IMU data and measured interaction forces. To validate the system with respect to ground truth, two experiments (fast motion and interaction force) were carried out on a robot equipped with all three sensor types. For comparison, IK, OBIK and a marker/IMU-based kinematic extended Kalman filter (EKF) were used together with ID to estimate kinematics and kinetics as well. The IEKFs estimated joint angles with a root mean square error (RMSE) between 0.33◦ (markers and interaction forces only) and 1.58◦ (IMUs only, fast motion). The marker-based IEKF and the IMU-based IEKF outperformed IK and OBIK respectively in both experiments. The IMU-based IEKF improved joint velocity RMSE from 4.13 deg/s to 1.10 deg/s in the fast motion experiment. Sharp peaks in the joint torque signal were only estimated accurately using IMU data directly. The marker/IMU IEKF was the only method that estimated joint angles, velocities and torques with RMSEs below 1◦ , 1.5 deg/s and 1.5 Nm respectively in both experiments. It is concluded that using IMU data in a tightly coupled system improves joint velocity and torque estimation. Assuming accurate sensor registration and no soft tissue artifacts, a tightly coupled IMU-only method can be sufficiently accurate in practice.