Assessing Angular Momentum, Kinetics, and Energetics of a Rigid Body Using a Single Inertial Measurement Unit

Angular momentum, kinetics, and energetics, including total mechanical energy and its rate of change in relation to power exchange, are important quantities when analyzing human motion in sports, physical labor, and rehabilitation. Inertial measurement units (IMU)-based motion capture (MOCAP) systems provide a portable solution for the ambulatory analysis of these quantities which optical MOCAP systems do not offer. Yet, evaluating IMU-based estimates of these quantities by referencing optical systems is limited by the fact that these systems only measure positions, not kinetic and energetic quantities. To evaluate the accuracy of an IMU-based method for estimating kinetic and energetic quantities without using any external reference, firstly, we propose an estimation method only using angular velocity and acceleration signals supplied by an IMU, and apply this to a single rigid body with known mass and inertia. Then, we propose a novel experimental validation method against physical conservation and action/reaction laws that apply during ballistic movements, using a suitably designed and reconfigurable rigid body with a structure of three orthogonal dumb-bells. The results demonstrated that we could estimate the angular momentum, kinetics, and energetics of a rigid body by only using angular velocity and acceleration signals of an IMU, and the estimation accuracy was well evaluated by the proposed validation method. However, the results showed that the errors in original IMU measurements under dynamic conditions especially concerning angular velocity, uncertainties in calculating rigid body parameters, and vibration propagation due to limited rigidity of tubes of the rigid body influenced the estimation accuracy.