Rapid and Inexpensive Inertia Tensor Estimation from a Single Object Throw

TL;DR

This work tackles the challenge of measuring a rigid body's inertia tensor and centre of gravity with minimal hardware by attaching a low-cost IMU and reaction wheel to the object and performing a vertical spinning throw. A dynamical model based on Euler's rotation dynamics yields a linear-in-parameters formulation that can be identified from single-throw data, while a two-configuration calibration procedure determines the wheel inertia and device CoG. Corrections via the parallel-axis theorem enable isolation of the object's inertia, and a CoG estimate is obtained from centripetal/ tangential accelerations during tumbling. Experiments and simulations show mean principal-inertia errors around 2% and principal-axis alignment within a few degrees, with CoG localization at sub-millimeter precision, making the method a practical, inexpensive alternative to traditional pendulum-based approaches.

Abstract

The inertia tensor is an important parameter in many engineering fields, but measuring it can be cumbersome and involve multiple experiments or accurate and expensive equipment. We propose a method to measure the moment of inertia tensor of a rigid body from a single spinning throw, by attaching a small and inexpensive stand-alone measurement device consisting of a gyroscope, accelerometer and a reaction wheel. The method includes a compensation for the increase of moment of inertia due to adding the measurement device to the body, and additionally obtains the location of the centre of gravity of the body as an intermediate result. Experiments performed with known rigid bodies show that the mean accuracy is around 2%.

Figures (6)

• Figure 1: We propose a simple measuring device and procedure to determine inertial properties.
• Figure 2: "Object" under test and rigidly attached measuring "Device". The body-frame $B$ is defined at the location of the IMU, as shown.
• Figure 3: Depiction of the method. Subprocedures on the diagonal, required inputs vertically above, outputs on the right.
• Figure 4: Overview of the experimental hardware.
• Figure 5: Simulation of the angular velocities, based on an initial condition at the dashed line, and the filtered flywheel rotation compared to measured and filtered angular velocities.