Determining the acceleration field of a rigid body using three accelerometers and one gyroscope, with applications in mild traumatic brain injury

TL;DR

This paper introduces a novel algorithm to accurately reconstruct the full acceleration field of a rigid body using minimal sensors, improving injury prediction in sports and biomechanics by avoiding noisy differentiation and restrictive sensor placement.

Contribution

The paper presents a linear-equation-based method for reconstructing acceleration fields from three accelerometers and one gyroscope, avoiding complex optimization and differentiation.

Findings

Validated in soccer heading experiments with accurate acceleration prediction

Demonstrated robustness and flexibility in sensor placement

Applicable to injury prediction and biomechanical analysis

Abstract

Mild traumatic brain injury (mTBI) often results from violent head motion or impact. Most prevention strategies explicitly or implicitly rely on motion- or deformation-based injury criteria, both of which require accurate measurements of head motion. We present an algorithm for reconstructing the full acceleration field of a rigid body from measurements obtained by three tri-axial accelerometers and one tri-axial gyroscope. Unlike traditional gyroscope-based methods, which require numerically differentiating noisy angular velocity data, or gyroscope-free methods, which may impose restrictive sensor placement or involve nonlinear optimization, the proposed algorithm recovers angular acceleration and translational acceleration by solving a set of linear equations derived from rigid body kinematics. In the proposed method, the only constraint on sensor placement is that the accelerometers must be non-collinear. We validated the algorithm in controlled soccer heading experiments, demonstrating accurate prediction of accelerations at unsensed locations across trials. The proposed algorithm provides a robust, flexible, and efficient tool for reconstructing rigid body motion, with direct applications in contact sports, robotics, and biomechanical injury prediction.