Unsupervised Physics-constrained Learning for Upper-limb Joint Angle Estimation From IMU Sensors

In Learning from demonstration, accurate and continuous capture of human upper-limb motion during actual work is essential for accumulating large-scale robot training data, and can also populate a digital twin with realistic human motion for safe pre-deployment policy validation. However, acquiring such data at scale using optical motion capture is impractical because of its cost and limited capture volume. This paper proposes a Physics-Informed Neural Network (PINN) that estimates shoulder and elbow joint angles using two IMUs attached to the upper arm and forearm, trained solely using physical constraints and no external ground-truth labels. The loss combines a quaternion/angle kinematics residual, a gravity-vector consistency term, an anatomical range-of-motion constraint, and an initial-alignment anchor, requiring no ground-truth trajectory. Training uses unlabeled IMU data; a limited set of encoder-based angle references from a mechanical device is reserved exclusively for evaluation. Experiments using real IMU data show the proposed label-free method outperforms raw gyroscope integration and, on a slow repetitive motion trial, even outperforms a supervised PINN trained with the same encoder labels, while also revealing a gap in generalization when the model is asked to extrapolate beyond its training window.