Curling Stone Trajectory and Collision Prediction Using a Hybrid Model Integrating Physical Models and Machine Learning

This study proposes and evaluates a hybrid framework for predicting curling stone motion by combining physical models with machine learning. Motion capture data from a curling sheet were used to train modules for sliding trajectory prediction and post-impact collision prediction. These modules were connected in an integrated rollout from a single preprocessed-frame state 1 m before the tee line to predict resting position and in-play/out-of-play status. Huber regression was used for trajectory prediction and random forest regression for collision prediction, with hybrid variants learning residual corrections to physical-model outputs. The framework was evaluated using five-fold cross-validation. In trajectory prediction, ML and hybrid variants reduced velocity error relative to the default physical model, while the tuned physical model remained competitive for direction-angle estimation. In collision prediction, ML and hybrid models improved direction-angle and angular-velocity prediction over the perfectly elastic baseline. In the integrated simulation, 867 trials were evaluated after excluding 21 trials with both measured stones out of play. The hybrid rollout achieved the lowest stop-position MAE and SD for the colliding stone and, for the collided stone, an MAE comparable to that of the ML model with the lowest SD. These results show that residual correction of simple physics-based baselines improves local prediction and final-position stability.