A Hybrid Ball Trajectory Prediction Method AcrossMultiple Ball Sports

Abstract

This paper proposes a real-time, generalizable trajectory prediction framework that integrates neural networks with physical modeling, applicable to various ball sports. Unlike existing methods that are tailored to specific ball types and lack scalability, our approach addresses two core challenges: (1) large aerodynamic and morphological differences across balls (e.g., shuttlecocks vs. table tennis balls), and (2) significant trajectory variation due to ball wear. To overcome these issues, we introduce a two-stage prediction pipeline. In <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Stage One</b>, we design <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BEPNet</b>, a neural network that predicts the robot's target point early in the flight, enabling timely motion. In <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Stage Two</b>, we first apply a fitting-prediction method to predict the ball's pre-bounce trajectory. Then, using the fitted trajectory, we estimate the post-bounce state (such as velocity) via a neural network named <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BounceNet</b>. Finally, the post-bounce trajectory is simulated using a simplified aerodynamic model. This hybrid approach leverages both data-driven and physics-based components to achieve accurate prediction, while mitigating the limitations of purely learning-based bounce modeling. We deploy the full system on a versatile robot and validate its effectiveness across multiple sports, including badminton, table tennis, pickleball, and tennis. Experiments confirm its strong accuracy, generality, and real-time performance. A video (including badminton, table tennis, pickleball and tennis) demonstration is available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://youtu.be/MH6kcMGMXxM</uri>