A Universal Model Combining Differential Equations and Neural Networks for Ball Trajectory Prediction

This paper presents a data driven universal ball trajectory prediction method integrated with physics equations. Existing methods are designed for specific ball types and struggle to generalize. This challenge arises from three key factors. First, learning-based models require large datasets but suffer from accuracy drops in unseen scenarios. Second, physics-based models rely on complex formulas and detailed inputs, yet accurately obtaining ball states, such as spin, is often impractical. Third, integrating physical principles with neural networks to achieve high accuracy, fast inference, and strong generalization remains difficult. To address these issues, we propose an innovative approach that incorporates physics-based equations and neural networks. We first derive three generalized physical formulas. Then, using a neural network and observed trajectory points, we infer certain parameters while fitting the remaining ones. These formulas enable precise trajectory prediction with minimal training data: only a few dozen samples. Extensive experiments demonstrate our method superiority in generalization, real-time performance, and accuracy.

YO-CSA-T: A Real-time Badminton Tracking System Utilizing YOLO Based on Contextual and Spatial Attention

The 3D trajectory of a shuttlecock required for a badminton rally robot for human-robot competition demands real-time performance with high accuracy. However, the fast flight speed of the shuttlecock, along with various visual effects, and its tendency to blend with environmental elements, such as court lines and lighting, present challenges for rapid and accurate 2D detection. In this paper, we first propose the YO-CSA detection network, which optimizes and reconfigures the YOLOv8s model's backbone, neck, and head by incorporating contextual and spatial attention mechanisms to enhance model's ability in extracting and integrating both global and local features. Next, we integrate three major subtasks, detection, prediction, and compensation, into a real-time 3D shuttlecock trajectory detection system. Specifically, our system maps the 2D coordinate sequence extracted by YO-CSA into 3D space using stereo vision, then predicts the future 3D coordinates based on historical information, and re-projects them onto the left and right views to update the position constraints for 2D detection. Additionally, our system includes a compensation module to fill in missing intermediate frames, ensuring a more complete trajectory. We conduct extensive experiments on our own dataset to evaluate both YO-CSA's performance and system effectiveness. Experimental results show that YO-CSA achieves a high accuracy of 90.43% mAP@0.75, surpassing both YOLOv8s and YOLO11s. Our system performs excellently, maintaining a speed of over 130 fps across 12 test sequences.