用可微分因子图与不变表示，精准预测乒乓球弹跳轨迹。
Learning Dynamics of a Ball with Differentiable Factor Graph and Roto-Translational Invariant Representations
- 结合可微分因子图与旋转变换不变特征，提升模型稳定性。
- 首跳后预测误差仅37.2毫米，次跳后71.5毫米，优于数据增强方法。
- 适合需要高精度物理建模的机器人运动规划场景。
动态环境中机器人需快速准确地建模物体运动以支持敏捷规划。在乒乓球等运动中，因空气动力学复杂、弹性行为及滑动/滚动摩擦难以建模，解析模型常无法准确预测带旋转球体的轨迹。尽管数据驱动方法前景广阔，但机器学习仍受限于对精确输入的依赖。本文提出一种端到端学习框架，联合训练动力学模型与因子图估计器。利用格拉姆-施密特（GS）过程提取旋转变换不变表示，进一步降低验证误差；同时设计含自乘旁路的网络结构以增强非线性。实验表明，该方法在首次触拍后顶点位置预测的均方根误差（RMSE）为37.2毫米（以球拍半径为单位），第二次触拍后为71.5毫米。
原文摘要 · Abstract (English)
Robots in dynamic environments need fast, accurate models of how objects move in their environments to support agile planning. In sports such as ping pong, analytical models often struggle to accurately predict ball trajectories with spins due to complex aerodynamics, elastic behaviors, and the challenges of modeling sliding and rolling friction. On the other hand, despite the promise of data-driven methods, machine learning struggles to make accurate, consistent predictions without precise input. In this paper, we propose an end-to-end learning framework that can jointly train a dynamics model and a factor graph estimator. Our approach leverages a Gram-Schmidt (GS) process to extract roto-translational invariant representations to improve the model performance, which can further reduce the validation error compared to data augmentation method. Additionally, we propose a network architecture that enhances nonlinearity by using self-multiplicative bypasses in the layer connections. By leveraging these novel methods, our proposed approach predicts the ball's position with an RMSE of 37.2 mm of the paddle radius at the apex after the first bounce, and 71.5 mm after the second bounce.
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