Learning Dynamics of a Ball with Differentiable Factor Graph and Roto-Translational Invariant Representations

2024-09-24

arXiv.org

AI Summary

Accurate and consistent trajectory prediction of fast-moving balls (e.g., in table tennis) remains challenging in high-speed dynamic environments due to complex aerodynamics, elastic impacts, and mixed friction effects. Method: This paper proposes an end-to-end differentiable dynamics learning framework. It introduces Gram–Schmidt orthogonalization to extract rotation- and translation-invariant representations; designs a self-multiplicative bypass network to enhance nonlinear modeling capacity; and jointly optimizes the dynamics model with a differentiable factor graph estimator. Contribution/Results: The approach achieves deep integration of physical plausibility and data-driven learning. Experiments on bounce apex localization show root-mean-square errors (RMSE) of 37.2 mm (normalized by racket radius) for the first bounce and 71.5 mm for the second—significantly outperforming data-augmentation baselines. These results validate the framework’s effectiveness and robustness in modeling intricate air resistance, elastic collisions, and hybrid friction dynamics.

Technology Category

• Search and Optimization: Learning to Search
• Intelligent Robots: State Estimation
• Computer Vision: Motion & Tracking

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Predicting ball trajectories with spins
• Improving dynamics model accuracy
• Enhancing nonlinearity in network architecture

Innovation

• Differentiable factor graph model
• Roto-translational invariant representations
• Self-multiplicative bypass architecture