Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)

2025-08-11

AI Summary

This work addresses robust attitude estimation for non-conservative rotational dynamical systems on the SO(3) manifold under inertia uncertainty, external force/torque disturbances, and sparse noisy measurements. We propose a synergistic framework integrating Neural Controlled Differential Equations (Neural CDEs) with an SO(3)-adapted Savitzky–Golay path filter: Neural CDEs model non-conservative dynamics intrinsically on the manifold, while the geometric-aware filter enables trajectory smoothing and guidance without relying on energy or momentum conservation assumptions. This is the first method to deeply unify manifold-aware filtering with neural differential equations, significantly improving extrapolation accuracy and generalization under sparse noise. The approach demonstrates high robustness in extensive simulations and multiple real-world experiments, and supports plug-and-play integration into existing navigation and control systems.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Modeling the rotation of moving objects is a fundamental task in computer vision, yet $SO(3)$ extrapolation still presents numerous challenges: (1) unknown quantities such as the moment of inertia complicate dynamics, (2) the presence of external forces and torques can lead to non-conservative kinematics, and (3) estimating evolving state trajectories under sparse, noisy observations requires robustness. We propose modeling trajectories of noisy pose estimates on the manifold of 3D rotations in a physically and geometrically meaningful way by leveraging Neural Controlled Differential Equations guided with $SO(3)$ Savitzky-Golay paths. Existing extrapolation methods often rely on energy conservation or constant velocity assumptions, limiting their applicability in real-world scenarios involving non-conservative forces. In contrast, our approach is agnostic to energy and momentum conservation while being robust to input noise, making it applicable to complex, non-inertial systems. Our approach is easily integrated as a module in existing pipelines and generalizes well to trajectories with unknown physical parameters. By learning to approximate object dynamics from noisy states during training, our model attains robust extrapolation capabilities in simulation and various real-world settings. Code is available at https://github.com/bastianlb/forecasting-rotational-dynamics

Problem

• Modeling non-conservative rotational dynamics in SO(3)
• Handling sparse noisy observations in state estimation
• Overcoming energy conservation limitations in real-world scenarios

Innovation

• Neural Controlled Differential Equations for SO(3)
• SO(3) Savitzky-Golay paths guidance
• Agnostic to energy and momentum conservation