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

TL;DR

This paper introduces a novel method for predicting the future orientations of moving objects in 3D space, effectively handling non-conservative forces and noisy data by leveraging neural differential equations on the rotation manifold.

Contribution

It proposes a physics-agnostic, noise-robust approach using Neural Controlled Differential Equations guided by SO(3) paths, improving extrapolation of rotational dynamics in complex scenarios.

Findings

Robust extrapolation in simulation and real-world data

Effective handling of non-conservative forces and noise

Generalizes to trajectories with unknown physical parameters

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