Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations

TL;DR

This paper introduces a novel continuous-time method for forecasting object rotations on SO(3) using Neural Controlled Differential Equations guided by Savitzky-Golay paths, effectively handling noisy, sparse data and complex dynamics.

Contribution

It presents a new approach that models rotational dynamics on SO(3) with neural controlled differential equations, respecting geometric structure and improving long-term forecasting.

Findings

Outperforms existing methods on real-world data

Handles noisy and sparse sensor observations effectively

Learns general latent dynamical systems for rotations

Abstract

Tracking and forecasting the rotation of objects is fundamental in computer vision and robotics, yet SO(3) extrapolation remains challenging as (1) sensor observations can be noisy and sparse, (2) motion patterns can be governed by complex dynamics, and (3) application settings can demand long-term forecasting. This work proposes modeling continuous-time rotational object dynamics on $SO(3)$ using Neural Controlled Differential Equations guided by Savitzky-Golay paths. Unlike existing methods that rely on simplified motion assumptions, our method learns a general latent dynamical system of the underlying object trajectory while respecting the geometric structure of rotations. Experimental results on real-world data demonstrate compelling forecasting capabilities compared to existing approaches.