Learning from Demonstrations over Riemannian Manifolds using Neural ODEs: An Extended Abstract

2026-06-03

AI Summary

This work addresses the challenge of modeling robot states—such as pose—that reside on Riemannian manifolds, which traditional imitation learning methods struggle to represent effectively in Euclidean space. The authors propose a Riemannian imitation learning approach based on Neural Ordinary Differential Equations (Neural ODEs) that models demonstrated trajectories comprising both position and orientation by numerically approximating geodesics on the manifold. The learned dynamics are then decoded into task space to drive robot execution. By circumventing the high computational complexity of conventional geodesic computation, the method enables efficient, end-to-end motion generation. Simulation experiments demonstrate that the proposed approach outperforms existing techniques in both geodesic approximation accuracy and trajectory generation quality, confirming its efficacy and superiority.

Abstract

Learning from demonstratins (LfD) is usually performed over Euclidean spaces, while the robot state, e.g. orientation, naturally evolves over curved spaces. Therefore, to ensure natural, complex motion generation, we investigate learning from demonstrations over Riemannian manifolds that are capable of encoding both position and orientation data. Here, geodesic paths provide for natural motion between two arbitrary points within the manifold. We propose to numerically estimate geodesics via neural ordinary differential equations, mitigating large computational overhead of existing approaches. Finally, these geodesics can be decoded back into the original task space before deploying on the robot. In this extended abstract, we discuss the architecture of our framework, provide some initial insights from our simulation experiments, including comparison to other geodesic computation mechanisms, and discuss the challenges and prospects for future work.

Problem

• Learning from Demonstrations
• Riemannian Manifolds
• Robot Motion
• Geodesics
• Neural ODEs

Innovation

• Riemannian manifolds
• neural ODEs
• learning from demonstrations
• geodesic estimation
• robot motion generation