2026-06-05原文2 min readUpdated: 2026-06-05

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

This paper proposes a novel method for learning from demonstrations (LfD) on Riemannian manifolds using neural ordinary differential equations (ODEs). While traditional LfD operates in Euclidean spaces, robot states like orientation naturally evolve on curved spaces. The method efficiently estimates geodesics via neural ODEs, enabling natural motion generation between arbitrary points on the manifold, and decodes the geodesics back to task space for robot deployment. Simulation experiments validate the framework's effectiveness.

SourcearXiv RoboticsAuthor: Diana Cuervo Espinosa, Mahathi Anand, Angela P. Schoellig

[2606.05422] Learning from Demonstrations over Riemannian Manifolds using Neural ODEs: An Extended Abstract

[Submitted on 3 Jun 2026]

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

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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.

Comments: 2 pages

Subjects:

Robotics (cs.RO)

Cite as: arXiv:2606.05422 [cs.RO]

(or arXiv:2606.05422v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2606.05422

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Mahathi Anand [view email] [v1] Wed, 3 Jun 2026 20:38:47 UTC (716 KB)

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