Learning from Demonstrations over Riemannian Manifolds using Neural ODEs: An Extended Abstract
For robotics researchers, this work addresses the challenge of learning complex motions on curved spaces, but it is an incremental extension of existing methods with preliminary results.
This paper proposes a method for learning from demonstrations over Riemannian manifolds using neural ODEs to estimate geodesics, enabling natural motion generation for robot orientation and position data. Initial simulation experiments show reduced computational overhead compared to existing approaches.
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.