LieSpline-DP: Lie-Group B-Spline Diffusion Policy for Smooth Robot Manipulation

Abstract:Diffusion Policy (DP) is a powerful Learning from Demonstration (LfD) method for robotic manipulation, yet it suffers from discontinuous and non-smooth trajectories. Spline-based action representations promote smooth motion within individual action chunks, but existing spline-based methods neither guarantee cross-chunk $C^2$ continuity nor account for the group structure of $\mathrm{SE}(3)$. We therefore propose LieSpline-DP, a Lie-group B-spline diffusion policy that generates end-effector trajectories directly on $\mathrm{SE}(3)$ and couples consecutive plans by sharing their boundary control poses, ensuring $C^2$ continuity throughout the entire planned trajectory. Across three real-robot tasks, LieSpline-DP produces lower trajectory jerk and higher task success rates than the DP baseline. The gains are particularly pronounced in real-world tasks involving liquids and flexible objects: in our real-robot experiments, LieSpline-DP achieved a 100% success rate on both pouring and bucket hooking, whereas the DP baseline achieved only 10% and 30%, respectively.

Robotics (cs.RO)

arXiv:2609.15162 [cs.RO]

(or arXiv:2609.15162v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.15162 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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