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

arXiv:2609.15162 · cs.RO · Submitted 2026-09-14 · Read on arXiv

cs.RO

Submitted: 2026-09-14

Updated: 2026-09-16

Project page: https://xieerxuan.github.io/LieSpline-DP

Terminology

• Diffusion Policy — 13× in this paper
• Transformer — 6× in this paper · explained in 2 episodes
• Alignment — 4× in this paper · explained in 1 episode
• Diffusion Model — 4× in this paper · explained in 8 episodes
• Benchmark — 3× in this paper · explained in 2 episodes
• Action Chunking — 2× in this paper · explained in 1 episode
• Decode — 2× in this paper · explained in 2 episodes
• Diffusion Models — 2× in this paper · explained in 6 episodes
• Generative Modeling — 2× in this paper · explained in 3 episodes
• KV cache — 2× in this paper · explained in 3 episodes
• Real-Time Chunking — 2× in this paper
• Action Chunking with Transformers — 1× in this paper
• Action Flow — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Diffusion Policy (DP) — 1× in this paper · explained in 2 episodes
• Distribution Shift — 1× in this paper · explained in 6 episodes
• Exponential Moving Average (EMA) — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Flow Matching — 1× in this paper · explained in 8 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Tokenization — 1× in this paper · explained in 2 episodes

Sources

• Training-Time Action Conditioning for Efficient Real-Time Chunking
• Spline Policy: A Structured Representation for Robot Policies
• B-spline Policy: Accelerating Manipulation Policies via B-spline Action Representations
• ABPolicy: Asynchronous B-Spline Flow Policy for Real-Time and Smooth Robotic Manipulation
• A micro Lie theory for state estimation in robotics

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