B-spline Policy: Accelerating Manipulation Policies via B-spline Action Representations

Modern imitation-learning policies for robot manipulation often represent actions as fixed-resolution action chunks, which are simple and effective but expose limited geometric and temporal structure before execution. This paper studies Spline Policy (SP), a structured representation that replaces action chunks with spline parameters while keeping the policy backbone unchanged. The predicted spline can be decoded as a compact continuous trajectory, queried at different temporal resolutions, constrained or edited in parameter space, and passed to downstream controllers. For quadratic spline outputs, the same representation can also be converted into a state-dependent vector field through an analytical distance-field construction. Under the regularity and projection assumptions of this construction, the induced dynamics do not increase the distance to the generated spline, yielding a principled local corrective mechanism around the predicted motion. The spline output further supports uncertainty propagation from observations to spline parameters, trajectories, and flow fields, and can be combined with classical control mechanisms such as null-space collision avoidance without retraining the policy backbone. We instantiate SP with diffusion, flow-matching, transformer-based, and vision-language-action backbones. Experiments in low-dimensional motion learning, simulated manipulation under matched backbones, dexterous manipulation, and real-robot case studies show that SP remains compatible with modern policy learners while exposing useful motion-structure properties, including compact decoding, temporal resampling, local correction around predicted motions, uncertainty evaluation, and controller compatibility.

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.

Previous imitation learning policies predict future actions at every control step, whether in smooth motion phases or precise, contact-rich operation phases. This uniform treatment is wasteful: most steps in a manipulation trajectory traverse free space and carry little task-relevant information, while a small fraction of \emph{key} steps around contacts, grasps, and alignment demand dense, high-resolution prediction. We propose a novel \emph{action relabeling} mechanism: at each timestep in a skip segment, we replace the behavior cloning target with the action at the entrance of the next key segment, enabling the policy to leap over redundant steps in a single decision. The resulting \textbf{Skip Policy (SkiP)} dynamically leaps over skip segments and intensively refines actions in key segments, within a single unified network requiring no learned skip planner or hierarchical structure. To automatically partition demonstrations into key and skip segments without manual annotation, we introduce \emph{Motion Spectrum Keying} (MSK), a fast, task-agnostic procedure that detects local motion complexity from action signals. Extensive experiments across 72 simulated manipulation tasks and three real-robot tasks show that SkiP reduces executed steps by $15$--$40\%$ while matching or improving success rates across various policy backbones. Project page: \texttt{https://pgq18.github.io/SkiP-page/}.