Dissecting Motion-Prior Regularization for Data-Scarce Robotic Insertion

Diffusion Policies (DPs) are able to perform complex manipulation tasks. However, DPs are typically trained by minimizing a denoising objective, which provides limited control over generalization in the finite-data regimes common in robotics. In this letter, we propose PAC-DP, an approach that increases the performance of DPs in robotic manipulation tasks. By modeling the DP as a Bayesian neural network, and defining a PAC-Bayes generalization bound, we derive a novel training objective that augments the standard denoising loss with a Kullback-Leibler divergence regularizer between the posterior and prior parameter distributions. From the theoretical perspective, our approach provides a principled approach to regularize the training of DPs without significantly increasing the training time. From the practical point of view, experimental results demonstrate improved denoising performance, lower variational negative log-likelihood, and higher success rates across multiple robotic manipulation benchmarks. Crucially, the largest improvements are observed in low-data training regimes and complex tasks, establishing PAC-DP as a theoretically grounded framework for robot policy learning.

Expert demonstrations are widely assumed to be the gold standard for robot imitation learning. Yet for fine-grained manipulation such as insertion, stacking, and alignment, we uncover a counterintuitive failure mode: fluent demonstrations can be poor teachers. A skilled teleoperator compresses the decisive moments of alignment and recovery into a brief temporal window, leaving the policy flooded with redundant free-space motion and starved of supervision exactly where precision determines success. We address this bottleneck at two levels. At the data level, slowing down near alignment and resampling critical segments both help, yet the gain comes mainly from broadening the coverage of recovery states the policy must learn, not from reweighting frames it already has. Such data-side fixes, however, leave the policy's per-frame view untouched: a single image still maps directly to an action, and the local motion that governs correction stays implicit. We therefore turn to the representation level and introduce STAIR (\textbf{S}patio-\textbf{T}emporal feature \textbf{A}s an \textbf{I}nterface for \textbf{R}obot learning), a compact dynamic feature that bridges the vision-language model and the action expert, distilling the short-horizon motion already recorded in each trajectory into dense, motion-aware supervision. Trained on fluent data alone, STAIR recovers most of the deliberate-demonstration gain ($50.0$ to $62.2\%$ overall, approaching the $64.4\%$ of deliberate demonstrations). These results call for a more pedagogical view of robot data, optimized for machine learnability rather than human efficiency alone.

Contact-rich precision insertion is a key manipulation skill in robotic assembly. Tight clearances make insertion more sensitive to alignment errors and prone to collisions and jamming, while variations in geometry and clearance across parts further complicate policy reuse. We present a reinforcement learning framework that trains insertion policies entirely in simulation for direct deployment without real-world demonstrations or policy fine-tuning. By combining target poses with compact three-dimensional fingertip force feedback, the policy learns to search for alignment and correct its motion despite errors in the estimated hole position. A decoupled gated reward coordinates alignment and insertion. Force-signal smoothing and state-independent standard deviations stabilize the learning process. The resulting policies perform real-world insertion across multiple hole geometries with a minimum nominal clearance of 0.02 mm and improve success while reducing peak contact forces under hole-position errors. Cross-clearance and cross-geometry evaluations further confirm policy generalization. The system achieved the first perfect score of 20/20 on ManipulationNet's peg-in-hole benchmark under its Human-in-the-Loop protocol, with fully autonomous insertion motions. A single policy trained only on a simulated hexagonal insertion task achieved an overall success rate of 95.0% across eight unseen real-world insertion tasks. These results show that learning entirely in simulation can yield precision insertion skills that can be deployed directly and reused across real-world tasks. The project website (https://mzhsoul.github.io/InsertAnything/) provides open-source simulation and real-robot experiment scripts, assets, and trained checkpoints.