Dissecting Motion-Prior Regularization for Data-Scarce Robotic Insertion

This study asks whether training-time motion-prior regularization can improve insertion success when a diffusion policy is learned from only 15 demonstrations. Minimum jerk discourages abrupt changes in predicted translational acceleration; speed-curvature regularization instead couples movement speed to path geometry. These are candidate mechanisms for task completion, not safety guarantees. We compare the priors individually and jointly, neither prior, and generic smoothness, with 80 real-robot trials per setting pooled over four recorded condition classes. Joint and minimum-jerk-only settings each achieved 70/80 successes (87.5%), versus 69/80 (86.3%) for speed-curvature only, 66/80 (82.5%) for neither prior, and 67/80 (83.8%) for generic smoothness. Success rates and Wilson 95% confidence intervals are visualized for direct comparison. Joint regularization exceeded neither by 5.0 percentage points but provided no observed gain over minimum jerk alone. The results motivate minimum jerk as the simpler candidate for replication, without establishing synergy, biomechanical specificity, improved safety, or distribution-shift robustness.