# SPECTRA: Context-Conditioned Spectral Movement Primitives for Robot Skill Generalization

arXiv: https://arxiv.org/abs/2607.06978 · HTML: https://mlsanity.com/paper/2607.06978/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 8 Jul 2026.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Abstract (arXiv)

Robot imitation learning for manipulation should preserve demonstrated task geometry while producing dynamically admissible robot motions. Existing pipelines often learn task-dependent trajectories and impose execution limits afterward through filtering, smoothing, clipping, or time scaling, which may distort task-critical end-effector paths. We propose the Spectral Movement Primitive (SMP), a frequency-domain imitation learning framework that couples task-space skill generation with joint-space execution regulation. Demonstrations are represented by truncated finite-horizon Fourier coefficients. An empirically selected low-frequency task band captures the dominant motion geometry, while higher harmonics contribute disproportionately to derivative growth. A frame-aware context-conditioned GMM/GMR prior predicts the task-band coefficients in a canonical task frame, and the resulting Cartesian trajectory is mapped to joint space through sequential inverse kinematics. A phase-coupled regulator then limits the requested phase progression without modifying the spectral coefficients, thereby enforcing joint velocity and acceleration limits while preserving the represented path. Experiments evaluate task-band reconstruction, robustness to composite demonstration corruption, out-of-distribution cross-board generalization, joint-space dynamic admissibility, end-effector path preservation, and deployment on a Franka Panda robot. Results show compact geometric reconstruction, consistent transfer across unseen task frames, substantial reductions in dynamic violations and jerk, and preservation of the intended end-effector path during phase regulation.