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This paper introduces the Spectral Movement Primitive (SMP), a novel framework for robot imitation learning that effectively integrates task-space skill generation with joint-space execution regulation. By utilizing truncated finite-horizon Fourier coefficients to represent demonstrations, the method captures essential motion geometry while ensuring dynamic admissibility through a phase-coupled regulator. Experimental results demonstrate that SMP achieves compact geometric reconstruction, robust generalization across unseen tasks, and significant reductions in dynamic violations while preserving critical end-effector paths.
Achieving robust robot skill generalization while maintaining critical motion geometry, SMP reduces dynamic violations and preserves end-effector paths during execution.
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.
