[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84165-en":3,"doc-seo-84165-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84165,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","SPECTRA: Context-Conditioned Spectral Movement Primitives for Robot Skill Generalization","Robot imitation learning for manipulation must keep demonstrated task geometry while generating robot motions that remain dynamically admissible at execution time. Existing methods learn task-dependent trajectories and then apply filtering, smoothing, clipping, or time scaling, which can distort end-effector paths that are task-critical. SPECTRA introduces a frequency-domain Spectral Movement Primitive that jointly models task-space skill generation and joint-space execution regulation using truncated Fourier task-band coefficients, context-aware prediction, inverse kinematics mapping, and phase-coupled constraint enforcement that preserves the represented path.","SPECTRA: Context-Conditioned Spectral Movement Primitives for  \nRobot Skill Generalization  \nBoxuan Zhang 1 , Sheng Liu 2 , Chenglin Ming 3 , Ahmed Abdelrahman 1  \n1 School of Computation, Information and Technology, Technical University of Munich, Germany  \n2 Karlsruhe Institute of Technology, Germany  \n3 The Department of Automation, Shanghai Jiao Tong University, China  \nCorrespondence: [boxuan.zhang@tum.de](boxuan.zhang@tum.de), [sheng.liu@student.kit.edu](sheng.liu@student.kit.edu)  \narXiv :2607 .06978v 1 [ cs .RO] 8 Jul 2026  \nAbstract—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.  \nWe 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.  \nExperiments evaluate task-band reconstruction, robustness to composite demonstration corruption, out-of-distribution crossboard generalization, joint-space dynamic admissibility, endeffector 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.  \nIndex Terms—Learning from demonstration, natural machine motion, motion control of manipulators, frequency-domain motion modeling.  \nI. INTRODUCTION  \nRobot imitation learning for manipulation must satisfy two tightly coupled requirements. First, a learned skill should generalize across task instances, such as changes in target position, orientation, scale, or task frame. Second, the generated motion should remain dynamically admissible at execution time, where joint velocity and acceleration must stay within acceptable ranges for hardware safety, tracking quality, and contact stability [1], [2] . In many existing pipelines, however, these requirements are handled in separate stages: contextual adaptation is learned in trajectory space or in a latent representation, while execution-time admissibility is imposed afterward through filtering, clipping, smoothing, or temporal rescaling [3], [4] . Sample-wise correction may distort taskcritical geometry, whereas path-preserving timing methods  \nFig. 1. Overview of the proposed framework. Demonstrations are encoded in a task-band spectral representation, generalized across task contexts in a frame-aware manner, and deployed on the real robot with shape-preserving phase regulation for dynamic admissibility.  \ntypically assume that the geometric path has already been specified. This separation leaves a structural gap between learning what motion should be performed and determining how it should be executed admissibly.  \nThis issue is particularly relevant to periodic and quasiperiodic manipulation skills, such as wiping, stirring, polishing, scrubbing, and rhythmic free-space motions [5] . In these tasks, successful execution depends not only on reaching a set of positions, but also on preserving the geometr","cbCaimrcprNE3PE9","https://ap.wps.com/l/cbCaimrcprNE3PE9","pdf",3817678,1,15,"English","en",105,"# Introduction\n## Problem and motivation\n## Frequency-domain formulation and periodic skills\n## Proposed SMP framework","[{\"question\":\"What limitation do existing imitation-learning pipelines have for manipulation tasks?\",\"answer\":\"They typically learn trajectories for each context and then enforce execution limits afterward via filtering or time rescaling, which can distort task-critical end-effector geometry and timing structure.\"},{\"question\":\"How does SPECTRA represent demonstrated skills?\",\"answer\":\"Demonstrations are encoded as truncated finite-horizon Fourier coefficients, using an empirically selected low-frequency task band to capture dominant motion geometry while higher harmonics are treated in how they affect derivatives.\"},{\"question\":\"How does SPECTRA enforce joint velocity and acceleration limits without changing the trajectory geometry?\",\"answer\":\"A frame-aware context-conditioned GMM/GMR predicts task-band coefficients in a canonical task frame, the Cartesian trajectory is mapped to joint space via sequential inverse kinematics, and a phase-coupled regulator limits phase progression while keeping the spectral coefficients and thus the represented path 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limitation do existing imitation-learning pipelines have for manipulation tasks?","Question",{"text":75,"@type":76},"They typically learn trajectories for each context and then enforce execution limits afterward via filtering or time rescaling, which can distort task-critical end-effector geometry and timing structure.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does SPECTRA represent demonstrated skills?",{"text":80,"@type":76},"Demonstrations are encoded as truncated finite-horizon Fourier coefficients, using an empirically selected low-frequency task band to capture dominant motion geometry while higher harmonics are treated in how they affect derivatives.",{"name":82,"@type":73,"acceptedAnswer":83},"How does SPECTRA enforce joint velocity and acceleration limits without changing the trajectory geometry?",{"text":84,"@type":76},"A frame-aware context-conditioned GMM/GMR predicts task-band coefficients in a canonical task frame, the Cartesian trajectory is mapped to 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