[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86205-en":3,"doc-seo-86205-105":29,"detail-sidebar-cat-0-en-105":82},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":11,"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},86205,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","CR-Solver GPU-Accelerated Kinematics Solver for Tendon-driven Continuum Robots","Continuum robots enable intrinsic compliance and dexterous interaction in confined, unstructured spaces, but precise motion generation remains hindered by planners built on rigid-body assumptions. CR-Solver introduces a two-stage, optimization-based GPU-accelerated solver that unifies inverse kinematics, path following, and trajectory planning in a single constrained nonlinear optimization framework. Validated on three tasks, it achieves >95% success rate and millimeter-level accuracy while significantly accelerating GPU parallel optimization over CPU solvers. Implemented in pure Python for extensibility and easier adoption.","CR-Solver: GPU-Accelerated Kinematics Solver for Tendon-driven  \nContinuum Robots  \nHeqing Yang1 Yang Yi1 Linqing Zhong1 Linjiang Huang1: Si Liu1:  \narXiv :2607 . 11340v1 [ cs .RO] 13 Jul 2026  \nAbstract—Continuum robots provide intrinsic compliance, high dexterity, and safe physical interaction, enabling navigation and manipulation in confined and unstructured environments. Despite recent advances in sensing and control, heightening the need for precise motion generation, most widely used planning libraries are grounded in rigid-body assumptions, creating a critical gap for fast and practical tools for continuum robots. To address this, we present CR-Solver, a two-stage, optimization-based solver for the motion generation of tendon-driven continuum robots. Our method unifies inverse kinematics, path following, and trajectory planning within a single constrained nonlinear optimization framework. Leveraging GPU-accelerated parallel optimization, CR-Solver delivers fast, accurate, and constraint-aware solutions. We validate our approach on three tasks, demonstrating significant speedups over traditional CPU-based solvers while achieving a consistently high success rate above 95% and millimeter-level accuracy. The solver is implemented in pure Python, reducing the barrier to adoption and offering a practical, extensible foundation for continuum robots’ high-performance motion planning.  \nI. INTRODUCTION  \nContinuum robots differ from conventional rigid-body manipulators by generating motion through deformation of a continuous backbone, which endows them with theoretically infinite degrees of freedom [1] . Their intrinsic structural compliance promotes safer human-robot interaction, while their slender morphologies enable navigation in confined, tortuous environments [2, 3] . These characteristics have motivated applications ranging from minimally invasive surgery to search-and-rescue [4, 5] .  \nHowever, the inherent flexibility that enables the high dexterity of continuum robots also creates significant computational challenges. Their hyper-redundancy and highly nonlinear dynamics make motion generation computationally demanding. A rich ecosystem of motion planning tools exists for rigid-body robotics, spanning from classical planners like OMPL [6] to modern GPU-accelerated solvers such as cuRobo [7] and PyRoki [8] . Nevertheless, these established frameworks are fundamentally incompatible. They are grounded in URDF-based [9] rigid link abstractions defined by discrete joint coordinates. In contrast, the configuration spaces of continuum robots are described by continuous deformation fields, rendering the core modeling assumptions of these conventional frameworks invalid. Bridging this gap would require substantial architectural changes, highlighting the need for a purpose-built solution.  \nThis research is supported in part by the National Natural Science Foundation of China (No. 62461160308, U23B2010, 62576024), the Beijing Natural Science Foun dation (No. L231011), the Fundamental Research Funds for the Central Universities (No. 501RCQD2025141003), BeiHang GanWei Project (No. 502GWXM2024141001)  \n: Corresponding authors. 1 Beihang University.  \n(a) Inverse Kinematics (b) Trajectory Planning (c) Path Following  \nFig. 1: Our framework provides three core capabilities for continuum robots: (a) inverse kinematics that computes feasible configurations for desired end-effector poses while avoiding obstacles,(b) trajectory planning that generates collision-free trajectories between start and goal configurations, and (c) path following that enables precise tracking of predefined end-effector trajectories. All three functionalities leverage GPU-accelerated parallel optimization for efficient computation.  \nWithin the continuum robotics community, existing strategies often mitigate this complexity by leveraging configuration-specific assumptions, such as the widely-used piecewise constant curvature (PCC) simplification [10, 11] . 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