Mechanism design, modeling, and trajectory planning for continuum robots: A comprehensive review

Continuum robots, characterized by slender and compliant mechanical structures with redundant degrees of freedom, enable navigation through narrow and tortuous environments and execution of tasks that are difficult for traditional rigid robots, demonstrating considerable potential in industrial, medical, aerospace, and other fields. In recent years, related research has flourished, with significant breakthroughs achieved in mechanism configurations, modeling theories, and planning strategies. Accordingly, this paper reviews the relevant literature from the past decade, systematically summarizing the existing design paradigms of continuum robots. The configurations are classified into three categories: externally actuated, intrinsically actuated, and hybrid actuated configurations, and their application scenarios are summarized. In terms of modeling, this paper provides a categorized review of geometric/kinematic models, mechanics-based static models, dynamic models, stiffness/load-dependent models, and data-driven models. With regard to trajectory planning, the analysis is carried out from three perspectives: motion patterns, planning algorithms, and planning objectives. On this basis, the paper discusses and compares the applicability and limitations of the various approaches. Finally, the major challenges in the field are identified, and future research directions are outlined, including the development of compact stiffening mechanisms, integration of reduced-order physical models with data-driven compensators, and establishment of hierarchical and generalizable planning frameworks, among others, thereby providing a systematic reference for future research.