Continuum Robot Control Strategies: From Model-Driven to Embodied Intelligence.

Continuum robots leverage intrinsic compliance and a high degree of freedom, making them well-suited for interaction in confined spaces. However, their distributed-parameter nature and pronounced nonlinearities pose major challenges for online closed-loop control. Guided by the origin of structural priors and by how control responsibilities are apportioned across the "brain-body-environment" loop, this survey charts the spectrum from model-driven control to embodied intelligence. Specifically, we organize model-driven control into physics-based, data-driven, and hybrid paradigms; summarize model-free control in terms of task-space feedback control, online mapping estimation, and input-output adaptive methods; and review embodied-intelligence control with an emphasis on morphological computation, distributed embodied sensing, policy learning and digital twins, and morphology-actuation-control co-design. This perspective provides a unified lens for synthesizing and comparing these three classes of control strategies.