Continuum and soft robots can transform automation tasks requiring compliant interaction in constrained or unstructured environments, including healthcare, agriculture, marine, and space applications. However, their complex mechanics introduce significant challenges in modeling and control. Low-dimensional continuum mechanical models, such as rod theories, effectively capture the large deformations of slender bodies in contact-rich scenarios while balancing accuracy and computational efficiency. This paper presents a vertical survey of rod models for continuum and soft robots, spanning their mathematical foundations, robot modeling, and control applications. We review the main rod theories adopted in soft robotics and introduce a deformation-based classification of rod models for continuum and soft robots. Furthermore, we survey recent model-based and learning-based control strategies leveraging rod models, highlighting their role in manipulation and physical interaction tasks. Finally, we discuss advantages, limitations, research gaps, and emerging directions of rod-based approaches. This paper aims to serve as a reference for developing models and control strategies for continuum and soft robots.

翻译：连续体与软体机器人能够在受限或非结构化环境中实现需要柔顺交互的自动化任务，涵盖医疗、农业、海洋及航天等领域。然而，其复杂的力学特性为建模与控制带来了显著挑战。低维连续介质力学模型（如杆理论）能在接触密集场景下有效捕捉细长物体的大变形，同时兼顾精度与计算效率。本文针对连续体与软体机器人的杆模型进行垂直综述，涵盖其数学基础、机器人建模及控制应用。我们回顾了软体机器人领域采用的主要杆理论，并基于变形特性提出了连续体与软体机器人杆模型的分类体系。此外，系统梳理了基于模型与基于学习的杆模型控制策略最新进展，重点阐释其在操作与物理交互任务中的作用。最后，本文讨论了杆方法的优势、局限性、研究空白及新兴方向。旨在为连续体与软体机器人的建模与控制策略开发提供参考依据。