Continuum and soft robots can positively impact diverse sectors, from biomedical applications to marine and space exploration, thanks to their potential to adaptively interact with unstructured environments. However, the complex mechanics exhibited by these robots pose diverse challenges in modeling and control. Reduced order continuum mechanical models based on rod theories have emerged as a promising framework, striking a balance between accurately capturing deformations of slender bodies and computational efficiency. This review paper explores rod-based models and control strategies for continuum and soft robots. In particular, it summarizes the mathematical background underlying the four main rod theories applied in soft robotics. Then, it categorizes the literature on rod models applied to continuum and soft robots based on deformation classes, actuation technology, or robot type. Finally, it reviews recent model-based and learning-based control strategies leveraging rod models. The comprehensive review includes a critical discussion of the trends, advantages, limits, and possible future developments of rod models. This paper could guide researchers intending to simulate and control new soft robots and provide feedback to the design and manufacturing community.

翻译：连续体和软体机器人因其具备与非结构化环境自适应交互的潜力，可在生物医学应用、海洋及太空探索等多个领域产生积极影响。然而，这些机器人所展现的复杂力学特性给建模与控制带来了诸多挑战。基于杆理论的降阶连续介质力学模型已成为一种前景广阔的框架，在精确捕捉细长体变形与计算效率之间取得了良好平衡。本综述论文探讨了用于连续体和软体机器人的基于杆的模型及控制策略。具体而言，本文首先总结了应用于软体机器人学的四种主要杆理论背后的数学基础。随后，根据变形类别、驱动技术或机器人类型，对应用于连续体和软体机器人的杆模型文献进行了分类。最后，综述了近期利用杆模型的基于模型与基于学习的控制策略。本综述包含对杆模型的发展趋势、优势、局限及未来可能发展的批判性讨论。本文可为旨在模拟和控制新型软体机器人的研究人员提供指导，并为设计与制造领域提供反馈。