Continuum robots with variable stiffness have gained wide popularity in the last decade. Layer jamming (LJ) has emerged as a simple and efficient technique to achieve tunable stiffness for continuum robots. Despite its merits, the development of a control-oriented dynamical model tailored for this specific class of robots remains an open problem in the literature. This paper aims to present the first solution, to the best of our knowledge, to close the gap. We propose an energy-based model that is integrated with the LuGre frictional model for LJ-based continuum robots. Then, we take a comprehensive theoretical analysis for this model, focusing on two fundamental characteristics of LJ-based continuum robots: shape locking and adjustable stiffness. To validate the modeling approach and theoretical results, a series of experiments using our \textit{OctRobot-I} continuum robotic platform was conducted. The results show that the proposed model is capable of interpreting and predicting the dynamical behaviors in LJ-based continuum robots.

翻译：具备可变刚度的连续体机器人在过去十年中广受欢迎。层阻塞作为一种简单高效的技术，可用于实现连续体机器人的刚度可调。尽管其优势明显，但针对这类特定机器人开发面向控制的动力学模型在文献中仍是一个开放问题。本文旨在提出首个解决方案，以填补这一空白。我们提出了一种基于能量且集成了LuGre摩擦模型的层阻塞连续体机器人模型。随后，我们对该模型进行了全面的理论分析，重点关注层阻塞连续体机器人的两个基本特性：形状锁定和刚度可调。为验证建模方法和理论结果，我们利用自主研制的\textit{OctRobot-I}连续体机器人平台开展了一系列实验。结果表明，该模型能够解释并预测层阻塞连续体机器人的动力学行为。