Snake robots have redundant kinematic structure which predetermines them for motion in rough and unstructured terrain with obstacles, narrow spaces or environments with different ground levels. Dynamic modeling of snake robots is an important element in the development of control strategies for them. This paper, deals with the dynamic model of a snake robot moving in a pipeline. The model is based on Newton's mechanics with consideration of the viscous as well as Coulomb friction model. The paper uses Hertz theory for modeling of contact between a snake robot and side walls of a pipeline. Based on optimization process results, the friction effects as well as analyses of snake robot propulsive force are investigated. The main contributions of the paper are the developed dynamic model for snake robot motion in a pipeline, open source code of the developed model in MATLAB, and analyses of individual parameters of snake robot motion.

中文翻译：

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蛇形机器人在有限空间内运动的数学框架

蛇形机器人具有冗余的运动结构，这预先决定了它们在有障碍物、狭窄空间或不同地面环境的崎岖和非结构化地形中的运动。蛇形机器人的动态建模是为其控制策略开发的重要元素。本文研究了蛇形机器人在管道中移动的动态模型。该模型基于牛顿力学，考虑了粘性模型和库仑摩擦模型。该论文使用赫兹理论对蛇形机器人与管道侧壁之间的接触进行建模。基于优化过程结果，研究了蛇形机器人推进力的摩擦效应和分析。本文的主要贡献是开发了蛇形机器人在管道中运动的动态模型，在 MATLAB 中开源了所开发模型的源代码，并对蛇形机器人运动的各个参数进行了分析。