The unique rigid-flex connection between the fin-rays and fin-surface in a bionic undulatory fin robot endows the fin-surface with both active flexibility and load-bearing capacity, enabling this robot to perform amphibious motions in underwater, terrestrial, and even marshy environments. However, investigations into dynamic modeling problems for the undulatory fin robot, considering the impact of nonlinear deformation and frictional contact on ground locomotion performance, are scarce. Given this, based on the absolute nodal coordinate formulation (ANCF), this paper presents an efficient and accurate nonlinear dynamic model for this robot to elucidate the fin's flexible deformation and motion law. This model considers material, geometric, and boundary nonlinearities, utilizing ANCF thin plate elements and reference nodes to individually describe the fin-surface and fin-rays of the undulatory fin. Then, by using the master-slave technique, a frictional contact formulation for the fin and the ground is proposed. Furthermore, we conduct in-depth research and analysis on the formation and undulatory motion of the undulatory fin, encompassing its static deformation, static contact deformation, and frictional contact motion, and successfully obtain its responses under various conditions. Research indicates that during fin-surface motion, longitudinal sliding or a tendency for sliding at the contact points results in the undulatory fin moving in a crawling gait. The proposed theoretical model correctly captures the fin's complex nonlinear deformations and frictional characteristics and reveals its ground locomotion mechanism, whose effectiveness and superiority are validated through numerical examples and experiments.

中文翻译：

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具有柔性变形和摩擦接触的地面起伏鳍机器人的非线性动力学研究。


仿生起伏鳍片机器人中鳍条和鳍片表面之间独特的软硬结合连接赋予了鳍片表面主动灵活性和承载能力，使该机器人能够在水下、陆地甚至沼泽环境中执行两栖运动。然而，考虑到非线性变形和摩擦接触对地面运动性能的影响，对起伏鳍机器人动力学建模问题的研究很少。鉴于此，本文基于绝对节点坐标公式 （ANCF），为该机器人提供了一种高效、准确的非线性动力学模型，以阐明鳍片的柔性变形和运动规律。该模型考虑了材料、几何和边界非线性，利用 ANCF 薄板单元和参考节点分别描述了起伏翅片的翅片表面和鳍条。然后，利用主从技术，提出了鳍片与地面的摩擦接触公式。此外，我们对起伏翅片的形成和起伏运动进行了深入研究和分析，包括其静态变形、静态接触变形和摩擦接触运动，并成功获得了其在各种条件下的响应。研究表明，在鳍表面运动过程中，纵向滑动或在接触点处滑动的趋势会导致起伏的鳍以爬行的步态移动。所提出的理论模型正确地捕捉了翅片复杂的非线性变形和摩擦特性，并揭示了其地面运动机制，其有效性和优越性通过数值算例和实验得到了验证。