【摘要】 蚯蚓、蛞蝓等无脊椎生物的连续体结构和波动驱动特性使其成为研究仿蠕虫机器人的理想对象，因此建立仿蠕虫连续体系统的动力学模型对于指导设计蠕虫类软体机器人有着重要意义．针对仿蠕虫系统的轴向运动，本文将细长圆形超弹性杆作为力学模型，综合超弹性Yeoh应变能、黏性摩擦，内部驱动力等多个关键因素，建立其轴向和径向耦合的非线性动力学模型，使用正弦平方应变波作为驱动，分析后退蠕动波对该系统运动的影响．由于所建立的连续体非线性动力学方程难以得到解析解，本文提出一种简化计算方法：通过径向变形与轴向位移之间的几何近似，展现轴-径非线性耦合变形特征，并将蠕动波代替驱动力进行简化计算．结果发现，本文的轴-径耦合动力学模型不但适用于小变形，而且可以提供大变形的计算分析．最后，通过一个一般算例，分析轴-径耦合模型的平均速度与正弦平方应变波的设计参数之间的联系，结果表明在应变能系数、摩擦系数、长细比不变的前提下，增大应变波的波幅，或者减小应变波的波宽与体长的比值，将有利于提高仿蠕虫系统轴向运动的平均速率.更多还原

【Abstract】 Invertebrates like earthworms and slugs exhibit continuum body structures and undulatory propulsion, making them ideal references for designing worm-inspired soft robots. Developing dynamic models of such biomimetic systems is essential for guiding robot design. This study investigates axial motion in a worm-like system using a slender circular hyperelastic rod as the mechanical model. We integrate axial and radial coupling effects by incorporating the Yeoh hyperelastic strain energy, viscous friction, and internal driving forces. A sinusoidal squared strain wave drives the system to study how retrograde peristaltic waves affect its motion. The derived nonlinear continuum equations are analytically challenging. To address this, we propose a hybrid analytical-numerical method: First, geometric approximations link radial deformation to axial displacement, capturing nonlinear coupling effects. Second, peristaltic wave propagation replaces direct force calculations in simulations. Results show the model works for both small and large deformations. Through a numerical case, the correlation between average locomotion speed and waveform parameters in the axial-radial coupling model is investigated. Under constant strain energy coefficient, friction coefficient, and slenderness ratio, increasing the sinusoidal squared strain wave amplitude or decreasing the wave-width-to-bodylength ratio enhances the worm-like system’s average axial propulsion velocity.更多还原