Biomimetic underwater robots use lateral periodic oscillatory motion to propel forward, which is seen in most fishes known as body caudal fin (BCF) propulsion. The lateral oscillatory motion makes slender-bodied fish-like robots roll unstable. Unlike the case of human-engineered aquatic robots, many species of fish can stabilize their roll motion to perturbations arising from the periodic motions of propulsors. To first understand the origin of the roll instability, the objective of this paper is to analyze the parameters affecting the roll-angle stability of an autonomous fish-like underwater swimmer. Eschewing complex models of fluid-structure interaction, we instead consider the roll motion of a nonholonomic system inspired by the Chaplygin sleigh, whose center of mass is above the ground. In past work, the dynamics of a fish-like periodic swimmer have been shown to be similar to that of a Chaplygin sleigh. The Chaplygin sleigh is propelled by periodic torque in the yaw direction. The roll dynamics of the Chaplygin sleigh are linearized and around a nominal limit cycle solution of the planar hydrodynamic Chaplygin sleigh in the reduced velocity space. It is shown that the roll dynamics are then described as a nonhomogeneous Mathieu equation where the periodic yaw motion provides the parametric excitation. We study the added mass effects on the sleigh's linear dynamics and use the Floquet theory to investigate the roll stability due to parametric excitation. We show that fast motions of the model for swimming are frequently associated with roll instability. The paper thus sheds light on the fundamental mechanics that present trade-offs between speed, efficiency, and stability of motion of fish-like robots.

翻译：仿生水下机器人通过横向周期性振荡运动向前推进，这常见于大多数鱼类，称为身体尾鳍（BCF）推进模式。横向振荡运动使得细长体型的仿鱼机器人产生横摇失稳。与人工设计的水下机器人不同，许多鱼类能够稳定因推进器周期运动引起的扰动所产生的横摇运动。为初步理解横摇失稳的根源，本文旨在分析影响自主仿鱼水下航行器横摇角稳定性的参数。我们摒弃复杂的流固耦合模型，转而研究受Chaplygin雪橇启发（其质心位于地面之上）的非完整系统的横摇运动。已有研究表明，类鱼周期性游泳机器人的动力学特性与Chaplygin雪橇具有相似性。Chaplygin雪橇通过偏航方向的周期性力矩驱动。本文在约化速度空间中，对平面流体动力学Chaplygin雪橇的标称极限环解进行线性化处理，建立其横摇动力学方程。结果表明，横摇动力学可描述为非齐次Mathieu方程，其中周期性偏航运动提供了参数激励。我们研究了附加质量效应对雪橇线性动力学特性的影响，并利用Floquet理论分析参数激励下的横摇稳定性。研究表明，游泳模型的快速运动通常与横摇失稳相关。本文揭示了仿鱼机器人运动速度、效率与稳定性之间权衡的基础力学机制。