Gait modeling and optimization for the perturbed Stokes regime
Gait modeling and optimization for the perturbed Stokes regime
复制标题
DOI：
10.1007/s11071-019-05121-3
复制
发表时间：
2019-09-01
影响因子：
5.6
通讯作者：
Revzen, Shai
中科院分区：
文献类型：
--
作者：
Kvalheim, Matthew D.;Bittner, Brian;Revzen, Shai
许多形式的运动，无论是自然的还是人工的，都是由粘性摩擦主导的，在这个意义上，如果没有动力消耗，它们很快就会停止。从几何力学，它是已知的，在“斯托克斯”（粘性;零雷诺数）极限游泳，运动是由降阶的“连接”模型，描述了身体形状的变化如何产生运动的身体框架相对于世界。在“扰动斯托克斯制度”的惯性力仍然占主导地位的粘度，但不可忽略（低雷诺数），我们表明，运动仍然是由形状速度和身体速度之间的函数关系，但这个函数不再是线性的形状变化率。我们推导出这个模型使用奇异摄动理论和非紧正常双曲不变流形理论的结果。使用这种降阶模型的理论特性，我们开发了一种算法，估计近似的动态附近的周期性身体形状的变化（“步态”）直接从观察数据的形状和身体运动。这扩展了我们以前的工作，假设运动学“连接”模型。为了比较新旧算法，我们分析了模拟游泳运动员在一个范围内的惯性阻尼比。我们的新的一类模型表现良好的斯托克斯政权和几个数量级以外的扰动斯托克斯政权，在那里它提供了显着提高预测精度相比，以前的工作。除了算法的改进，我们从而提出了一类新的模型，是独立的利益。它们在数据驱动建模中的应用提高了我们研究动物步态最优性的能力，以及我们使用硬件在环优化为机器人生成步态的能力。
Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the "Stokesian" (viscous; zero Reynolds number) limit, the motion is governed by a reduced-order "connection" model that describes how body shape change produces motion for the body frame with respect to the world. In the "perturbed Stokes regime" where inertial forces are still dominated by viscosity, but are not negligible (low Reynolds number), we show that motion is still governed by a functional relationship between shape velocity and body velocity, but this function is no longer linear in shape change rate. We derive this model using results from singular perturbation theory and the theory of noncompact normally hyperbolic invariant manifolds. Using the theoretical properties of this reduced-order model, we develop an algorithm that estimates an approximation to the dynamics near a cyclic body shape change (a "gait") directly from observational data of shape and body motion. This extends our previous work which assumed kinematic "connection" models. To compare the old and new algorithms, we analyze simulated swimmers over a range of inertia-to-damping ratios. Our new class of models performs well on the Stokesian regime and over several orders of magnitude outside it into the perturbed Stokes regime, where it gives significantly improved prediction accuracy compared to previous work. In addition to algorithmic improvements, we thereby present a new class of models that is of independent interest. Their application to data-driven modeling improves our ability to study the optimality of animal gaits and our ability to use hardware-in-the-loop optimization to produce gaits for robots.