Efficient sliding locomotion of three-link bodies
Efficient sliding locomotion of three-link bodies
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DOI：
10.1103/physreve.103.042414
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发表时间：
2021-04-16
影响因子：
2.4
通讯作者：
Alben, Silas
中科院分区：
文献类型：
--
作者：
Alben, Silas
我们研究了具有规定关节角运动的三连杆机构的滑动运动效率。物体在干（库仑）摩擦下无惯性地移动，干摩擦是各向异性的（在链接的法线和切线方向上不同）和定向的（在向前和向后的切线方向上不同）。摩擦系数空间可以被划分为几个区域，每个区域具有不同类型的有效运动学。这些运动学包括类似于具有非常各向异性摩擦的横向波动的运动学、小幅度的往复运动学、接近各向同性摩擦的非常大幅度的运动学以及关于平坦状态非常不对称的运动学。在双参数形状空间中，椭圆轨迹的零净旋转主要发生在双边或对映对称的情况下。这些对称子空间具有与全空间大致相同的峰值效率，但具有小得多的维度。添加二次或三次谐波大大增加了效率的局部最优值的数量，但仅适度增加了峰值效率。具有较高谐波的随机系综具有在某一非零值附近达到峰值并快速衰减到最大效率的效率分布。提出了一种随机优化算法，用于计算高次谐波的最优解。这些是简单的闭合曲线，在大多数情况下是椭圆最优的锐化版本，并且主要针对小的法向摩擦实现高得多的效率。对于线性（粘性）阻力定律，最佳轨迹在大部分摩擦系数空间中是相似的，并且除了非常大的法向摩擦之外，相对效率要低得多。
We study the efficiency of sliding locomotion for three-link bodies with prescribed joint angle motions. The bodies move with no inertia, under dry (Coulomb) friction that is anisotropic (different in the directions normal and tangent to the links) and directional (different in the forward and backward tangent directions). Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics. These include kinematics resembling lateral undulation with very anisotropic friction, small-amplitude reciprocal kinematics, very large-amplitude kinematics near isotropic friction, and kinematics that are very asymmetric about the flat state. In the two-parameter shape space, zero net rotation for elliptical trajectories occurs mainly with bilateral or antipodal symmetry. These symmetric subspaces have about the same peak efficiency as the full space but with much smaller dimension. Adding the second or third harmonics greatly increases the numbers of local optimal for efficiency, but only modestly increases the peak efficiency. Random ensembles with higher harmonics have efficiency distributions that peak near a certain nonzero value and decay rapidly up to the maximum efficiency. A stochastic optimization algorithm is developed to compute optima with higher harmonics. These are simple closed curves, sharpened versions of the elliptical optima in most cases, and achieve much higher efficiencies mainly for small normal friction. With a linear (viscous) resistance law, the optimal trajectories are similar in much of the friction coefficient space, and relative efficiencies are much lower except with very large normal friction.