三连杆机构的有效滑动运动
Efficient sliding locomotion of three-link bodies
摘要：
我们研究了干摩擦（库仑）存在下的三连杆机构的滑动运动的效率。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、小振幅往复运动学、接近各向同性摩擦的非常大振幅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。增加两到三倍基频的模式大大增加了效率的局部最优值的数量，但只能适度地增加峰值效率。具有更高频率的随机系综具有在某个非零值附近达到峰值并迅速衰减到最大效率的效率分布。一个随机优化算法的发展，以计算最优与更高的频率。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。对于线性阻力律，最优轨迹在摩擦系数空间的大部分是相似的，并且除了非常大的法向摩擦之外，相对效率低得多。
英文摘要：
We study the efficiency of sliding locomotion for three-link bodies in the presence of dry (Coulomb) friction. 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 modes with two or three times the basic frequency greatly increases the numbers of local optimal for efficiency, but only modestly increases the peak efficiency. Random ensembles with higher frequencies 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 frequencies. 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 resistance law, the optimal trajectories are similar in much of friction coefficient space, and relative efficiencies are much lower except with very large normal friction.
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