Efficient sliding locomotion for two- and three-link bodies

We study the possibility of efficient intermittent (inertia-based) locomotion for two-link bodies that open and close periodically in time. The anisotropy ratio of the sliding friction coefficients is a key parameter. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes. We find these motions in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively, and with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction. We then discuss efficient locomotion for three link bodies.