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Undulation is a form of propulsion in which waves of bending propagate along an elongated, slender body. This locomotor strategy is used by organisms that span orders of magnitude in size and represent diverse habitats and species. Despite this diversity, common neuromechanical phenomena have been observed across biologically disparate undulators, as a result of common mechanics. For example, neuromechanical phase lags (NPL), a phenomenon where waves of muscle contraction travel at different speeds than the corresponding body bends, have been observed in fish, lamprey, and lizards. Existing theoretical descriptions of this phenomenon implicate the role of physical body-environment interactions. However, systematic experimental variation of body-environment interactions and measurement of the corresponding phase lags have not been performed. Using the nematode we measured phase lags across a range of environmental interaction regimes, performing calcium imaging in body wall muscles in fluids of varying viscosity and on agar. A mechanical model demonstrates that the measured phase lags are controlled by the relative strength of elastic torques within the body and resistive forces within the medium. We further show that the phase lags correspond with a difference in the wave number of the muscle activity and curvature patterns. Hence, the environmental forces that create NPL also act as a filter that shapes and modulates the gait articulated by the nervous system. Beyond nematodes, the simplicity of our model suggests that tuning body elasticity may serve as a general means of controlling the degree of mechanical wave modulation in other undulators. 

A diversity of organisms live within underground environments. However, visualizing subterranean behavior is challenging because of the opacity of most substrates. We demonstrate that laser speckle imaging, a non-invasive technique resolving nanometer-scale movements, facilitates quantifying biological activity in a granular medium. We monitored fire ants (Solenopsis invicta) at different developmental stages, burial depths (1–5 cm) and moisture fractions (0 and 0.1 by volume) in a container of 0.7 mm glass particles. Although the speckle pattern from the backscattered light precludes direct imaging of animal kinematics, analysis of integrated image differences revealed that spiking during ant movement increased with the developmental phase. Greater burial depth and saturation resulted in fewer and lower magnitude spikes. We verified that spiking correlated with movement via quasi-2D experiments. This straightforward method, involving a laser and digital camera, can be applied to laboratory and potentially field situations to gain insight into subterranean organism activities. 

Much of the Earth and many surfaces of extraterrestrial bodies are composed of non-cohesive particulate matter. Locomoting on such granular terrain is challenging for common robotic devices, either wheeled or legged. In this work, we discover a robust alternative locomotion mechanism on granular media-generating movement via self-vibration. To demonstrate the effectiveness of this locomotion mechanism, we develop a cube-shaped robot with an embedded vibratory motor and conduct systematic experiments on granular terrains of various particle properties and slopes. We investigate how locomotion changes as a function of vibration frequency/intensity on such granular terrains. Compared to hard surfaces, we find such a vibratory locomotion mechanism enables the robot to move faster, and more stably on granular surfaces, facilitated by the interaction between the body and surrounding grains. We develop a numerical simulation of a vibrating single cube on granular media, enabling us to justify our hypothesis that the cube achieves locomotion through the oscillations excited at a distance from the cube’s center of mass. The simplicity in structural design and controls of this robotic system indicates that vibratory locomotion can be a valuable alternative way to produce robust locomotion on granular terrains. We further demonstrate that such cube-shaped robots can be used as modular units for vibratory robots with capabilities of maneuverable forward and turning motions, showing potential practical scenarios for robotic systems. 

This review focuses on how the modeling of dense granular media has advanced over the last 15 years. The jumping-off point of our review is the μ( I) rheology for dry granular flow, which opened the door to generic flow field modeling but was primarily geared toward problems involving small monodisperse grains of simple shapes. Our review focuses on advances in modeling more material types and behaviors including new approaches for modeling finite-grain-size effects or nonlocality, polydispersity and unmixing, and nontrivial grain shapes. We also discuss growing application areas with tractable order-reduction strategies with a focus on intrusion and locomotion problems.