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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. 

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as “serpenoid templates”). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization. 

The study of plant root growth in real time has been difficult to achieve in an automated, high-throughput, and systematic fashion. Dynamic imaging of plant roots is important in order to discover novel root growth behaviors and to deepen our understanding of how roots interact with their environments. We designed and implemented the Generating Rhizodynamic Observations Over Time (GROOT) robot, an automated, high-throughput imaging system that enables time-lapse imaging of 90 containers of plants and their roots growing in a clear gel medium over the duration of weeks to months. The system uses low-cost, widely available materials. As a proof of concept, we employed GROOT to collect images of root growth ofOryza sativa,Hudsonia montana, and multiple species of orchids includingPlatanthera integrilabiaover six months. Beyond imaging plant roots, our system is highly customizable and can be used to collect time- lapse image data of different container sizes and configurations regardless of what is being imaged, making it applicable to many fields that require longitudinal time-lapse recording. 

Limbless locomotors, from microscopic worms to macroscopic snakes, traverse complex, heterogeneous natural environments typically using undulatory body wave propagation. Theoretical and robophysical models typically emphasize body kinematics and active neural/electronic control. However, we contend that because such approaches often neglect the role of passive, mechanically controlled processes (those involving “mechanical intelligence”), they fail to reproduce the performance of even the simplest organisms. To uncover principles of how mechanical intelligence aids limbless locomotion in heterogeneous terradynamic regimes, here we conduct a comparative study of locomotion in a model of heterogeneous terrain (lattices of rigid posts). We used a model biological system, the highly studied nematode wormCaenorhabditis elegans, and a robophysical device whose bilateral actuator morphology models that of limbless organisms across scales. The robot’s kinematics quantitatively reproduced the performance of the nematodes with purely open-loop control; mechanical intelligence simplified control of obstacle navigation and exploitation by reducing the need for active sensing and feedback. An active behavior observed inC. elegans, undulatory wave reversal upon head collisions, robustified locomotion via exploitation of the systems’ mechanical intelligence. Our study provides insights into how neurally simple limbless organisms like nematodes can leverage mechanical intelligence via appropriately tuned bilateral actuation to locomote in complex environments. These principles likely apply to neurally more sophisticated organisms and also provide a design and control paradigm for limbless robots for applications like search and rescue and planetary exploration.