Mechanical Intelligence Simplifies Control in Terrestrial Limbless Locomotion

TL;DR

This study provides insights into how neurally simple limbless organisms like nematode worm Caenorhabditis elegans can leverage mechanical intelligence via appropriately tuned bilateral actuation to locomote in complex environments.

Abstract

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 worm Caenorhabditis 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 in C. 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.

Figures (22)

• Figure 1: Biological and robophysical limbless systems for understanding mechanical intelligence. (A) Nematode Caenorhabditis elegans, the biological model of this study (image credit: Ralf J. Sommer), along with a cross-sectional anatomy (reproduced from WormAtlas) showing two pairs of bilaterally activated muscle bands. (B) The limbless robophysical model, implementing a bilaterally actuation mechanism. (C) Schematics of body postures and muscle activities over one gait period in the biological model. (D) Schematics of body postures and cable activities over one gait period in the robophysical model. (E) A nematode moves on a slice of the rotten peach, a rheologically complex natural environment. (F) The robophysical model locomotes on a pile of rocks, a rheologically complex natural environment. (G) Biological and robophysical locomotion in comparable laboratory terrestrial environments: (i) lattices, (ii) granular media, and (iii) narrow channels.
• Figure 2: Nematode kinematics and performance imply the role of mechanical intelligence. (A) Overlaid snapshots, effective body curvature, gait paths in the shape space, the first two dominant modes (solid lines are the principal components and dashed lines are the best fits to $\sin$ and $\cos$ shape bases) of nematode locomotion in laboratory environments with varied pillar density. (B) Locomotion speed (wave efficiency $\eta$) as a function of obstacle density (measured as the ratio of body length and obstacle spacing $L/d$) for nematodes. Error bars represent standard deviations. Error bars represent SDs (n = 26 individuals in open and sparse lattices, n = 20 individuals in the medium lattice, and n = 24 individuals in the dense lattice).
• Figure 3: Programmable and quantifiable body compliance in the robophysical model. Three representative compliant states of the robophysical model under varied generalized compliance $G$: (A) bidirectionally non-compliant, (B) directionally compliant and (C) bidirectionally compliant. The first column illustrates schematics of cable activation, where red cables are shortened whereas blue cables are lengthened. The second column shows how cables are lengthened at varied suggested angles according to the control scheme, where solid lines represent implemented cable lengths whereas dashed lines represent "exact" lengths of cables to form the suggested angle. The third column shows how much a feasible emergent angle $\zeta$ (yellow region) is allowed to deviate from the suggested angle $\alpha$ (dashed line), where solid blue and red lines represent upper and lower boundaries of $\zeta$. The last column shows the how much a feasible emergent gait path in the shape space (yellow region) is allowed to deviate from the suggested circular gait path (dashed line), where solid blue and red lines represent outer and inner boundaries of feasible emergent gait paths.
• Figure 4: Open-loop robot performance reveals the importance of mechanical intelligence. (A) Overlaid snapshots, emergent joint angles, gait paths in the shape space and shape basis of robophysical locomotion ($G=0.75$) in laboratory environments with varied obstacle density. (B) Locomotion speed (wave efficiency $\eta$) of the robophysical model as a function of generalized compliance $G$ in environments with varied obstacle density (open, sparse, medium and dense). Error bars in represent SD across three repetitions per experiment. (C) Comparison of locomotion speed as a function of obstacle density between the biological model C. elegans (reproduced from Fig. 2B) and the robophysical model with $G=0.75$, accompanied with example time traces of splined points along the body as the nematode and the robophysical model move in the open and dense environments (insets). Error bars represent the SD across three repetitions per experiment.
• Figure 5: Force-deformation characterization for the robophysical model. (A) External force versus emergent joint angle curves that show behaviors of a joint reacting to external forces under different compliance states. (B) Force-deformation maps of the robophysical model with varied $G$ that show the robophysical model body compliance can be programmatically tuned.