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1. Closer Appendage Spacing Augments Metachronal Swimming Speed by Promoting Tip Vortex Interactions

   https://doi.org/10.1093/icb/icab112  

   Ford, Mitchell P ; Santhanakrishnan, Arvind ( May 2021 , Integrative and Comparative Biology)

   null (Ed.)

   Abstract Numerous species of aquatic invertebrates, including crustaceans, swim by oscillating multiple closely spaced appendages. The coordinated, out-of-phase motion of these appendages, known as “metachronal paddling,” has been well-established to improve swimming performance relative to synchronous paddling. Invertebrates employing this propulsion strategy cover a wide range of body sizes and shapes, but the ratio of appendage spacing (G) to the appendage length (L) has been reported to lie in a comparatively narrow range of 0.2 < G/L ≤ 0.65. The functional role of G/L on metachronal swimming performance is unknown. We hypothesized that for a given Reynolds number and stroke amplitude, hydrodynamic interactions promoted by metachronal stroke kinematics with small G/L can increase forward swimming speed. We used a dynamically scaled self-propelling robot to comparatively examine swimming performance and wake development of metachronal and synchronous paddling under varying G/L, phase lag, and stroke amplitude. G/L was varied from 0.4 to 1.5, with the expectation that when G/L is large, there should be no performance difference between metachronal and synchronous paddling due to a lack of interaction between vortices that form on the appendages. Metachronal stroking at nonzero phase lag with G/L in the biological range produced faster swimming speeds than synchronous stroking. As G/L increased and as stroke amplitude decreased, the influence of phase lag on the swimming speed of the robot was reduced. For smaller G/L, vortex interactions between adjacent appendages generated a horizontally oriented wake and increased momentum fluxes relative to larger G/L, which contributed to increasing swimming speed. We find that while metachronal motion augments swimming performance for closely spaced appendages (G/L <1), moderately spaced appendages (1.0 ≤ G/L ≤ 1.5) can benefit from the metachronal motion only when the stroke amplitude is large. 

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2. A new propulsion enhancement mechanism in metachronal rowing at intermediate Reynolds numbers

   https://doi.org/10.1017/jfm.2023.739  

   Lionetti, Seth ; Lou, Zhipeng ; Herrera-Amaya, Adrian ; Byron, Margaret L. ; Li, Chengyu ( November 2023 , Journal of Fluid Mechanics)

   Metachronal rowing is a biological propulsion mechanism employed by many swimming invertebrates (e.g. copepods, ctenophores, krill and shrimp). Animals that swim using this mechanism feature rows of appendages that oscillate in a coordinated wave. In this study, we used observations of a swimming ctenophore (comb jelly) to examine the hydrodynamic performance and vortex dynamics associated with metachronal rowing. We first reconstructed the beating kinematics of ctenophore appendages based on a high-speed video of a metachronally coordinated row. Following the reconstruction, two numerical models were developed and simulated using an in-house immersed-boundary-method-based computational fluid dynamics solver. The two models included the original geometry (16 appendages in a row) and a sparse geometry (8 appendages, formed by removing every other appendage along the row). We found that appendage tip vortex interactions contribute to hydrodynamic performance via a vortex-weakening mechanism. Through this mechanism, appendage tip vortices are significantly weakened during the drag-producing recovery stroke. As a result, the swimming ctenophore produces less overall drag, and its thrust-to-power ratio is significantly improved (up to 55.0 % compared with the sparse model). Our parametric study indicated that such a propulsion enhancement mechanism is less effective at higher Reynolds numbers. Simulations were also used to investigate the effects of substrate curvature on the unsteady hydrodynamics. Our results illustrated that, compared with a flat substrate, arranging appendages on a curved substrate can boost the overall thrust generation by up to 29.5 %. These findings provide new insights into the fluid dynamic principles of propulsion enhancement underlying metachronal rowing.

    

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3. Hydrodynamics of Metachronal Motion: Effects of Spatial Asymmetry on the Flow Interaction Between Adjacent Appendages

   https://doi.org/10.1115/FEDSM2022-86967  

   Lou, Zhipeng ; Herrera-Amaya, Adrian ; Byron, Margaret L. ; Li, Chengyu ( August 2022 , ASME 2022 Fluids Engineering Division Summer Meeting)

   Metachronal motion is a unique swimming strategy widely adopted by many small animals on the scale of microns up to several centimeters (e.g., ctenophores, copepods, krill, and shrimp). During propulsion, each evenly spaced appendage performs a propulsive stroke sequentially with a constant phaselag from its neighbor, forming a metachronal wave. To produce net thrust in the low-to-intermediate Reynolds number regime, where viscous forces are dominant, the beat cycle of a metachronal appendage must present significant spatial asymmetry between the power and recovery stroke. As the Reynolds number increases, the beat cycle is observed to change from high spatial asymmetry to lower spatial asymmetry. However, it is still unclear how the magnitude of spatial asymmetry can modify the shear layers near the tip of appendages and thus affect its associated hydrodynamic performance. In this study, ctenophores are used to investigate the hydrodynamics of multiple appendages performing a metachronal wave. Ctenophores swim using paddle-like ciliary structures (i.e., ctenes), which beat metachronally in rows circumscribing an ovoid body. Based on high-speed video recordings, we reconstruct the metachronal wave of ctenes for both a lower spatial asymmetry case and a higher spatial asymmetry case. An in-house immersed-boundary-method-based computational fluid dynamics solver is used to simulate the flow field and associated hydrodynamic performance. Our simulation results aim to provide fundamental fluid dynamic principles for guiding the design of bio-inspired miniaturized flexible robots swimming in the low-to-intermediate Reynolds number regime.

    

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4. Mantis Shrimp Locomotion: Coordination and Variation of Hybrid Metachronal Swimming

   https://doi.org/10.1093/iob/obad019  

   Hanson, S. E. ; Ray, W. J. ; Santhanakrishnan, A. ; Patek, S. N. ( June 2023 , Integrative Organismal Biology)

   Across countless marine invertebrates, coordination of closely spaced swimming appendages is key to producing diverse locomotory behaviors. Using a widespread mechanism termed hybrid metachronal propulsion, mantis shrimp swim by moving five paddle-like pleopods along their abdomen in a posterior to anterior sequence during the power stroke and a near-synchronous motion during the recovery stroke. Despite the ubiquity of this mechanism, it is not clear how hybrid metachronal swimmers coordinate and modify individual appendage movements to achieve a range of swimming capabilities. Using high-speed imaging, we measured pleopod kinematics of mantis shrimp (Neogonodactylus bredini), while they performed two swimming behaviors: burst swimming and taking off from the substrate. By tracking each of the five pleopods, we tested how stroke kinematics vary across swimming speeds and the two swimming behaviors. We found that mantis shrimp achieve faster swimming speeds through a combination of higher beat frequencies, smaller stroke durations, and partially via larger stroke angles. The five pleopods exhibit non-uniform kinematics that contribute to the coordination and forward propulsion of the whole system. Micro-hook structures (retinacula) connect each of the five pleopod pairs and differ in their attachment across pleopods—possibly contributing to passive kinematic control. We compare our findings in N. bredini to previous studies to identify commonalities across hybrid metachronal swimmers at high Reynolds numbers and centimeter scales. Through our large experimental dataset and by tracking each pleopod's movements, our study reveals key parameters by which mantis shrimp adjust and control their swimming, yielding diverse locomotor abilities.

    

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5. Directionally Compliant Legs Enabling Crevasse Traversal in Small Ground‐Based Robots

   https://doi.org/10.1002/aisy.202200258  

   Lathrop, Emily ; Tolley, Michael T. ; Gravish, Nick ( January 2023 , Advanced Intelligent Systems)

   Small ground‐based robots show promise for locomotion on complex surfaces. A critical application area for such robots is movement over complex terrain and within constricted space such as narrow gaps in rubble. To contend with this terrain complexity, robots typically require high degree‐of‐freedom (DOF) limbs. However, for small robot platforms, this approach of high DOF legs is impractical due to actuator limitations. This presents an opportunity to design robots whose morphology enables the outsourcing of computational tasks to the robot body through the use of compliant elements (morphological computation). Herein, a novel robot appendage is developed that can passively compress in a programmed direction in response to environmental constrictions. A robot equipped with these appendages can enter narrow spaces down to 72% of the robot's sprawled body width as well as low ceilings down to 68% its freestanding height. The robot is able to step onto and over small terrain features ( hip height) and navigate various natural terrain types with ease. The results show that these compressible appendages enable versatile robot locomotion for robot exploration in previously unmapped environments.

    

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