A bio-robotic platform for integrating internal and external mechanics during muscle-powered swimming

Christopher T Richards,Christofer J Clemente

doi:10.1088/1748-3182/7/1/016010

Abstract

To explore the interplay between muscle function and propulsor shape in swimming animals, we built a robotic foot to mimic the morphology and hind limb kinematics of Xenopus laevis frogs. Four foot shapes ranging from low aspect ratio (AR = 0.74) to high (AR = 5) were compared to test whether low-AR feet produce higher propulsive drag force resulting in faster swimming. Using feedback loops, two complementary control modes were used to rotate the foot: force was transmitted to the foot either from (1) a living plantaris longus (PL) muscle stimulated in vitro or (2) an in silico mathematical model of the PL. To mimic forward swimming, foot translation was calculated in real time from fluid force measured at the foot. Therefore, bio-robot swimming emerged from muscle–fluid interactions via the feedback loop. Among in vitro-robotic trials, muscle impulse ranged from 0.12 ± 0.002 to 0.18 ± 0.007 N s and swimming velocities from 0.41 ± 0.01 to 0.43 ± 0.00 m s−1, similar to in vivo values from prior studies. Trends in in silico-robotic data mirrored in vitro-robotic observations. Increasing AR caused a small (∼10%) increase in peak bio-robot swimming velocity. In contrast, muscle force–velocity effects were strongly dependent on foot shape. Between low- and high-AR feet, muscle impulse increased ∼50%, while peak shortening velocity decreased ∼50% resulting in a ∼20% increase in net work. However, muscle-propulsion efficiency (body center of mass work/muscle work) remained independent of AR. Thus, we demonstrate how our experimental technique is useful for quantifying the complex interplay among limb morphology, muscle mechanics and hydrodynamics.

Highlights

The mechanics of aquatic locomotion is a rich field for both engineers and biologists
We explored a question that is difficult to address with conventional methods: how does fin morphology influence the muscle mechanical requirements for swimming? Aspect ratio (AR = fin span2/fin area) is a key descriptor of fin shape and an important determinant of fluid-dynamic performance (Vogel 1981, Combes and Daniel 2001, Dong et al 2006)
Bio-robot swimming velocity (m/s) generated enough force to accelerate the foot in rotation causing a steep increase in hydrodynamic force

Summary

Introduction

The mechanics of aquatic locomotion is a rich field for both engineers and biologists. Engineers have shown great interest in fish fin motion Engineering approaches inform biologists, using robotic (e.g. Tangorra et al 2007) or mathematical models (e.g. Daniel and Meyhofer 1989, Tytell et al 2010), to measure parameters (e.g. fluid dynamic or muscle force) which are difficult to measure in vivo. Despite shared motivations to understand aquatic propulsion, neither field has fully characterized how external properties (e.g. fin shape) couple to musculoskeletal properties to confer effective swimming. Despite the diversity of propulsor morphology in fishes (Thorsen and Westneat 2005) and frogs (Goldberg and Fabrezi 2008), little is known about the influences of fin morphology on muscle mechanical output and hydrodynamic performance. We lack experimental tools for testing muscle contraction dynamics

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