Extremely Deformable Structures

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Extremely Deformable Structures

Unlike most soft robots currently under development, the Softworms do not rely on pneumatic or fluidic actuators but are electrically powered and actuated using either shape-memory alloy microcoils or motor tendons, and they can be modified to accept other muscle-like actuators such as electroactive polymers.

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The technology is extremely versatile, and different designs can be quickly and cheaply fabricated by casting elastomeric polymers or by direct 3D printing. Softworms can crawl, inch or roll, and they are steerable and even climb steep inclines. Softworms can be made in any shape but here we describe modular and monolithic designs requiring little assembly. These modules can be combined to make multi-limbed devices. We also describe two approaches for controlling such highly deformable structures using either model-free state transition-reward matrices or distributed, mechanically coupled oscillators.

To decouple one rotation from the other, the nylon lines that drive the fin rays pass through the center of the cylinder, and are routed to the servomotors through mandrel-bent tubes. Curvature of the fin ray is modulated using a nylon line that runs along the length of a fin ray and terminates at the fin ray's tip Phelan et al. The line is tensioned using either a dedicated servomotor or an SMA wire.

An advantage of the servomotor is that it can tension the tendon along a continuum, whereas the SMA is difficult to control except in a binary—tensioned or not tensioned—fashion.

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A disadvantage to the servomotor is that it affects the sweep of the fin ray when it tensions the line used to control curvature. In contrast, the SMA can be placed along the length of the fin ray, in parallel or in lieu of the nylon line, so that it does not interfere with the sweep motions. The positioning of the drive mechanisms, and the angle at which each fin ray is attached to its base, are arranged so that the fin naturally cups about its spanwise axis as it is swept forward.

Deformable and elastic tensile-integrity structure

This is the fundamental movement underlying steady swimming. The in-plane rotation allows for significant deviation from the cupping motion. For example, the entire fin can be rotated, expanded, or collapsed in area, and coordination of the sweep and in plane rotation enables sweep to occur with nearly no cupping Fig. To trust that results had relevance to the biological system, the biorobotic fins were validated as models by comparing their motions, forces, and flows against those of the biological fins and of the CFD simulations.

Since the robotic fins had not been designed to replicate the biological fins, it was not necessary for them to perform exactly as the biological fin. However, it was very important that they exhibit the dynamic movements that are essential to the production of forces and to create forces and flows that had the key features of the biological profiles. Although the robotic fins used purely passive fin rays and were driven with trajectories derived from just a few of the underlying modes, the fins exhibited the complex bending and curvatures of the biological fins Fig.

The magnitude of the forces created by the fins did not always match the magnitudes predicted by CFD exactly, but properly tuned pectoral fins did create peaks of thrust during the steady swimming outstroke and instroke Fig. Motions were compared visually A and B and using the 3D coordinates C and D of the biological left in panel and robotic fins right in panel as the fin executed its beat. Similar to the biological fin during steady swimming, the robotic fin produced thrust throughout the fin beat, lift during the outstroke, and a downward force during the instroke E.

Forces are shown for the pectoral fin flapping at a frequency of 1. To help understand the strategies that fish can use to modulate propulsive forces, experiments were conducted with the biorobotic fins to determine the effects of kinematic patterns and of flexural rigidity of the fin ray on the force exerted by the fin. These flexural rigidities were selected so that the larger, five-ray robotic fins would bend like the biological fin when moved through the water. This scaling is presented in detail by Tangorra et al.

The pectoral fins were flapped at frequencies from 0. Steady swimming gaits were tested over the full range of conditions and yaw-turn maneuvers were tested over a reduced, but still large, range of conditions. Biorobotic caudal fins with six independent fin rays and flexural rigidities scaled to , , , and times those of the biological fins were evaluated at flapping frequencies of 0.

For all patterns except the rolling motion, the fin rays followed sinusoidal trajectories and were swept through the same amplitudes. In the flat pattern, there was no difference in phase among the fin rays. For the rolling motion, all fin rays moved sinusoidally and in phase, but the amplitude of the sinusoid decreased linearly from the dorsal to the ventral fin ray.

Two of the five caudal fin patterns. A symmetric cupping A and B and an asymmetric undulation C and D as executed by the fish left and the robotic caudal fin right. The robotic fins were supported from an air-bearing carriage that was mounted above the tank.

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The carriage allowed the fins to swim freely against the flow, and could be locked against force transducers so that forces could be measured in two directions. Pectoral fins were oriented so that thrust and lateral force and thrust and lift forces were measured. The caudal fin was oriented so that thrust and lift forces were measured. Changes to the kinematics of the fin included switching the gait, making less extreme changes to the trajectories or to the phase relationships of the fin rays within a gait, and altering the frequency at which the fin was flapped.

For example, the motions of the pectoral fin during steady swimming and during the turn maneuver are quite different, and so were the resultant forces. In steady swimming, the fin is led by an upper and lower leading edge, cups about its spanwise axis, and bends back a great deal as it moves into the flow A beautiful vortex pattern is shed from the upper and lower leading edges Dong et al. This causes a strong lateral jet to be created and results in drag, which slows the fish and a large contralateral force which rotates the fish Gottlieb et al. The peak lateral force is nearly four times the peak drag force, whereas during steady swimming, the peak thrust and peak lateral forces are about equal.


During the instroke, thrust and an ipsilateral force are created which reorient the fish back towards the flow. Thrust horizontal and lift vertical forces for pectoral fins executing normal and modified steady-swimming gaits. Normal, full-fin steady swimming for three levels of stiffness A. Mean values of the force during the outstroke and instroke B. Forces from the fin when a linearly increasing lag in phase was used for subsequent rays C and D. Forces from the individual dorsal E and ventral F halves when the other half was held still. The forces can be moved around the thrust-lift space without switching the underlying gait pattern by altering the stiffness and the coordination of the fin rays.

For example, rather than driving the fin rays synchronously in phase as in normal steady swimming, the fin rays were driven out of phase to create an undulatory motion. This undulatory motion looked very different from the normal cupping and sweep motion, and redirected fin forces so that a great amount of lift and a net drag was created Fig. The undulation could also be led by ventral most fin ray, which resulted in a strong downward force and a net thrust Fig. Smaller differences in phase between fin rays resulted in less significant changes to the baseline forces of steady swimming.

Altogether, this demonstrates that steady-swimming forces can be shaped and moved throughout the thrust-lift plane without switching gait patterns, but by adjusting the coordination of the fin rays within an underlying gait pattern. The asymmetrical shape of the fin causes the dorsal half—which is longer and has greater area—to dominate the production of force. To prevent the fin rays from fracturing or the opposing half of the fin from being pulled into the flow, the isolated dorsal and ventral halves were swept through a smaller displacement than was the full fin.

This was an experiment that would have been very difficult to conduct with real fish. The forces produced by the dorsal half of the fin were qualitatively similar to the forces produced when the entire fin was flapped Fig. Thrust was produced during both the outstroke and the instroke, but in contrast to the full fin, in the majority of trials the magnitude of the thrust during the outstroke was greater than during the instroke.

Despite the limited displacement of the fin, the thrust and the lift created by the dorsal half of the fin during the outstroke were similar in magnitude to those created by the full fin.

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However, the thrust and lift produced during the instroke were significantly smaller in magnitude. Like the full fin, the combined thrust and lift from the dorsal half would have the tendency to drive the fish upward and forward during the outstroke, and downward and forward during the instroke. The ventral half of the fin created a small amount of drag and negative lift during the outstroke, and created thrust and lift during the instroke.

With the exception of the thrust during the instroke, the forces from the ventral half of the fin were opposite to the forces created by the dorsal half of the fin. If operated alone, the ventral half of the fin would have the tendency to move the fish downward and slightly back during its outstroke followed by upward and forward during its instroke. This is exactly what was observed for the yaw-turn maneuver, during which the ventral half of the fin led much of the movement.

Although caudal fins have often been modeled simply as foils that oscillate back and forth, similar to the pectoral fin, the caudal fin exhibits a wide range of motions and these motions produce significantly different force profiles. In general, the symmetric motions produced a peak of thrust as the fin passed the midline of the robot-fish's body Fig. The magnitude of the thrust dropped and became drag as the fin slowed at the end of the fin beat and changed direction.

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  7. Lift forces were very small relative to the thrust, and, as expected, were on average, zero. The asymmetric motions produced a thrust profile that was similar to thrust for the symmetric motions, but in contrast to the symmetric motions, they also produced lift Fig. For example, when the undulation was led by the dorsal-most fin ray, peaks of lift were created that could be as strong as the thrust. The magnitude of the lift, relative to the thrust, could be adjusted by altering the phase difference between the fin rays, and the direction of the lift could be shifted to negative by leading with the ventral ray.

    Caudal fin forces. Lift and thrust from a caudal fin flapped at 1. Forces are shown for one cycle of the cupping profile A and C and for the undulation B and C. Mean values for fins with different levels of stiffness are shown in D. The magnitude changes with stiffness but the direction of the average force vector changes little.

    As long as a fin was flapped sufficiently fast to cause an appropriate dynamic interaction with the fluid, forces tended to increase with increases in the frequency of flapping and with decreases in the speed of flow. An interesting phenomenon was observed in several of the datasets. At the highest frequencies of flapping, forces decreased. This is believed to have been caused by the flexible fins behaving like a well-damped, low pass system [1]. This response was most evident in the caudal fin. Unfortunately, this behavior occurred at frequencies near the upper limit of the servomotors and so could not be evaluated thoroughly.

    Studies conducted with flapping ribbons Lauder et al.

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    Perhaps the most interesting results detailed the importance of structural properties of the fin ray for creating the appropriate propulsive forces, and demonstrated that significant changes to both the magnitude and the direction of the force could be made by actively altering the stiffness of the fin rays. The relationship between fin force and flexural rigidity of the fin ray is discussed in detail for the pectoral fin by Tangorra et al.

    Although the patterns traced by the force vector over the course of the fin beat looked similar as stiffness of the pectoral fin changed, the magnitude and direction of the forces changed. The average magnitude of the 2D force vector—thrust and lift combined Fig.

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    Extremely Deformable Structures Extremely Deformable Structures
    Extremely Deformable Structures Extremely Deformable Structures
    Extremely Deformable Structures Extremely Deformable Structures
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