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First published online August 9, 2007
Journal of Experimental Biology 210, 2767-2780 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.000265

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Fish biorobotics: kinematics and hydrodynamics of self-propulsion

George V. Lauder^1,*, Erik J. Anderson², James Tangorra³ and Peter G. A. Madden¹

¹ Museum of Comparative Zoology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA
² Department of Engineering, Grove City College, 100 Campus Drive, Grove City, PA 16127, USA
³ Bioinstrumentation Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

View larger version (102K): [in this window] [in a new window]   Fig. 1. (A,B) Bluegill sunfish Lepomis macrochirus, hovering in still water, and (C) snowy grouper Epinephelus niveatus skeleton, showing the positions of the major fins and their internal skeletal supports. The pectoral and pelvic fins are paired, while the dorsal, anal and caudal fins are median (midline) fins. The dorsal and anal fins of ray-finned fishes have internal skeletal supports (pterygiophores), which support musculature that moves the fin rays. Fin rays are labeled in yellow for the dorsal and anal fins. The caudal fin also has a complex series of intrinsic musculature that allows fishes to actively control tail conformation (Drucker and Lauder, 2001; Lauder, 1982; Lauder, 1989). Metal supporting elements for the grouper skeleton have been digitally removed for clarity.

View larger version (96K): [in this window] [in a new window]   Fig. 2. Motion of the pectoral fin in a bluegill sunfish (17 cm total length, L) during steady locomotion at 0.5 L s–1. Each row shows frames from simultaneous lateral, ventral and posterior digital videos (taken at 250 Hz) at three time intervals, 97 ms (A), 142 ms (B) and 174 ms (C), during a single pectoral fin beat. Yellow arrows indicate the major fin motions (smaller amplitude movements of the fin surface are not labeled with yellow arrows), the small red and blue arrows show the position of the upper (dorsal) and lower (ventral) pectoral fin edges respectively, and the green arrow shows the location of the `dimple' on the dorsal fin margin that forms as a wave of bending passes out along the fin from base to tip. The large blue arrows and dot in A show the direction of water flow, which is perpendicular to the page in the posterior view. Note the considerable twisting and bending of the fin, and the cupped shape as the upper and lower fin margins move away from the body at the same time (A: posterior view). The fin beat begins at time 0 ms. Scale bars, 1.0 cm.

View larger version (82K): [in this window] [in a new window]   Fig. 3. Hydrodynamic function of the pectoral fin in bluegill sunfish swimming at 0.5 L s–1, as seen in posterior view looking upstream. A laser-generated sheet of light illuminates a thin slice of water flow as well as the pectoral fin and body, which casts a shadow to the right. Laser light penetrates the translucent fin, allowing flow between the fin and the body to be quantified. Water flow in this figure is out of the page, toward the reader. Images were obtained from 500 Hz digital video. (A–C) Particle image velocimetry images showing the movement of the fin illuminated by the laser light sheet in relation to the body and position of the other fins. Duration of movement shown=0.48 s from panels A–C. Yellow arrows show the key fin movements: note the cupped fin shape in A and B. (D–F) Water flow patterns as a result of pectoral fin movement. This column is from a different sequence than the frames in the left column. Yellow arrows indicate water velocities (every other vector is shown), and the background color scheme is coded so that black color indicates free stream flow velocity (7 cm s–1), red color flow accelerated by the fin to greater than free stream velocity, and blue color showing flow slowed below free stream. Note that the pectoral fin accelerates flow on both the outstroke and return stroke (red color in E and F).

View larger version (116K): [in this window] [in a new window]   Fig. 4. Hydrodynamic analysis of the dorsal fin and caudal fin in swimming bluegill sunfish, to show that these two fins can act as dual flapping foils in series, and that flow leaving the dorsal fin can affect caudal fin function. The caudal fin of ray-finned fishes does not move through undisturbed free stream flow, but rather has its flow environment highly modified by upstream fins. The left panels show the laser-imaged dorsal fin and tail of a bluegill sunfish (16.5 cm L) swimming at 17 cm s–1; laser light illuminates from top to bottom in these images, and the dorsal fin and tail cast shadows toward the bottom. Yellow arrows in B show the left–right oscillatory motion of the dorsal fin and tail as seen from above. In the right panels these images are analyzed to show water flow velocities around the fins (vectors were not calculated in the fin shadows) and vorticity. The views shown in this figure are from above, looking down on the upper surface of the fish with the dorsal fin and tail (also see Fig. 1). In A, the dorsal fin has shed a clockwise vortex that is moving toward the tail. This vortex passes above the tail (B) while the dorsal fin sheds a new vortex of opposite sign on the return stroke. This pattern repeats as a clockwise vortex is just leaving the dorsal fin again (C). Note that flow in the gap between the dorsal fin and tail is nearly orthogonal to free-stream flow. Free-stream flow has been subtracted from the right panel images to reveal flow structure; images on the left have been contrast-enhanced.

View larger version (25K): [in this window] [in a new window]   Fig. 5. Schematic figure to illustrate two different categories of fish-like aquatic robot design and the measurements that might be made from each design. (A) Robot is attached to a sting (a rod holding the robotic model vertically from the carriage above) and either fixed in place while forces are measured on the sting, or towed at a fixed velocity on a moving carriage. In either case, the robot is not self-propelled, but rather moves at externally imposed speed. In this case, there need be no equality between thrust and drag forces, as it is not known if the robot is generating sufficient thrust to overcome drag. (B) Robot swims at a self-propelled time-averaged constant speed as a result of thrust generated by heave and pitch motions, and mean thrust force per cycle must equal the mean drag force. The flow speed in the tank is adjusted to a value, Ueq, where the robot propels itself at a constant equilibrium X position, termed Xeq. The robot is free to move itself upstream and downstream on a low friction air bearing system. Once Xeq is determined for a particular heave and pitch motion pattern during self-propulsion, the robot can be fixed in position at Xeq to measure forces and torques while the same motion pattern and flow speed used for self-propulsion are imposed. This allows force measurement under conditions identical to self-propulsion, when thrust and drag forces must be equal.

View larger version (122K): [in this window] [in a new window]   Fig. 6. Design of the self-propelled robotic pectoral fin with bilaminar fin rays. (A) Carriage that holds the robotic fin mounted above the flow tank on air bearings that allow horizontal translation in the X-direction with little friction. The pectoral fin can be seen submerged in the flow tank below the array of black actuating motors. (B) Base plate that holds the fin and compliant base support, and guides the nylon tendons to the fin rays. (C) Design of the base plate and the bilaminar fin rays that mimic the curvature control of fin rays in fin ray-finned fishes (Alben et al., 2007; Lauder, 2006). Note the two separate heads for each half of the fin ray, which receive separate nylon tendons. (D–G) Motion of the robotic pectoral fin from the rest position to show expansion, curling and cupping of the fin. Black lines have been drawn on the two leading edges of the fin to more clearly show the motion in F and G. Cupping, bending and expansion of the bluegill sunfish fin, as shown in Figs 2 and 3, are well replicated by the robotic model. Pectoral fin rest length=12.8 cm at the longest ray; fin width at base and tip is 5.5 cm and 8.0 cm, respectively. The base plate is 5.5 cmx8.5 cm. The fin rays vary from 9.0 cm to 12.5 cm long and the rays are 0.1 cm thick and 0.4 cm wide.

View larger version (9K): [in this window] [in a new window]   Fig. 7. Force in the X-direction (see Fig. 5) reflecting thrust and drag, measured from the robotic pectoral fin during a single fin beat under three different imposed movement patterns (shown in different colors). Robotic models of the pectoral fin allow analysis of the effects of different movement patterns in a way not possible with studies of live animals alone. When the fin executes a cupping motion only (black trace), a force curve with two distinct peaks is produced with no drag force at the transition from outstroke (abduction) to instroke (adduction). A cupping and sweeping motion (blue trace) generates considerably higher thrust forces as well as a small drag force during the transition. Moving the fin in sweep only (red trace), produces large drag forces on the outstroke and roughly equivalent thrust on the return stroke.

View larger version (136K): [in this window] [in a new window]   Fig. 8. Design of the self-propelled dual flapping foil robot to study fish fin function. (A) Carriage that holds the dual foils, with the heave and pitch motors for each foil mounted above the flow tank on air bearings that allow horizontal translation in the X-direction with little friction. This design feature is critical to allowing self-propulsion. In this image, the two foils are suspended above the flow tank. (B) Close view of the two foils (NACA 0012 in cross-sectional shape); the foils are 6.85 cm in chord length (width) and 19 cm high. (C) Close view of the pitch and heave motors for one foil mounted on the carriage and air bearing system.

View larger version (126K): [in this window] [in a new window]   Fig. 9. Hydrodynamics of the dual flapping foil robot, self-propelling at a speed of 53 cm s–1. The distance between the foils is fixed at 0.5 chord lengths. The two foils have been programmed to move in sinusoidal motion with a 140° phase lag difference between them and a period of 588 ms. The front foil has a 20° pitch amplitude and a 2.5 cm heave distance, while the rear foil moves with 30° pitch amplitude and a 3.5 cm heave distance. These parameters are similar to those established in experimental and computational studies of bluegill sunfish dorsal and anal fins (Akhtar et al., 2007; Drucker and Lauder, 2001). The left panels show the foils and water illuminated by a laser light sheet from top to bottom in these images; the foils cast shadows toward the bottom. Video sample rate was 500 Hz. In the right panel these images are analyzed to show water flow velocities and vorticity around the two foils (vectors were not calculated in the fin shadows), as in the previous analysis of the sunfish dorsal and anal fins (Fig. 4). A distinct thrust wake is visible at 0 ms. Notice how vorticity from Foil 1 impacts Foil 2 as it moves inline with the first foil at 110 ms (B). An attached leading edge vortex is visible on Foil 2 at 160 ms, enhanced by incoming vorticity from Foil 1. Note also that water flow in the gap between the two foils is nearly orthogonal to free stream flow at 0 and 160 ms, similar to flow patterns observed between the dorsal fin and tail in sunfish (Fig. 4). Every other vector is shown for clarity in the right column; images on the left have been contrast-enhanced.

View larger version (105K): [in this window] [in a new window]   Fig. 10. Hydrodynamics of a single, flexible, flapping foil self-propelling at a speed of 24 cm s–1. The white arrow shows the heave motion (3.5 cm heave amplitude) of the rod that actuates the flexible foil, composed of a plastic sheet of the same dimensions as the foils in Fig. 9. Foil thickness is 0.32 mm, foil length=19 cm, foil height=6.8 cm, and the video sample rate is 250 Hz. The left panels show the flexible foil and water illuminated by a laser light sheet from top to bottom; the flexible foil casts a shadow toward the bottom of each image; these images have been contrast-enhanced. Large yellow arrows in the left-hand panels show the direction of foil surface motion from one panel to the next. The actuating rod to which the foil is attached and the thin black foil itself have been enhanced by a white dot and line, respectively, for clarity. In the right panels these images are analyzed to quantify water flow velocities and vorticity around the flexible foil (vectors could not be calculated in the fin shadows), as in the previous analysis of two foil self-propulsion (Fig. 9). Note that an attached leading edge vortex (LEV) is visible at 0 ms as the foil leading edge nears the end of its downward motion and begins to move up. This attached LEV persists throughout the duration of the downstroke, until almost 930 ms (not shown). A distinct thrust wake is evident behind the flexible foil, with a strong side component.