Abstract— The remarkable swimming abilities of bony fish are the result of multiple interacting subsystems, each tuned to perform certain roles. These subsystems, which include the statically unstable body, multiple highly actuated fins, oscillatory neural controllers, and distributed senses, are not often studied as mutually dependent systems. This research program is developing biorobotic models of these systems and integrating the systems into a biorobotic fish so that interdependencies can be explored during free swimming. The robot body was derived from a bluegill sunfish, and has a tunable mass distribution and a mixture of rigid and flexible sections so that dynamical characteristics of the fish body can be explored. Five highly deformable fins have structural properties scaled to those of biological fins and can create gait patterns for steady swimming and maneuvers. A first generation artificial CPG has been programmed for each fin on a network of five low power microcontrollers. Finally, a dedicated biorobotic pectoral fin has been developed and instrumented with distributed sensory systems so relevant physical (e.g., fin curvature) and hydrodynamic (e.g., pressure) data can be identified and used to predict fin force for closed loop control.

I. INTRODUCTION IOROBOTIC models of the bluegill sunfish (Lepomis macrochirus) locomotor and sensorimotor systems are

being developed to experimentally investigate the interplay of multi-fin mechanics, sensing and control (Fig. 1). These are designed as subsystems of a robotic fish, and when integrated into a single system will enable the interdependencies of the systems to be explored during free swimming. The designs of these model systems are based on detailed studies of the anatomy and physiology of sunfish, and were evolved from biorobotic fins (Fig. 2) that have been used to investigate how fin-rayed fins create and modulate forces [1-4]. The body and fins of the robotic fish have been designed so that as the robotic fish swims and maneuvers it creates forces, fluid flows, and physical

Manuscript received March 28, 2011. This work was supported in part

by ONR N00014-09-1-0352 and by NSF EFRI 0938043. J. L. Tangorra is with the Laboratory for Biological Systems Analysis ,

Drexel University, Philadelphia, PA 19104 USA (ph 215-895-2993, fax 215-895-1468, tangorra@coe.drexel.edu)

A.P. Mignano is with the Laboratory for Biological Systems Analysis, Drexel University, Philadelphia, PA 19104 USA (apm49@drexel.edu).

G.N.Carryon is with the Laboratory for Biological Systems Analysis, Drexel University, Philadelphia, PA 19104 USA (gcarryon@drexel.edu).

J.C.Kahn is with the Laboratory for Biological Systems Analysis, Drexel University, Philadelphia, PA 19104 USA (jck83@drexel.edu).

movements that closely approximate those of the sunfish. This is crucial for creating the physical and sensory information required to understand the coupling of locomotor mechanics and sensory processing [5].

The bluegill sunfish (Fig. 1) was selected as our biological model because it is representative of a large class of bony fish (Teleostei) that use multiple fins and multiple swimming gaits, and that integrate a great deal of sensory information to swim with extraordinary agility across a wide range of fluidic conditions. Swimming forces are created through a dynamic interaction between the fish body, the fluid, and seven highly deformable fins. The fish controls the magnitude and direction of the hydrodynamic forces by manipulating the kinematics and mechanical properties of the bony fin rays within each of its fins [1]. Although multi-fin swimming may seem complicated by engineering standards, the fish directs the activity of the hundreds of muscles that control its fins and body using networks of a relatively small group of neurons (central pattern generators) that require little direct input from higher brain processes [6]. Stroke by stroke differences that occur in fin behavior suggests strongly that the fins are under closed loop control, and that information from sensory systems that are extrinsic (visual, vestibular, lateral line) and potentially intrinsic

Biologically Derived Models of the Sunfish for Experimental Investigations of Multi-Fin Swimming

James L. Tangorra, Member IEEE, Anthony P. Mignano, Gabe N. Carryon, Jeff C. Kahn, Jr.

B

Fig. 2. Biorobotic models of the sunfish pectoral (A, B) and caudal fins (C, D, E)

Fig 1. Bluegill sunfish with fins extended during hover (A). Biorobotic model of sunfish with five fin-rayed fins hovering in water tank (B). The sunfish pelvic fins are not modeled.

2011 IEEE/RSJ International Conference onIntelligent Robots and SystemsSeptember 25-30, 2011. San Francisco, CA, USA

978-1-61284-456-5/11/$26.00 ©2011 IEEE 580

(mechano- and proprio-ceptors) to the fins is used to modify the output of the CPGs.

An underlying premise of this research is that the remarkable performance of a biological organism is not due to the superior performance of any single system, but rather the collective behavior of interdependent, highly-specialized subsystems. Thus, to fully understand how the fish achieves its extraordinary swimming behaviors, the performance of the fins, the dynamics of the body, and the behaviors of the senses and neural controllers must be considered together. To do this, the biorobotic models of these systems will be studied under natural swimming conditions so that systems receive the stimuli to which the biological systems evolved to respond, and so that important interactions among the subsystems are stimulated [7, 8].

This manuscript will focus on presenting designs for a multi-fin biorobotic fish, a neural oscillator based controller, and an instrumented biorobotic pectoral fin for sensory investigations. A brief summary of the biology behind each system is provided at the beginning of each section. Design and experimental results for all systems are presented.

II. DESIGN OF BIOROBOTIC FISH

A. Multi-fin swimming Sunfish swim and maneuver using patterned locomotor

gaits [9, 10] that involve orchestrated movements of seven fins and a flexible tail (Fig. 1). The roles of the fins change with gait, and the motions of the fin rays within a pattern alter when the fluid environment changes [11, 12]. Swimming forces at low speeds are produced primarily by the pectoral fins [11, 13], with the ventral fins being recruited at higher speeds and during accelerations and maneuvers [14]. Although swimming appears effortless, the fish's body is unstable and negatively buoyant [11, 15], indicating that the fish may trade the effort required to actively maintain position and orientation for increased maneuverability.

B. Design of biorobotic fish The biorobotic fish (Fig. 1, B) is designed to serve as

an experimental platform from which to investigate the mechanics, sensing and control used in multi-fin swimming. In order to investigate the complex interplay between the sunfish body, the fins, and the surrounding fluid, it is important to capture and synthesize physical characteristics of the sunfish while still allowing for the parametric manipulation necessary for experimentation. The robot is comprised of: 1) a modular body that approximates the mechanics and hydrodynamics of multi-fin swimming and that generates similar fluidic responses; 2) five fin-rayed fins that execute steady swimming and maneuvering gaits; 3) a network of microcontrollers joined via a Controller Area Network (CAN) bus for decision making and for driving fin and body motions; and 4) a distributed sensor system for sensing body movement and hydrodynamic interactions of the fins and body.

The body of the robotic fish was modeled directly from the body of a 140 mm long bluegill sunfish which was used

to create a parameterized surface model of the fish body and of fin insertions (Pro/Engineer, PTC, Needham, MA). This parameterization allows the robot’s dimensions, and relationships between coupled dimensions, to be easily manipulated, while still eliciting biologically relevant hydrodynamics and kinematics. The model was scaled to increase internal volume and allow more flexibility in the choice of actuators and sensors as the experimental requirements develop with research.

The water-tight body is divided transversely into five modular sections; a head, pectoral, middle, tail and peduncle section. This allows for individual sections to be designed for a specific function (e.g., to house a sensor), and for modules to be altered without requiring modification of the entire system. In the current design, the head houses sensors and auxilliary electronics. The pectoral section is sub-divided into dorsal and ventral halves. The dorsal half houses a microcontroller for supervisory control and data acquisition and the ventral half provides a rigid platform for the pectoral fins. The actuators and control electronics for the pectoral fins are located in the middle section. This section also has connections for the umbilical cord (for power and control signals) and mounts for attachment to a rigid mast for testing. The dorsal and anal fins are attached to the tail section, which also houses these fins’ actuators and controllers, and additional weight compartments. The tail also houses the caudal fin’s actuators and controllers, and is currently rigid, but can be made flexible so that it can be actuated to undulate like the biological fish. The peduncle contains the base for caudal fin (Fig. 3, D).

The locations of the robot’s center of mass (CM) and center of buoyancy (CB) can be adjusted, by distributing weights throughout cavities within the individual body sections (Fig. 4), to tune its stability and buoyancy. The robot is currently configured with the CM below the CB, such that the body is statically stable and neutrally-buoyant. As our understanding of body dynamics improves, the distance between the CM and the CB can be reduced and eventually inverted, which will make the system want to flip upside down. This ability will be used to explore the interdependencies of dynamic instability of the body and its maneuverability/controllability.

Sensors (described in Section IV) are placed on the body surface and internally to measure changes body orientation and the surrounding fluid flow. This information will be used to augment our understanding of fin-fin and fin-body interactions. The head section contains an inertial measurement unit (IMU) that represents the vestibular sense of the fish (SEN-10010, Sparkfun Electronics, Boulder, CO) [16]. Pressure sensors can be placed within grooves along

Fig. 3. Close-ups of biorobotic system showing the left pectoral fin base (A), the hard and soft dorsal fin rays (B), sensor grooves (C), and the peduncle with caudal fin rays (D).

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the lateral surfaces of the middle section. The grooves are located in regions where fluidic pressures have been shown experimentally to correlate with fin forces [4].

The current robotic fish swims using five active fins (two pectoral fins, the caudal, anal, and dorsal fins) and two passive pelvic fins. Each of the fins is made of multiple fin rays (Fig. 3) covered in a polyester-elastane (84%/16%) webbing. The pectoral fin geometry is based on the sunfish pectoral girdle and is designed so that the fins cup about their spanwise axes when they are swept forward [17]; which an essential feature of the steady-swimming gait. The caudal fin has a curved base with fin-rays in the sagittal plane (Fig. 3, D) such that it also cups along its spanwise axis, and is capable of performing several gait patterns, including undulation and cupped-sweeping. The anal fin and the active portion of the dorsal fin have similar geometry and can be actuated laterally. The hard dorsal fin in a sunfish is predominately a control surface and in the robot it is not actuated laterally, but can be fixed flat along the dorsal edge of the body or expanded to investigate its effect on propulsive performance and maneuvers.

Fin ray lengths is scaled the same as the body, and as described in [1], the cross sections of the fin rays taper from base to tip so that they exhibit a scaled flexural rigidity and distributed bending along their axis. This allows the fins to bend like the biological fins as they are flapped through the water. Each fin ray is connected to a hinge and is driven by a dedicated servomotor. This gives each fin ray a single degree of actuated freedom (Fig. 3, B, D) which is sufficient for steady swimming and some maneuver gaits. Subsequent generations of the robotic fish will incorporate multi-DOF actuated fins as described in [2, 4], that can emulate multiple gait patterns observed in the sunfish. Each fin-ray is actuated by low-friction, stainless steel wire rope routed through a length of flexible nylon conduit in a pull-pull configuration. The fixed length of conduit allows for flexibility in the relative placement of each fin ray and its associated servomotor while maintaining wire tension, which is necessary when considering a flexible body where the distances and positions of the fins and servomotors vary during movement.

Each fin is driven by an actuator module (Fig. 4) that includes servomotors and a microcontroller within a waterproof enclosure, with the wire tendons connecting the servomotors to the fin bases (Fig. 3, A). Fin microcontrollers and a central microcontroller communicate via a CAN bus. This common architecture was devised so that multiple configurations of fins could be introduced easily into the robotic system and to mimic the distributed neurological architecture of its biological counterpart. The distributed controllers also enable different configurations of neural controllers to be implemented as our understanding of the sunfish neuro-anatomy develops. The modularity of the system allows for the incorporation or replacement of different controllers while the rest of the electronic and mechanical architecture remains the same.

Currently, the modules use the open-source Arduino development platform, based on an 8-bit AVR microcontroller (ATmega328, Atmel Corp., San Jose, CA).

The Arduino was chosen because it is a small, but very versatile platform that is easy to program and use, with a large developer community for technical support. The ATmega328 has integrated hardware capabilities that can easily implement a bus network, analog-to-digital conversion for sensor integration, pulse-width modulation for servomotor control and integrated power circuitry to power peripheral integrated circuits. Each microcontroller has also been programmed to act as a motor driver, as needed, for direct PC control of the servomotors. In this way, new control schemes and fin motions can be more easily tested using MATLAB and the greater processing power of a PC microprocessor before porting them to the on-board microcontroller for self-contained control.

Initial swimming trials involved the pectoral fins following a Fourier-series approximation of the steady-swimming gait with the body in a stable mass-buoyancy configuration (Fig. 1, B). With a statically stable body, the free-swimming robot was able to produce thrust during both phases of the steady swimming stroke. Active control of the three tails fins introduces difficulties with coordinating the moments of all of the fins on the CM. Future efforts will attempt to characterize these forces through the integration of distributed sensory systems (Section IV).

III. NEURAL OSCILLATOR BASED CONTROLLER

A. Central Pattern Generators Current neurobiological research in fish motor control

suggests that certain locomotor motions are driven by networks of rhythm producing neurons called central pattern generators (CPGs) [6]. CPGs consist of interconnected neurons, with excitatory and inhibitory connections, that produce oscillatory outputs which can be modified by sensory input corresponding to environmental changes.

The nonlinear differential equations used to model the behavior of neurons in CPGs ([18, 19]) exhibit several characteristics that make them attractive for use in robotics, such as stable limit cycles, distributed implementation,

Fig. 4. CAD rendering of biorobotic fish with mass distribution cavities circled and pectoral fin module boxed

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Several groups have used CPGs as controllers for aquatic

robots, typically incorporating paddle fins for propulsion

[20]. A few studies have implemented CPGs for fins

comprised of fin rays, notably the work of [21]. This work

focuses on implementing a CPG to control the motion of a

sunfish pectoral fin during low speed, steady swimming.

B. Design requirements and implementation of oscillator

model

For this work the CPG model is required to: 1) generate

approximations of the biological swimming gaits, 2) be

related to the neural anatomy so that so that knowledge

acquired about the architecture of fish CPGs can be

incorporated readily into the existing the mathematical

framework, 3) be able to change gait in response to

environmental and supervisory feedback, and 4) be

implemented on a microcontroller for use in the control of

the biorobotic fish.

The Matsuoka neural oscillator model was selected for our

initial CPG. The Matsuoka framework satisfied these design

criteria reasonably well, was a good framework from which

to understand how parameters affected gait, and has been

implemented successfully to drive numerous robotic systems

such as humanoid robots [22], six-legged cockroach-like

robots [23], and fish robots [20].

The basic Matsuoka CPG model is composed of two self-

inhibiting neurons excited by tonic input and connected by

reciprocal inhibition [24]. The Matsuoka model can be

extended to N interconnected neurons. In matrix form the

equations can be written as:

Where z is a column matrix of neuron states with elements:

x11 v11 x12 v12 ∙∙∙ xN1 vN1 xN2 vN2, in which xN1 represents the

membrane potential and vN1 represents the self-inhibition of

the Nth neuron. The term, τ, is a diagonal matrix with

diagonal elements: τ11 τ12 τ11 τ12 ∙∙∙ τN1 τN2 τN1 τN2 (all other

elements = 0), representing the time constants for membrane

potential and self-inhibition. The tonic input (TI in Figure 5)

to the network is represented by a diagonal matrix C, with

diagonal elements: C1 0 C1 0 ∙∙∙ CN 0 CN 0, and determines

the amplitude of the oscillator output [24]. The matrix

element β represents the fatigue rate of the Nth neuron. The

γ matrix elements represent the coupling weights between

neurons within the CPG network. The β and γ elements

affect the shape of the output waveform and can be

represented by sparse 4N by 4N matrices. The term [z]+ =

max(z,0). The neurons can respond to any number of

sensory feedback (SF in Figure 5) signals through the matrix

g and are weighted by the matrix H. The feedback terms are

structured to excite one neuron while inhibiting the other

[23]. The output of the oscillator is taken ass the difference

between the firing rates of each neuron [23]. This output

signal is mapped to a servo motor position in order to

generate the oscillatory behavior exhibited by the fins. For a

more detailed description of the Matsuoka model see the

work of [19, 22, 23].

The two neurons that make up each CPG can be

representative of an extensor and a flexor neuron pair. The

CPG coupling architecture was taken from [25] (Fig. 5), and

the architecture is arranged so that the extensor neuron of a

given CPG is coupled to the flexor neuron of its neighboring

CPGs. The coupling weights between these neurons are

varied to produce different gaits.

The Matsuoka equations were implemented on an

Arduino Duemilanove development board. The Matsuoka

equations were solved using the 4th order Runge-Kutta

method. Low-power, and computationally efficient,

microcontrollers are necessary as we aim to make the robot

autonomous. The Arduino’s capabilities, low cost, and

ubiquity within the robotics community made it a desirable

choice as a development board. The Arduino has a

maximum usable program memory of 30720 bytes and the

Matsuoka equations along with the Runge-Kutta

approximation take up 5272 bytes. The memory taken up by

one Matsuoka CPG suggests that up to five CPGs can be

stored on one Arduino. In the future, as the complexity of

the CPG architecture increases, we may reach the limits of

the computational power of the ATmega328.

Implementation on a field programmable gate array (FPGA)

may be necessary to support an autonomous system.

The oscillator produced trajectories that are reasonable

approximations of the steady swimming and undulation

motions exhibited by the sunfish (Fig. 6). During steady-

swimming the fin rays make a ―cupping‖ motion on the

outstroke, while on the instroke the fin rays align vertically

as they are pulled to the body, and each fin ray travels

through scaled versions of the same path. This made it

possible to drive four fin rays using one CPG with four

scaled output signals, thus reducing computational

workload. The CPG network is able to produce fin gait

frequencies that are similar to those exhibited by the sunfish,

0.5-2 Hz. CPG parameters are taken from [23], β = 2.5, γ =

Fig. 5. CPG coupling architecture. The extensor neuron of a given

CPG is coupled to the flexor neuron of the neighboring CPG.

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frequencies that are similar to those exhibited by the sunfish, 0.5-2 Hz. CPG parameters are taken from [23], β = 2.5, γ = 2.5, τ1:τ2 = 1:2, and produce stable oscillations. To produce the steady swimming gait the coupling weights between oscillators are: h21 = 0.9, h23 = 0.5, h24 = 0.9, h42 = 0, all other coupling weights are equal to zero. To produce the undulation motion the couplings weights are set to: h12 = 0.5, h14 = 0.15, h23 = 0.5, h34 = 0.5; h41 = -0.4, all other coupling weights are equal to zero. The gait transition between steady swimming to undulation (Fig. 6) took roughly 3 cycles. Although undulation is not a common gait displayed by the sunfish pectoral fin, this gait was selected to show that the Matsuoka model is able to transition between gaits by varying a single parameter.

Future work will focus on deploying the CPG network onto the multi-finned fish body (described in Section II), which will require the coordination of up to 32 CPGs. We will also investigate in more detail the effects of multi-modal sensory feedback on CPG output. In order to produce more biologically accurate gaits other oscillator models will be explored, as the Matsuoka model gives the user limited control over the shape of the output. This may necessitate the use of adaptive oscillators (e.g, Hopf oscillators [26]), although these oscillators can be less representative of the biology.

IV. INSTRUMENTED PECTORAL FIN

A. Fish sensory systems Fish have multiple sensory systems both intrinsic and

extrinsic to their fins that contribute to closed loop control of the kinematics and mechanical properties of fins. Sensory systems extrinsic to the fins include the visual system, the vestibular system, and a lateral line. The lateral line uses canal and surface neuromasts to measure the pressure gradient and velocity of the fluid along the body [27]. Fish vestibular sense mediates their sense of balance, providing information about body state through linear acceleration and rotational velocities [28].

unlike for terrestrial vertebrates, little is known about sensors intrinsic to the fins of bony fish. Pectoral fin innervation in sunfish and zebrafish [29] has shown that afferent nerves enter the dorsal fin base and branch out through the bony fin ray segments, densely innervating a large portion of the dorsal region of the fin. These innervations suggest the existence of sensing within the fin.

Recent research has demonstrated that the nerves within the fin respond to fin ray bending. It is also speculated that the fish might sense pressure along the fin surfaces and the force and displacement in the fin musculature.

B. Research and Design Goals of the Instrumented Fin A biorobotic model of the pectoral fin and its sensory

system has been developed and used to investigate relationships between distributed sensory data and the propulsive forces produced by the fin (Fig. 2A). The fin is able to produce motions, forces, and flows like the biological fin for steady swimming, yaw turn maneuvers, and hovering. Its design was described in detail in [4, 17]. The fin is instrumented with a distributed sensory system that relates to our best understanding of sensors likely to be associated with the fins. Twelve differential static pressure sensors (PX26-001D, Omega Engineering, Stamford, CT) located along the fin’s body plate represent the fish’s lateral line (Fig. 2A). A six-DOF IMU (SEN-10010, Sparkfun Electronics, Boulder, CO) attached to the fin’s support structure represents the vestibular system. The vestibular sense is relevant when the robotic fin is allowed to swim freely while supported by an air bearing carriage [4]. Rotary encoders on the servomotors that drive the fin rays are representative of muscle spindles. Strain gage sensors (SGT-3S/350, Omega Engineering, Stamford, CT) are used to measure the curvature of the fin rays to represent proprioception. Catheter-style pressure sensors (SPR-524, Millar Instruments, Houston, TX) are sewn into the fin membrane along the dorsal leading edge at proximal and

distal locations (Fig. 7A) and aligned with the sensing area orthogonal to the fin webbing. Force sensors (LSB200, Futek Advanced Sensor Technology, Inc., Irvine, CA) are affixed to a low friction air-bearing carriage (New Way S301301, New Way Air Bearings, Aston, PA) to measure forces in the thrust-lateral reference plane.

C. Experimental Methods Experiments were conducted to determine how dorsal

leading edge pressures related to the fin’s propulsive forces as two important parameters were varied: flapping frequency and fluidic environment. These experiments built upon past experiments (described in [4]) that identified important relationships between the fin’s force and distributed measures of fin ray curvature and body pressure. Although

Fig. 6 CPG network undergoing gait transition from steady swimming to undulation. The solid line represents CPG1, the long tick marks represent CPG2, the short tick marks represent CPG3, and the circles represent CPG4. The network transitions within three cycles.

Fig. 7. Pectoral fin’s flexible Lycra® webbing with sewn on rubber pockets for catheter sensors (A). Sensors are held orthogonal to the fin webbing through the stroke (A, inlay). Dorsal leading edge pockets (distal and proximal, left to right) indicated. Jet perturbation with dye contrast during experiments (20psi, 800x fins, steady swimming outstroke)(B).

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these measures were related to fin force, they were insufficient to predict the magnitude and direction of the force for control. CFD studies ([30]) and fin experiments have shown that strong vortices develop along the dorsal leading edge, and that these effects contribute to propulsion. In light of this information, the dorsal leading edge was instrumented with catheter pressure sensors to examine the relationship between fin forces and local pressures. Further, since it is not known how fluidic perturbations affect sensory measures or force production, the fin was tested under jet perturbations during steady swimming with this new sensing modality. For varied flapping frequencies, it was hypothesized that pressure signals along the dorsal leading edge would lead the two strong peaks of thrust during the fin's outstroke and instroke, and that the magnitude of pressure would trend with the magnitude of force. Under fluidic perturbations, it was hypothesized that thrust forces would decrease through the entire stroke, and that lateral forces would increase in magnitude through the outstroke.

In experimentation, forces and the pressures along the fin’s leading edge (proximal and distal segments) were collected during a steady swimming gait at multiple flapping frequencies: 0.65, 1.00, 1.30, 1.65Hz (Fig. 8). The fin executed five cycles of the steady swimming gait per test at each flapping frequency. Additionally, experiments were conducted to evaluate the effect of fluidic jet perturbations on these sensory measures (Fig. 7B). For these, a jet was propelled through a circular aperture (11mm diameter; 55±3mm diameter at impact) at 20psi (velocity of 108mm/s). Data were sampled at 200 Hz using a National Instruments PXI data acquisition crate and user-defined LabVIEW programs. Data were filtered using a low pass filter at a

cutoff frequency of 8 Hz to evaluate overall trends and improve display.

D. Results and discussion The results of these experiments indicate that the

magnitude of the pressure along the inner dorsal leading edge is a leading indicator of the forces (thrust and lateral) that develop during steady swimming. Specifically, during the outstroke dorsal pressures led lateral forces, but during the instroke dorsal pressures led thrust forces. Just before the start of the instroke, pressures begin to rise rapidly from near zero magnitude. A sharp rise in force through the instroke follows about 400ms later. The pressures peak at the middle of the instroke and begin a slow decline through the next

outstroke. This pressure decline leads a decline in forces that occurs just 400ms later (Fig. 8). In both cases, the pressure signal leads the force signal in rapid increase and decrease with peaks and troughs in similar phase lag relationships.

Pressures along the dorsal leading edge were nearly equivalent when the sensors were placed on both the outer and the inner faces of the pectoral fin (Fig. 8). We expect that this was due to the permeability of the fin membrane, causing fluidic events to permeate both sides of the fin. Further experiments with non-permeable and highly permeable membranes could clarify causality in this case.

Through all tested frequencies, proximal fin pressure (closer to the fin base) had a lower peak amplitude than

Fig. 8. 2D force magnitude (GREY STEM) and on-fin pressures shown for an 800x fin flapped at 0.65Hz flapping frequency. Plot shows the effects of sensor placement on inner and outer faces of the fin, as well as forces measured during steady swimming. Pressures on the inside (DASHED) and outside (SOLID) fin faces were measured for both distal (THICK) and proximal (THIN) placements. The commanded fin position (DOUBLED) is shown for comparison of instroke (rising edge) and outstroke (falling edge) effects. Data were sampled at 200Hz and low pass filtered at 8Hz for viewing ease.

Fig. 9. Forces and on-fin pressures shown as flapping frequency (an important locomotive parameter) varies. Increasing flapping frequency tends to increase peak magnitudes in 2D forces (A: thrust and lateral plane) while having more complex effects on the proximal (C) and distal (B) dorsal leading edge pressures.

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distal (further from the fin base) fin pressures, consistent with CFD analysis and expectation (Fig. 9). This is expected because as the dorsal leading edge vortex develops, it's velocity and energy increases along the length of the leading edge.

Increasing flapping frequency seems to cause a decrease in the overall magnitude of pressure (Fig. 9), which runs counter to hypotheses above. These trends show complexities in fin pressure data that are not well understood. Further testing with different styles of pressure sensors (static, dynamic) and sensor orientations (parallel and orthogonal to webbing) will likely yield a better understanding of this phenomenon.

Jet perturbations to the dorsal leading edge caused an increase in lateral forces during the outstroke and a decrease to peak thrust forces during the instroke. The perturbation's effect on the sensory system was negligible on the outstroke but significant on the instroke (where thrust forces dominate). The experiments with perturbations showed that both forces and sensory measures could be affected in complementary ways through a change in fluidic environment.

There are several notable relationships between the distal and proximal pressure signals that support leading edge vortex shedding shown in other experiments and predicted in CFD analyses. The proximal pressure peak leads the distal peak by a very short time interval (30 ms). We expect that this delay occurs due to the propagation speed of the vortices developing along the dorsal leading edge. Peak pressure on the distal sensor was much greater than peak pressure on the proximal sensor (83.0±0.2% difference through all trials). At the beginning of the instroke, both the proximal and distal pressures begin to develop, with the distal pressure developing at a faster rate than the proximal pressure. These

experimental findings confirm the CFD analysis in [30] that expects forces on the dorsal tip to be greater than forces on the proximal segments due to greater linear velocity at the tip. The development of a leading edge vortex is a key mechanism for propulsion on the instroke and therefore information from the pressure sensors is valuable in estimating instroke propulsive force.

As to the authors' knowledge, this is the first time we observe experimental pressure data on a highly deformable ray-finned robot, and this is likewise the first time the effects of a fluidic perturbation have been evaluated on the intrinsic sensory system of a robotic fin. The impact of these results is that on-fin pressure has the potential to supply information about force production, fluidic environment (perturbations or reduced efficiencies), and even fin flapping frequency. By knowing more about system state through sensory measures, more effective control strategies are made possible. Future research will aim to fully understand the complex relationships between sensory measures (e.g. on-fin pressure, fin ray bending, body plate pressure) through experiments with multiple fin stiffnesses, several gaits, and a larger network of distributed heterogeneous sensors.

V. CONCLUSION Biorobotic models of the sunfish body and fins, and of the

fin sensory systems and a neural controller have been developed. These individual systems are intended as subsystems of a complete fish robot that will enable detailed investigations of multi-fin mechanics, sensing and control during free swimming. The models for the fish body and the artificial CPGs are first generation designs, and have undergone only preliminary evaluation. The modular body has distributed mass control so that its buoyancy and stability can be tuned. It can be balanced to maintain a stable, upright position in water, and also can be made so that it flips when lightly perturbed. The artificial CPGs are able to drive multiple fins with trajectories that approximate the steady swimming gaits of the sunfish, and are able to adjust the flapping frequency of the fins in order to modulate propulsion forces.

The biorobotic pectoral fins and its sensory systems are mature designs and were used to experimentally investigate relationships between the fin’s propulsive forces and pressure along the leading edge of the fin. These are the first measures of pressure along highly deformable fins during flapping of which the authors are aware. The shape and time course of the pressure signals along the leading edge were highly correlated with the force trace of the fins. This suggests strongly that these signals, especially when coupled with other sensory measures of the fin (e.g. fin bending from strain gages [4]), will allow fin force to be predicted from distributed sensory measures. This is crucial for designing a sensory based feedback strategy that modulates the motions and mechanics of the fin to effectively control fin forces.

Principles learned about multi-fin swimming can obviously be applied to underwater vehicles, but the

Fig. 10. Graph showing the effect of fluidic jet perturbations on on-fin pressures and force components (2D magnitude, thrust-lateral plane). Fluidic jet perturbations were directed at the dorsal leading edge, distal segment. Forces (THICK) and pressures (THIN) are shown for perturbed (DASHED) and non-perturbed (SOLID) cases. The programmed fin motion (DOUBLED) is shown for reference of outstroke (rising edge) and instroke (falling edge). Representative data shown for an 800x stiffness steady swimming fin at 1.3Hz flapping frequency with a 20psi jet perturbation.

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applications are much broader. The manner in which the sunfish integrates the mechanics of the fins, distributed sensing and information processing, and neural control to create complex swimming behaviors can be generalized and applied to a broad range of engineered systems that have multiple propulsors, distributed sensing, and the ability to modulate plant properties.

ACKNOWLEDGMENT The authors are very grateful to Prof. Kin Huat Low and

to Prof. George Lauder and the members of the Lauder Laboratory for many helpful discussions about fish robots, neural control and fin based swimming.

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