BoxyBot: a swimming and crawling fish robot controlled bya central pattern generator

Daisy Lachat, Alessandro Crespi, and Auke Jan IjspeertSchool of Computer and Communication Science

Swiss Federal Institute of Technology, Lausanne (EPFL)Station 14, CH-1015 Lausanne, Switzerland

{daisy.lachat, alessandro.crespi, auke.ijspeert}@epfl.ch

Abstract We present a novel fish robot capable of swim-ming and crawling. The robot is driven by DC motorsand has three actuated fins, with two pectoral fins and onecaudal fin. It is loosely inspired from the boxfish. The controlarchitecture of the robot is constructed around a centralpattern generator (CPG) implemented as a system of couplednonlinear oscillators, which, like its biological counterpart,can produce coordinated patterns of rhythmic activity whilebeing modulated by simple control parameters.

Using the CPG model, the robot is capable of performingand switching between a variety of different locomotor be-haviors such as swimming forwards, swimming backwards,turning, rolling, moving upwards/downwards, and crawling.These behaviors are triggered and modulated by sensory inputprovided by light and water sensors. Results are presenteddemonstrating the agility of the robot, and interesting prop-erties of a CPG-based control approach such as stability ofthe rhythmic patterns due to limit cycle behavior, and theproduction of smooth trajectories despite abrupt changes ofcontrol parameters.

Index Terms Fish robot, under water robotics, centralpattern generator, swimming, crawling.

I. I NTRODUCTION

The agility and efficiency of animal locomotion tendto fascinate engineers. The skills to coordinate multipledegrees of freedom (DOFs), using compliant actuators(muscles and tendons), and massively parallel control (thecentral nervous system), give animals an agility and en-ergy efficiency rarely replicated in man-made robots. Oneof the most impressive features of animals is how theyeffortlessly deal with multiple redundancies: redundanciesin the number of articulated joints, redundancies in themusculature (there are multiple muscles acting on a singlejoint, and often single muscles acting on multiple joints)and redundancies in muscles (a single muscle is decom-posed into multiple motor units). To a large extent, theproblem of dealing with these redundancies is solved bycentral pattern generators, i.e. neural networks capable ofproducing coordinated patterns of rhythmic activity withoutany rhythmic inputs from sensory feedback or from highercontrol centers [1]. Even completely isolated CPGs in aPetri dish can produce patterns of activity, called fictivelocomotion, that are very similar to intact locomotion whenactivated by simple electrical or chemical stimulation [2].Typically, varying simple stimulation allows modulation of

This work is supported by a Young Professorship grant from the SwissNational Science Foundation to A.J. Ijspeert

both the speed and direction of locomotion. From a controlpoint of view, CPGs therefore implement some kind offeedforward controller, i.e. a controller that knows whichtorques need to be rhythmically applied to obtain a givenspeed of locomotion. Interestingly, CPGs combine notionsof stereotypy (steady state locomotion tends to show littlevariability) and of flexibility (speed, direction and typesofgait can continuously be adjusted).

In this article, we apply the concept of CPGs to thecontrol of a novel fish robot. We are interested in testinghow a CPG implemented as a system of coupled nonlinearoscillators can be used to control swimming and crawling.Our purpose is to demonstrate that such a system can bea useful basis for producing and modulating a variety ofdifferent locomotor behaviors, and for rapidly switchingbetween them. This work follows several related projectson the use of CPGs for controlling a simulated lamprey [3],a simulated salamander [4], [5], and a humanoid robot [6].

In the next sections, we first make a brief overview ofrelated work (Section II). We then present the design of ourrobot (Section III), and its control architecture (SectionIV).Experiments demonstrating different locomotor behaviorsare presented in Section V, and our approach is discussedin Section VI.

II. RELATED WORK

Multiple fish robots have been designed and realized.Most robots implement anguiliform or carangiform swim-ming modes, which use mainly the body and the tailto propelled ([7],[8]). Ostraciiform or labriform modes,which use pectoral fins and almost no body motions, havebeen less studied. Relatively few fish robots are fully au-tonomous, capable of swimming in 3D and reacting to theirenvironment. For instance, the well-known RoboTuna fromMIT, which has been designed to study speed optimization,is attached to a horizontal guide [9].

Several groups are very active in designing autonomousfish robots ([10],[11],[12]). The National Marine ResearchInstitute (NMRI) in Japan, for instance, is working onmultiple projects, including maneuvering, swimming per-formance and modular robotics for water; each robot isbuilt for a particular purpose like up-down motion, highturning performance, or high speed swimming [13]. TheUniversity of Essex developed a 3D swimming roboticfish called MT1 which is fully autonomous [14]. A micro

robotic fish actuated by PZT bimorph actuators has recentlybeen built by the University of California, Berkeley, [15]mimicking a boxfish.

Most of these robots are controlled using traditionalcontrol methods that combine (algorithmic) sine-based tra-jectory generators, and PID feedback controllers. Recently,the concept of CPGs is increasingly used as an alternativeapproach for online rhythmic trajectory generation [16],[17], [5]. In most cases, the CPGs are implemented asrecurrent neural networks or systems of coupled nonlinearoscillators.

To the best of our knowledge, CPGs have rarely beenapplied to the control of a swimming robot. Arena and Ay-ers groups have independently used CPG models inspiredby the lamprey locomotor network for controlling tetheredlamprey-like robots [18], [19]. The robots were capable ofproducing traveling waves for propulsion, but autonomousswimming was to the best of our knowledge not explored.In this article, we would like to contribute to underwaterrobotics in several ways: (1) with the design of a novel fishrobot capable of ostraciiform (and labriform) swimmingmodes and crawling, and (2) with a CPG-based controllerthat allows agile locomotion in a fully autonomous fishrobot.

III. T HE FISH ROBOTBOXYBOT

A. Mechanical design

The body of the robot is made of two principal parts: thehead module, providing two independent joints around thepitch axis (pectoral fins), and the body module, providinga joint around the yaw axis (caudal fin). The modulesare rigid cases and are attached together with a rigid part(Figure 1).

The fish robot is designed to implement labriform or os-traciiform swimming modes. Fishes that uses ostraciiformor labriform modes have often inflexible cases for body,like our body and head modules. The caudal fin activated bythe body module can be used as a rudder like in labriformmode. Hybrid propulsion (caudal and pectoral) can alsobe implemented like in ostraciiform mode. However, theconcept of the robot is modular and additional modulescould easily be added, e.g. to form a body made of a chainof modules. The body module is indeed the same as the oneused in an amphibious snake robot that we developed [5].

Casings are molded in polyurethane lightened with phe-nol microballs. Specific O-rings and grease are used tomake the robot waterproof. Total robots length is 25 cm.The density is slightly higher than that of water and afloater is added to adjust its density to just below 1000[Kg/m3].

The fins are actuated by 2.83 Watt Faulhaber DC motorsand purpose-made gearboxes (reduction factors of 50 and97.2 for the pectoral and caudal fins). Pectoral fins canmake complete rotations, while the motion of the caudalfin is limited to 60. The fins are made of 2-mm thickPE plates. The caudal fin has an aspect ratio of 2.9 for 35cm2, while pectoral fins have 0.6 for 50 cm2. The fins canvery easily be changed.

Fig. 1. View from side of the internal components of BoxyBot.The leftside of the robot is placed above the right side. On the left isthe bodymodule with caudal fin and on the right is the head module with pectoralfins

Fig. 2. BoxyBot (view from above)

B. Electronics and sensors

The robot is fully autonomous. It is controlled by aPIC18F2580 microcontroller at 40 MHz in the head whichis used for behavior and locomotion control, with threeadditional microcontrollers (PIC16F876A) for implement-ing PD controllers for each motor. The robot locomotioncontroller (see next Sections) communicates with the motorcontrollers with an I2C bus and act as the master. Themotors are controlled in position using PD controllers.Power is provided by three 4.2 V Li-Ion batteries (twoin the head module and one in the body module).

Light and water sensors are placed in the front of thehead in an interchangeable part. The two light sensors areplaced in the horizontal plane in transparent polymer tubesmaking a 60 angle from one another, a light filter is placedaround the tube and can be easily replaced depending onthe environment. The water sensor is simply made of twoelectrical contacts that provide anon signal when the robotis immersed in water (due to water conduction) and anoffsignal otherwise. A two axis accelerometer (ADXL203)measures accelerations around the roll and pitch axes, butit is not used in the results presented in this article.

IV. L OCOMOTION CONTROL

The locomotion controller is composed of a CPG modelfor producing coordinated oscillations extended by a finitestate machine for modulating the CPG and implementingvarious locomotor behaviors.

A. CPG model

Our locomotion controller is based on a CPG modelimplemented as a system of three coupled amplitude-controlled phase oscillators, one per fin (Figure 3). Anoscillator i is implemented as follows:

i = i (1)

+

j

(ijrj sin(j i) + ijrj cos(j i))

ri = ar(br(Ri ri) ri) (2)

xi = ax(bx(Xi xi) xi) (3)

i = xi + ri cos(i) (4)

wherei is the oscillating set-point (in radians) extractedfrom the oscillator, andi, ri, andxi are state variables thatencode respectively the phase, the amplitude, and the offsetof the oscillations (in radians). The parametersi, Ri,andXi are control parameters for the desired frequency,amplitude and offset of the oscillations. The parametersij andij are constant coupling weights which determinehow oscillator j influences oscillatori. The parametersar, br, ax andbx are constant positive gains.

The constant parameter values used throughout the ar-ticle are ar=20 [rad/s], br=5 [1/s], ax=20 [rad/s], bx=5[1/s] andij=0.0 [1/s],ij=0.0 [1/s] for alli andj except12=21=31=32=0.5 [1/s] (oscillators 1,2,3 respectivelycorrespond to the left-pectoral, right-pectoral, and caudalfins). These values were chosen such that the state variablesri and xi approachRi and Xi in a critically dampedfashion, and the oscillations of the three fins have a zero-phase lag (as long as their intrinsic frequenciesi are nottoo different). The differential equations are solved withEuler integration on the PIC microcontroller with a 7 msintegration step.

Such a CPG model has several nice properties. Thefirst interesting property is that the system exhibits limitcycle behavior, i.e. oscillations rapidly return to the steady-state oscillations after any transient perturbation of thestate variables. The second interesting property is thatthe control parametersi, Ri, and Xi can be abruptlyand/or permanently varied while inducing only smoothmodulations of the set-point oscillations (i.e. there are nodiscontinuities nor jerks). This property will extensivelybe used in the Results section (Section V) for varying thelocomotor behaviors. Another interesting feature is thatfeedback terms can be added to Equations 1-3 in orderto maintain entrainment between control oscillations andmechanical oscillations (however this will not be exploredin this article).

Fig. 3. Diagram of the complete control architecture. Whileusing apredefined behavior the values from light sensors are not used. The valuesof pitch and roll were not used during the experiments described in thispaper.

B. Complete control architecture

The diagram of the complete control architecture is givenin Figure 3. The CPG model produces the set-pointsifor PD controllers of the three fins. Different locomotorbehaviors can be obtained by modulating the CPG controlparametersi, Ri, andXi for the three fins.

Examples of locomotor behaviors include:

swimmingforwards, by oscillating only the caudal fin,both pectoral fins, or all fins.

swimming backwards, by setting the pectoral offsets(X1 andX2) to and stopping the oscillations of thecaudal fin (R3=0).

spinningaround the roll axis, by setting the pectoraloffsetsX1 andX2 to /2 and/2.

turning (around the yaw axis) while swimming, byhaving a non zero offsetX3 for the caudal fin.

turning on the spot, by oscillating the pectoral fins,with one of the pectoral offset to.

swimming up (or down), by setting an offset forboth pectoral fins (X1=X2) between 0 and/2 (-/2),proportionally to the desired vertical speed.

crawling, by stopping the oscillations of the fins(R1=R2=R3=0), and applying a continuously increas-ing offset (X1 and X2) to both pectoral fins. Twopossibilities are withX1 = X2 (both pectoral finsrotate in phase) orX1 = X2 + (pectoral fins rotatein anti-phase).

For all these behaviors, the speed of locomotion can bevaried by adjusting the frequenciesi and/or the ampli-tudesRi of oscillations. Typically the speed of locomotionincreases with those parameters until the torque limits ofthe motors are reached.

We made two types of experiments for testing thesedifferent locomotor behaviors. In a first set of experiments,the choice of behavior is done sequentially in a prefixedorder without sensory inputs to test the different locomotorbehaviors and the transitions between them.

In a second set of experiments, the behavior controlleris programmed as a finite state machine to implement asimple phototaxis both in water and on the ground. A

strong halogen lamp is used as a movable light source anda behavior is chosen on the basis of the values of bothlight sensors and of the water sensor. The default behavioris to track the light. But if the robot is not in water, itstarts to crawl. If the light sensors signal is too weak, itturns on the spot until it finds the light source again. Andif the signals are saturated (i.e. the robot is too close to thelamp), the robot stops.

Once a behavior has been chosen, a second finite statemachine determines the 9 control parameters (amplitude,frequency and offset of each motor) to obtain that behavior.For example, if light tracking is chosen, the speed of therobot is controlled inversely proportionally to the amplitudeof light by adjusting both the frequency (5) and the ampli-tude (6) of the oscillations. The caudal offset is controlledproportionally to the difference of light (7).

i = ki 1

l1 + l2i = 1, 2, 3 (5)

Ri = kRi 1

l1 + l2i = 1, 2, 3 (6)

X3 = kX3 (l1 l2) X1 = 0, X2 = 0 (7)

where thekij are gains of the regulator andl1, l2 theamplitude of the two light sensors. Note that the CPG neverneeds any resetting and is continuously running while the9 control parameters are modified.

V. RESULTS

A. Sequentially testing the locomotor behaviors

We tested the ability of the CPG to produce the differenttypes of locomotor behaviors presented above. Figure 4presents a sequence of transitions from one behavior to theother. In that sequence, the CPG makes transitions betweenswimming straight with both pectoral and caudal fins(t2s), turning with a caudal offset (2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

pi/2

0

pi/2

Pec

tora

l lef

t

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

pi/2

0

pi/2

Pec

tora

l rig

ht

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

pi/2

0

pi/2

Cau

dal

Time [s]

Fig. 8. Acceleration during swimming.

0 2 4 6 80

0.1

0.2

0.3

0.4

0.5

Frequency of fin oscillations [Hz]

For

war

d sp

eed

[m/s

]

0 20 40 60 800.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Amplitude of fin oscillations []

For

war

d sp

eed

[m/s

]

Fig. 9. Variation of forward speed with pectoral fins. On the left, variationwith oscillations frequency at a fixed amplitude of 20. On the right,variation with oscillation amplitude at a fixed frequency of2 Hz. Speedis obtained with the measure of distance covered and time, error bars arecalculated from the precision of those two measures.

B. Evaluating the speed of locomotion

The speed of locomotion can be adjusted by graduallyincreasing both the frequency and/or amplitude parametersof the CPG. Figure 8 shows the activity of the CPG whenboth are increased simultaneously.

In order to test how the speed of locomotion dependson the frequency and amplitude of oscillations, we carriedout a series of swimming tests. Steady-state speed wasmeasured at different levels of frequencies and amplitudesof all fins. Figure 9 shows the results for variations offrequency at a fixed amplitude (on the left) and for varia-tions of amplitude at a fixed frequency (on the right). Ascould be expected, the speed of swimming increases withthe frequency until the motors reach their torque limits.Similarly, at a fixed frequency, the speed of swimmingincreases with the amplitude until the oscillations becometoo large and create braking wakes. Overall, the robot canswim up to 0.37 [m/s] (i.e. 1.4 body lengths per second)at a frequency of 8 Hz and amplitudes of40 with bothpectorals and caudal fins.

C. Phototaxis

Using the phototaxis behavior described above, the fishrobot is able to reach a static bright light (brighter thanthe environment) from a maximal distance of 50 cm andto keep station near the light. It is also able to follow alight that moves slowly (Figure 10). If the light moves too

Fig. 10. Snapshots of phototaxis (from top left to bottom right), 2 secondsbetween each pictures.

quickly on the side, the robot cannot track it because thecontrol law for choosing the speed and caudal offset isvery basic (only proportional gains are used). The robotthen slowly turns on itself until the light comes into viewagain, in which case it resumes the light tracking behavior.

VI. D ISCUSSION

BoxyBot has demonstrated its capacity of maneuverabil-ity. Using only three fins, it can move in 3D with differenttypes of maneuvers and go out of water using a crawlinggait. Finally, the robot can reach a bright light and followit slowly.

The CPG model proved to be very useful for the onlinegeneration of the fin trajectories. It provides the possibil-ity to abruptly change control parameters while ensuringsmooth variations of behavior. Producing continuous andsmoothly varying set-points is indeed important to limitmechanical damage to the motors and gearboxes, butalso to avoid jerks that could destabilize the swimmingand crawling gaits. In addition, the phototaxis experimentshowed that the CPG model can be continuously modulatedand can therefore readily be used by higher level behav-ior controllers. This is not unlike locomotion control invertebrate animals where CPGs in the spinal cord producethe rhythmic patterns necessary for locomotion, and highercontrol centers such as the motor cortex and the cerebellumgenerate signals for the modulation of speed and direction.

We will extend this work in several directions. First ofall, we will explore whether our CPG can be designedto use simpler command signals for initiating and mod-ulating locomotion. In vertebrates, simple tonic (i.e. non-oscillating) signals are sufficient to modulate the speedof locomotion and even to induce gait transitions. In ourmodel, several control parameters need to be changedsimultaneously to obtain certain transitions of behavior,and

we would like to see if this could be simplified. Anotherpoint that we intend to explore is whether more complexsignal shapes could lead to more efficient swimming. Wecurrently use harmonic (i.e. sine-like) oscillations, anditmight be that relaxation-like oscillations (i.e. oscillationsthat have both a fast and a slow mode) provide fasterlocomotion for similar frequencies and amplitudes. Thiswill require the use of other types of oscillators in the CPGmodel. Finally, we would like to explore the integration ofsensory feedback in the CPG (not only through modulationof command parameters as done during the phototaxisexperiment). In the lamprey, for instance, stretch receptorsin the spinal cord ensure that the travelling neural waveremains coordinated with the travelling mechanical wave,and rhythms in the CPG synchronize with externally forcedmovements of the tail. The CPG model can easily beextended to include similar types of sensory feedback,and we will explore the benefits of such entrainmentphenomenon.

ACKNOWLEDGMENT

We gratefully acknowledge the technical support ofAndre Guignard and Andre Badertscher in the design andthe construction of the robot. We also would like to ac-knowledge Sacha Constantinescu and Ariane Pasquier fortheir contribution in designing the light sensors and testingthe robot. This work was made possible thanks to the SwissNational Science Foundation (Young Professorship Awardto Auke Ijspeert).

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