Evolution of an Amphibious Robot withPassive Joints

Jared M. Moore & Philip K. McKinleyDepartment of Computer Science and Engineering

Michigan State UniversityEast Lansing, Michigan, USA

Email: {moore112,mckinley}@cse.msu.edu

Abstract—Passive joints provide a means to reduce the me-chanical complexity of a robot because they do not requiredirect actuation from a motor. However, the inclusion of suchcomponents complicates the design process, as their behavioris highly dependent on external stimuli in combination withactuation of other robot components. In this paper, we describea study on the coevolution of morphological characteristics andcontroller parameters for an amphibious robot with passive armjoints. Results show that this approach is able to exploit theproperties of passive joints to produce effective locomotion inboth aquatic and terrestrial environments. Evolved solutionsdemonstrated a strong coupling between fin morphology andcontrol strategy with respect to performance.

I. INTRODUCTION

Natural organisms exhibit an astounding array of func-tionality via complex interactions among muscles, bones andnerves. Primary movement is typically produced throughmuscles guided by the nervous system, but often passiveparts of morphology (such as fins, feathers and webbed feet)enhance these movements. Passive components can increaseperformance in robots, by emulating capabilities found inbiological organisms. For example, a passive flexible caudalfin (tail) has been shown to produce more thrust than arigid fin when oscillated at the appropriate frequency [1].Moreover, integrating passive components reduces the numberof actuators, and correspondingly the mechanical complexity,needed by the system, which is particularly important in smallrobots.

Despite these advantages, the introduction of passive com-ponents into the robot poses numerous challenges in the designof embedded computer systems that can effectively controlsuch robots. Because the joints are not directly actuated, anycontrol strategy must incorporate the movement characteristicsof the passive materials as a component of the overall system.Our approach is to combine evolutionary computation withefficient methods for modeling materials and their interac-tion with the environment. Whereas evolutionary computationguides the search process, computationally efficient models de-termine how constituent materials behave when acted upon byforces, enabling accurate evaluation of the robot in simulation.This approach, coupled with 3D printing for rapid prototypingof robots with passive capabilities, provides us with an oppor-tunity to begin to bridge the gap between artificial and naturalsystems in terms of agility and maneuverability.

In this paper, we present an evolutionary approach todiscovering effective combinations of morphology and control

for an amphibious robot with passive arm joints. Candidatesolutions are evaluated using a rigid body physics simulationenvironment with successive generations created through aprocess of selection, mutation and crossover. Each evolvedsolution comprises a body plan and two controllers, one forcrawling on a flat surface and another for swimming in water.This two-controller approach exploits the ability to changecontrol patterns between different environments, whereas themorphology of a robot is fixed after fabrication.

The contributions of this paper are as follows. First, wedemonstrate evolved solutions that harness the properties ofpassive joints to move effectively in both the terrestrial andaquatic environments. The passive joints become an integralpart of locomotion for the individuals. Second, we showthat the coevolutionary process finds solutions whose controland morphology are highly intertwined, demonstrating theimportance of exploring both facets together. We fabricatedthe best evolved solution using a multi-material 3D printerand have conducted preliminary experiments with it on anevolutionary robotics testbed.

The remainder of this paper is organized as follows.Section II presents related work. Methods are discussed inSection III, and experimental results are presented in Sec-tion IV. Key aspects of the study are discussed in Section V,and conclusions are presented in Section VI.

II. RELATED WORK

Over the past 15 years, extensive progress has been madein several aspects of evolutionary robotics [2]–[8]. A variety ofapproaches have yielded controllers adapted to tasks, includingevolution of neurocontrollers for walking [9]–[17], graspingan object [18], control of finless rockets [19], swimming [1],[8], station keeping [20], and complex behaviors such asforaging and game playing [7], [21]–[29]. While many studiesfocus on evolving controllers for fixed morphologies [2], [3],[5]–[7], [30]–[34], several recent investigations have addressedthe evolution of morphology [8], [35]–[38], and even the co-evolution of morphology and control [13], [15], [33], [39]–[42]. Brain-body approaches have proven successful in a broadrange of problems from the development of a catapult [43],locomotion [40], [44], and object manipulation [33]. Coevo-lutionary approaches are particularly well suited to problemswhere solutions involve complex interactions among sensors,actuators, control, active and passive physical components, andthe surrounding environment. However, the co-evolution of

controllers and morphologies for robots with passive com-ponents, addressed in this paper, is a relatively new area ofstudy [37].

A major hurdle to any simulation-developed solution ishow well it transfers into a physical robot. A so-called “reality-gap” arises when solutions that appear to work well in asimulated environment face issues in a physical environmentthat were either unforeseen or incorrectly modeled [3], [42],[45]. Approaches to addressing this problem include evolvingthe simulator in conjunction with a robot [46] and directlyrewarding solutions for performing similarly in reality andsimulation [42]. In the latter approach, only solutions that havea high transferability (a low disparity between simulation andreality) are deemed highly fit. The introduction of flexible ma-terials and passive properties into the robot design potentiallywidens the reality gap, as the material properties and how theyare affected by actuators, need to be captured accurately insimulation. The study described in this paper addresses thisproblem in the context of amphibious robots.

III. METHODS

This study focuses on developing a robot whose passivejoints not only reduce motor requirements but also enhanceperformance. Many aspects of the robot (dimensions, mate-rials, controller parameters) are evolved, as described later,while others (for example, mechanical components) systemsare designed. The following sections describe the specificsof the robot, the simulation model, the evolutionary approachused, and the fabrication of the physical model.

A. Robot Overview

The robot used in this study features a main body and twoarms placed to each side at the front; a simulation model isshown in Figure 1. Battery, controller, and motors are assumedto be contained within the main body, with the arms connecteddirectly to the motors.

Fig. 1. Simulation model of the robot used in this study. The arms movein a sweeping motion pivoting at the top of the fins through a passive hingejoint.

Each arm features a passive, hinge joint between the armand flipper, as illustrated in Figure 2, enabling locomotion inboth terrestrial and aquatic environments. The arms functionsimilarly to the pectoral fins of fish and move in a sweepingmotion from the front to back. The passive joint between arm

and fin locks at vertical on the power stroke, providing a largersurface area for swimming or acting as a leg to lift the bodyoff of the ground for crawling. As the arms move forwardon the recovery stroke, the fin collapses backward, reducingdrag. Since the passive joint does not require a dedicatedmotor, it reduces both the power requirements imposed onthe robot as well as the complexity of the physical design.Instead, the passive joint moves with a combination of gravityor hydrodynamic drag in concert with the actuated arms drivenby a motor at the base of each arm. Hence, complexity isshifted to the controller, which (along with the dimensions andcharacteristics of the arms and fins) is the focus of optimizationduring the evolutionary process.

Fig. 2. CAD model of the passive hingejoint used in the fin structure. Thearm can be seen extending from the body and is waterproofed by a flexiblegasket. The arm attaches to the fin in a passive manner allowing the fin tomove according to the forces acting upon it.

Control of the arms is governed by a sinusoidal input withparameters related to joint limits and the speed of oscillation.The control parameters are optimized through the evolutionaryprocess and are executed by a controller that moves both limbssynchronously. An individual robot also has two controllers,one for each environment.

B. Treatments and Evaluation

Three evolutionary treatments were conducted. In Treat-ments 1 and 2, respectively, simulated robots evolved in aterrestrial or an aquatic environment. These single environmenttreatments served as benchmarks for comparison of solutionsevolved in Treatment 3, where evolved robots were evaluatedin both environments. Evaluation of each candidate solutionwas based on the total distance traveled forward in 10 secondsof simulated time.

The two evaluation environments were built atop the OpenDynamics Engine (ODE) [47], a three-dimensional real-timephysics simulation engine. ODE accounts for physical con-ditions such as friction and gravity, as well as handling ofcollisions. The terrestrial environment emphasizes parametersrelevant to locomotion across a flat surface, such as a sidewalkor tabletop. In the aquatic environment, forces are requiredto account for the propulsion component of the fins and thehydrodynamic drag on the robot components during forwardmovement. Hydrodynamic forces were simulated using twoprincipal components. First, the drag force on the front fact ofthe main body and arms was calculated using the standard drag

equation. Similarly, the propulsive force was also calculatedusing the drag equation with the propulsion applied to eachfin as it moved throughout the simulated fluid.

C. Evolutionary Process

Populations comprised 250 individuals and were evolvedfor a total of 400 generations. Each treatment was conductedusing 20 replicate runs in order to produce statistically signif-icant results. The initial population was seeded with individ-uals containing randomly generated genomes for the differentparameters. At each generation, the individual solutions wereevaluated in the simulator, and the next generation was formedbased on a two phase selection process. Elitism was usedto maintain the best performing solution across generations.Remaining parent solutions were selected using a tournamentselection process to fill out the parent solutions for the nextgeneration with a tournament size of 3. New individuals werecreated using single point crossover with a probability of 25%or through mutation with a 30% chance to alter a gene in agenome.

1) Genome: Each genome consists of 11 real-valued pa-rameters, listed in Table I. Practical constraints are also placedon certain genes such that the simulated robot is more readilytransferable into physical designs. For example, fin width isallowed to range between 1 and 3 centimeters, while alsobeing constrained to being only as wide as the overall armwidth. Other intergene constraints impose restrictions on thetotal width of the robot body and arms as well as to keep thelimits of joint oscillation from crossing the high and low limitsof a servo motor.

TABLE I. INDIVIDUAL GENE LIMITS

Parameter Min. Value Max ValueLower Fin Height 1cm 5cmLower Fin Width 1cm 3cm

Body Width 4.5cm 7.5cmArm Width 1cm 5cm

Arm Friction 0.7 1.0Osc. Freq. Land .25Hz 1HzHigh Limit Land -70 ◦ 70 ◦

Low Limit Land -70 ◦ 70 ◦

Osc. Freq. Water .25Hz 1HzHigh Limit Water -70 ◦ 70 ◦

Low Limit Water -70 ◦ 70 ◦

Under this encoding scheme, the morphological parame-ters, except for fin friction, which is primarily used in theterrestrial environment, are subject to competing environmentalpressures. Over the course of evolution, parameters relatingto the robot morphology reach values that allow the robot tomove in both environments. The control parameters, oscillationfrequency and joint limits, are specific to each environment.High and low joint limits were incorporated into the controllerto evaluate different ranges of motion. In this way, a con-troller can define the range of movement, within the physicalconstraints of the motor, to use in locomotion. This approachproduces a robot whose morphology is adapted for movementin both environments, but with controllers specifically adaptedto each environment and its morphology.

2) Fitness: In Treatments 1 and 2, fitness is defined simplyas the forward movement in 10 seconds of simulation time. ForTreatment 3, fitness is a function of performance in the twoenvironments, as defined by Equation 1:

Fitness = [4− (2− aqua dist)− (2− terr dist)]2, (1)

where aqua dist represents the normalized distance travelledin the aquatic environment and terr dist represents the nor-malized distance travelled in the terrestrial environment. Themaximum fitness possible under this scheme is 16 and the min-imum possible is 0. This fitness function places an emphasison individual solutions that perform well in both environments.

D. Prototype Fabrication

Taking the best evolved solution from Treatment 3 as amodel, a prototype robot was fabricated using an Objet Connex350 multi-material 3D printer. The prototype is shown inFigure 3. The controller was implemented using an Arduinomicro-controller with servo motors actuating the arms. Thisphysical model was used to validate the results of evolutionand identify any differences in movement characteristics andperformance when transferring from simulation to reality.

Fig. 3. 3D printed robot of the best performing solution in this study. Thepassive hinge joint can be seen between the arm and fin. The fins collapsebackwards as the arms move forward allowing the robot to move in bothterrestrial and aquatic environments.

IV. EXPERIMENTS

The following sections describe the results of the threeindividual treatments, followed by a discussion of differencesamong them.

A. Treatment 1 - Terrestrial Environment Only

In a terrestrial environment, the primary challenge facedby any robot is how to move the body efficiently. Doingso generally involves minimizing the contact area with theground. Not surprisingly, Treatment 1 arrived at solutions withfins that were significantly taller than the main body in 19of the 20 replicate runs. An evolved individual, shown inFigure 4(a), lifted the body off of the surface and rockedforwards as the arms moved towards the rear of the body. Thisgait allowed the individual to move forward at a relatively rapidpace. Furthermore, the main body evolved to its narrowestallowable value, while the fin friction evolved to be near itsmaximum value. Evolved controllers tended to move the armsnear the fastest allowable frequency while also favoring the

largest range of motion. The greater range of motion allowedthe robot to keep its body off of the ground for a longer periodduring the rocking gait, increasing the distance travelled duringa simulation.

Fig. 4. The three different morphologies that evolved in the differenttreatments. Subfigure (a) represents the dominant morphology that emergedin Treatment 1, note the tall pectoral fins. The dominant morphology forTreatment 2 is presented in (b) and is characterized by shorter pectoral fins.The morphology that emerged in Treatment 3 can be seen in (c). This adaptivemorphology exhibits a compromise in the pectoral fin height between theterrestrial and aquatic morphologies, enabling the robot to perform well inboth environments.

B. Treatment 2 - Aquatic Environment Only

In contrast to robots in the terrestrial environment, indi-viduals in an aquatic environment tend to perform better byreducing the surface area exposed to the direction of travel. Asa result, fins of robots in the aquatic environment evolved tobe, on average, only 29% the height of those in the terrestrialenvironment, although fin widths were similar. An example isshown in Figure 4(b). Shorter fins produce less drag duringthe recovery stroke and also accelerate the transition to a fully

vertical position during the power stroke. Bodies of individualsin this treatment evolved toward the narrowest allowed value,even more so than Treatment 1, in order to minimize drag.Unlike Treatment 1, however, the oscillation frequency of theevolved controllers exhibited more variation, apparently tied tothe different fin height values observed in this treatment. Thisrelationship is discussed later in this section.

C. Treatment 3 - Amphibious Environments

Treatment 3 produced morphologies and controllers thatperformed well in both environments, specifically, fins thatare tall enough to propel the robot forward in the terrestrialenvironment while also being effective swimmers. However,the gaits in the terrestrial environment were characteristicallydifferent than those from Treatment 1. Due to shorter fins,which were better for swimming, the terrestrial gait resembleda sliding motion, where the fins were able to lift the bodyslightly off the ground, dragging the body instead of liftingit. In terms of swimming, the evolved solutions solutionsreached approximately 75% of the average distance traveledby solutions in Treatment 2. Figure 4(c) shows the dominantmorphology that emerged in this Treatment. In comparisionto the first two treatments, the evolved fin widths that wereapproximately 66% as wide, further indicating a likely com-promise between fin height and width.

D. Fitness Evaluation

The fitness landscape of solutions found in Treatment 3is illustrated in Figure 5, where each of 2,000,000 individualsolutions is represented by a small circle. This plot includesall individuals found during the evolutionary run showingthe landscape covered by evolution. In this figure, the darkershaded areas indicate regions where many solutions performedsimilarly. The axes represent the fitness for each respectiveenvironment. Solutions that fall along one of the two axesperformed well in one environment at the expense of perfor-mance in the other environment. Many individual solutionsdid not perform well in either environment, as indicated bysolutions in the lower left of the plot. These solutions arelikely the earlier generations of evolutionary runs. The area ofspecific interest in this plot is surrounded by the dashed boxin the upper right corner. Here we can see the solutions thatperformed relatively well in both environments. In analyzingthe results, we found that the best solutions from Treatment3 performed in the terrestrial environment about 95% as wellas those evolved only from Treatment 1 and in the aquaticenvironment about 75% as well as those from Treatment 2. Inthis region, we also see clusters of solutions, as indicated bythe darker shaded points. This area also demonstrates that thereare multiple possible solutions, each of which arrives at slightlydifferent fitnesses while being effective in both environments.

Figure 6 plots the normalized performance of solutionsfrom Treatment 3 in each environment over evolutionary time.Fitness values in this figure have been normalized to the bestresults from Treatments 1 and 2 respectively. In this figure, wesee that evolved solutions tend to perform approximately 75%in the aquatic environment when compared to the normalizedfitness from Treatment 2 and 95% as well as those in Treatment

Fig. 5. Fitness landscape of all individuals over the evolutionary trials forsolutions evolved in Treatment 3. Fitness values have been normalized usingthe best values from the respective environments to allow comparison betweensingle environment evolved individuals and amphibious individuals. Darkershaded areas indicate a large number of solutions with similar performance.The box in the top right contains solutions that perform well in bothenvironments.

1. This plot demonstrates that the fitness progression in theterrestrial environment increases at a relatively stable rate,whereas the aquatic environment experiences more variationover the course of evolution.

E. Treatment Comparisons

In two validation tests, we evaluated the controllers evolvedfor one environment, when integrated with morphologiesevolved in the other environment. These tests demonstratethe shortcomings of only evolving morphology for one en-vironment when compared to Treatment 3. When insertingthe evolved morphology for the Treatment 1 into an aquaticenvironment, for example, the performance was only 38% ofthe optimal distance travelled by solutions for Treatment 2.Moreover, as is apparent in Figure 4, the morphology fromTreatment 2 is not even capable of moving in the terrestrialenvironment, since its fins do not touch the ground. These twotests demonstrate the coupled dynamics that form between avirtual robot’s brain and body and the importance of the findimensions for effective swimming. Disrupting these dynamicsby swapping morphologies proved to be extremely disruptiveto their function.

Treatment 3 addresses these shortcomings by evaluatingsolutions in both environments. Each environment was allowedto have its own controller in this treatment, as switchingbetween controllers is considered to be a trivial process. Inboth environments, controllers evolved joint limits near theirmaximum values, indicating that a shortened stroke is not

Fig. 6. Average performance of the best individual solutions per trial fromTreatment 3 over evolutionary time. Fitness was based on the performancein both environments, as such, the performance does not necessarily increaseover each generation.

beneficial in either environment. Although the range of motionwas similar, controllers for the two environments differedsignificantly (p < 0.001) in the speed of moving the arms.Average values of 0.6 Hz evolved in the aquatic environment,while values in the terrestrial environment were closer to 1 Hz.

Effects of brain/body coevolution become apparent whencomparing evolved results of Treatments 2 and 3. Specifically,the best controller from Treatment 2 exhibited an oscillationfrequency of 0.89 Hz, while that of the best aquatic controllerin Treatment 3 had an oscillation frequency of 0.6 Hz. Thefinal distributions of evolved oscillation frequencies were sig-nificantly different (p < 0.001) between the two treatments,however, a relationship between oscillation frequency and finarea can be seen in Figure 7. In the figure, two distinctdistributions between the treatments with regards to the finarea can be seen, which is the direct result of the dominantfin morphologies and oscillation frequency that emerged ineach treatment. A quadratic regression model demonstratesa relationship between the fin morphology and oscillationfrequency in the aquatic environment. The fin area distributionsfor the two treatments were significantly different (p < 0.001)

with these differences further evident in Figures 4(b) and 4(c).In the regression model, fin area accounts for 90% of thevariation in the oscillation frequency (p < 2 x 10-16), indicatinga strong relationship between the two parameters. Further-more, this model provides insight into the strong relation-ships that form between a robot’s controller and morphology.Specifically, as the fin area increased (morphology), a sloweroscillation frequency (controller) was used to reach optimallocomotion strategies. Coevolutionary approaches can discoverthese relationships during the evolutionary process to optimizean overall design. This feature is especially beneficial whenintegrating structures such as passive joints into a design, asthese dynamics are not always known a priori.

Fig. 7. Distribution of the oscillation frequency of the controllers in theaquatic environment in regards to fin area. The oscillation frequencies aredependent upon the fin area for a morphology with 90% of the variancein oscillation frequency being accounted for by the fin area with a p-value < 2 x 10-16.

F. Physical Validation

Upon conclusion of the simulation trials, we selected thebest performing solution from Treatment 3 and fabricated itusing a 3D printer. Figure 3 shows the printed model includingthe passive hinged fins. Initial experiments with this physicalmodel found movement similar to that of the simulation results.The passive joint moved as expected with the fin collapsingbackwards during the recovery stroke before returning to avertical position during the power stroke. Aquatic testingconducted with the physical robot was especially promising,as the robot was able to swim effectively (Figure 8), indicatingthat we had simulated the passive joint dynamic correctly.However, extensive testing was not possible due to designissues unrelated to the evolutionary process. Specifically, theservo to arm connection proved too fragile operating in aterrestrial environment. Consequently, real world trials and

possible comments on the reality gap [3], [42], [45] will beaddressed in future work upon fabrication of a more robustphysical model.

Fig. 8. Initial testing of the printed model in an aquatic environment verifiesthat the passively hinged fin performs similarly to the characteristics seen inthe simulation. During the recovery stroke, the fin flexes upwards, pivoting onthe passive joint, to reduce drag and enable forward movement of the robot.

V. DISCUSSION

Although the morphology of a robot is often fixed fol-lowing fabrication, the controller need not be static. Consider-ing the capabilities of current microcontrollers, maintainingmultiple controllers is a feasible approach that has beendemonstrated in amphibious robots [14]. Working under thisassumption, we coevolved both the morphology and basiccontroller scheme for our simulated robot. We demonstratedcontrollers that were uniquely tied to their respective mor-phologies, as such, performance of a robot with either analtered morphology or controller would not be expected toperform as well. Simulation results indicate that a unique setof control parameters exist for each environment given a staticmorphology. Accordingly, the two-controller approach used inthis study is an effective way to generate optimal locomotionacross different environments with the same robot.

Passive characteristics in materials and joints have thepotential to enhance robotic designs. Here, the use of a passivehinge joint allows each fin to be controlled by one servo motor,leading to a robot with a simple drive-train design and lessdependence upon gearboxes and other mechanical parts thatare subject to failure. Reducing the number of motors canproduce more efficient mobile sensor platforms as well aspotentially smaller robots. Additionally, the incorporation ofpassive joints in this robot design allows the motors, controllerand power supply to be housed inside the main body, reducingthe waterproofing requirements of the design and limiting thepotential failure areas. Coupled with an amphibious design,robots incorporating passive characteristics may be used fortheir ability to efficiently navigate in remote areas providingmobile sensing capabilities.

Simulating physical conditions accurately is a challengethat produces direct benefits to evolved solutions. The use ofaccurate mathematical models to develop simulations can alsogreatly increase the quality of simulation results facilitatingtransfer to physical designs potentially addressing the realitygap [3], [45]. Although simulating surface environments is rel-atively straightforward, developing models for hydrodynamics

is essential to obtaining accurate simulation results for aquaticsimulations. In this paper, we used an approximation for thehydrodynamic forces by estimating the drag forces the pectoralfins generate as they move through the water. Through thedevelopment of more robust mathematical models [1], [48]by working in concert with engineers, simulation qualitiescan be improved which in turn will increase the quality ofsimulation results. Additionally, performing simulation exper-iments and validating them in physical models allows forfurther refinement to the simulation environments used forthese experiments, thereby improving the results of futuretrials. Future work will seek to improve the physical robot’sdesign allowing for detailed trials which can then be used torefine our simulation.

VI. CONCLUSION

Passive characteristics of components offer potential ben-efits to robotic systems, including simplified motor layoutsand lower power requirements, but present many challengesto the designer. In this paper, we described a study in theevolution of amphibious robots that exploit the properties ofpassive joints. Evolved controllers demonstrated the abilityto locomote effectively in both terrestrial and aquatic envi-ronments. Compromises in the morphological developmentarose as evolution found solutions that moved effectively inboth terrestrial and aquatic environments. Optimal solutions inthis study tended to have a strong relationship between theircontrollers and morphologies, as shown through regressionanalysis. Our future work will focus on expanding the range ofbehaviors for robots as well as fabricating and testing a morerobust physical realization.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the contributions tothis work of Anthony Clark, Jianxun Wang and Profes-sor Xiaobo Tan. This research has been supported in partby National Science Foundation grants CNS-1059373, CNS-0915855, CNS-0751155, CCF-0820220, and DBI-0939454.Any opinions, findings, and conclusions or recommendationsexpressed in this material are those of the author(s) anddo not necessarily reflect the views of the National ScienceFoundation or other research sponsors.

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