Controlling Tensegrity Robots through Evolution

Controlling Tensegrity Robots through Evolution

Atil IscenOregon State University

Corvallis, OR, 97331, [email protected]

Adrian AgoginoUC Santa Cruz / NASA Ames

MS 269-3, Moffett Field, CA 94035, [email protected]

Vytas SunSpiralSGT Inc. / NASA Ames

MS 269-3, Moffett Field, CA 94035, [email protected]

Kagan TumerOregon State University

Corvallis, OR, 97331, [email protected]

ABSTRACTTensegrity structures (built from interconnected rods andcables) have the potential to offer a revolutionary new roboticdesign that is light-weight, energy-efficient, robust to fail-ures, capable of unique modes of locomotion, impact toler-ant, and compliant (reducing damage between the robot andits environment). Unfortunately robots built from tenseg-rity structures are difficult to control with traditional meth-ods due to their oscillatory nature, nonlinear coupling be-tween components and overall complexity. Fortunately thisformidable control challenge can be overcome through theuse of evolutionary algorithms. In this paper we show thatevolutionary algorithms can be used to efficiently controla ball shaped tensegrity robot. Experimental results per-formed with a variety of evolutionary algorithms in a de-tailed soft-body physics simulator show that a centralizedevolutionary algorithm performs 400% better than a hand-coded solution, while the multiagent evolution performs 800%better. In addition, evolution is able to discover diverse con-trol solutions (both crawling and rolling) that are robustagainst structural failures and can be adapted to a widerange of energy and actuation constraints. These successfulcontrols will form the basis for building high-performancetensegrity robots in the near future.

Categories and Subject DescriptorsI.2.6 [Artificial Intelligence]: Learning

General TermsAlgorithms, Design

KeywordsEvolution, Robotics, Tensegrity

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Figure 1: Tensegrity Structure. Tensegrities are com-posed of pure tension and pure compression elements (e.g.cables and rods). They can be light-weight, energy-efficientand robust to failures.

1. INTRODUCTIONTensegrity robots are part of an exciting emerging field of

soft-body robotics that are entirely composed of pure tensionand compression elements (cables and rods - see Figure 1).These structures are made of axially loaded compression el-ements encompassed within a network of tensional elements,and thus each element experiences either pure linear com-pression or pure tension. As a result, individual elementscan be extremely lightweight as there are no bending orshear forces that must be resisted. A unique property oftensegrity structures is how they can internally distributeforces. As there are no lever arms, forces do not magnifyinto joints or other common points of failure. Rather, ex-ternally applied forces distribute through the structure viamultiple load paths, creating a system level robustness andtolerance to forces applied from any direction. Thus tenseg-rity structures can be easily reoriented and are ideally suitedfor operation in dynamic environments where contact forcescannot always be predicted.

Tensegrities have a number of beneficial properties includ-ing:

• Light-weight: Forces align axially with componentsand shocks distribute through the tensegrity, allowing

tensegrities to be made of light-weight tubes/rods andcables/elastic lines.

• Energy efficient: Through the use of elastic tensilecomponents and dynamical gaits, efficient movementis possible.

• Robust to failures: Tensegrities are naturally dis-tributed systems and can gracefully degrade perfor-mance in the event of actuation or structural failure.

• Capable of unique modes of locomotion: Tenseg-rities can roll, crawl, gallop, swim or flap wings de-pending on construction and need.

• Impact tolerant and compliant: Since forces aredistributed upon impact, they can fall or bump intothings at moderate speed. In addition, their compli-ance ensures that they do minimal damage to objectsthey contact.

• Naturally distributed control: Characteristics offorce propagation in tensegrities allows effective localcontrollers.

The last property is the most subtle but important. In “tra-ditional” robots, distributed controls becomes messy due tothe need to communicate global state information to all thecontrollers with high precision, and thus often underminesthe very promise of distribution. Fundamentally, this stemsfrom the fact that a rigidly connected structure will magnifyforces internally through leverage, and will accumulate forceinto joints. Thus, the actions of a local distributed controllercan have disproportionate global consequences. These con-sequences can require a certain amount of global coordina-tion and state management, undermining the value of the lo-cal controller. Tensegrity structures are different, due to thetension network, there is no leverage in the structure. Thus,forces diffuse through the structure, rather than accumulatein joints. As a result, actions by a local controller diffusethrough the structure, integrating with all the other localcontrollers. While any one local controller will impact thestructure globally, that impact is locality relevant and notmagnified via leverage. Thus, the structure enables true dis-tributed control, because local actions stay (predominately)local.

Despite these desirable properties, tensegrity robots haveremained mostly a novelty for many years due to difficultcontrol properties that make them hard to control with tra-ditional control algorithms such as:

1. Complex oscillatory motions: Tensegrity robotstend to have oscillatory motions influenced by theirinteractions with their environment.

2. Elastic Nonlinear distributed interactions: A forcegenerated on one part of the tensegrity propagates ina nonlinear way through the entire tensegrity, causingshape changes, which further change force propaga-tions.

Fortunately the combinatorial optimization capabilities ofevolutionary algorithms combined with the distributed prop-erties of multiagent systems are a natural match to theseproblems. Evolutionary algorithms can learn complex con-trol policies that maximize a performance criterion without

needing to handle the oscillatory motions and distributedinteractions explicitly. In addition, increased performancecan be achieved by assigning evolving agents to differentcontrol points throughout the tensegrity. Then as a multi-agent system, the agents can co-evolve to create a unifiedcontrol policy.

In this paper, we present how both centralized evolutionas well as cooperative coevolutionary algorithms (CCEA)can be used to learn control policies that allow a six seg-ment tensegrity to roll through its environment. We presentdifferent approaches for fitness and test the best one againstdifferent environmental conditions. This paper is organizedas follows: Section 2 gives background on tensegrity robotsand previous work. Section 3 gives details about the tenseg-rity robot used in this paper. Section 4 shows different ap-proaches to evolving a control policy for the tensegrity robot.Section 5 presents experimental results. Section 6 discusseshardware details and Section 7 ends the paper with conclu-sions and future work.

2. BACKGROUND AND PREVIOUS WORKTensegrity structures are a fairly modern concept, having

been initially explored in the 1960’s by Buckminster Fuller[6] and the artist Kenneth Snelson [19]. For the first fewdecades, the majority of tensegrity related research was con-cerned with form-finding techniques [25, 9, 20, 15, 26, 12,14] and the design and analysis of static structures [1, 7,18]. Research into control of tensegrity structures was ini-tiated in the mid-1990’s, with initial efforts at formalizingthe dynamics of tensegrity structures only recently emerg-ing [18, 10, 24]. The very properties that make tensegritiesideal for physical interaction with the environment (com-pliance, multi-path load distribution, nonlinear dynamics,etc.) also present significant challenges to traditional con-trol approaches. A recent review [22] shows that there arestill many open problems in actively controlling tensegrities.

There are several approaches that have been taken to con-trol tensegrity robots. Most related to the work in this paperare approaches to locomotion of tensegrity robots using evo-lutionary algorithms [5]. Paul et al [13] shows two differenttensegrity robots that can perform a locomotion movement.These robots perform motion mostly by alternating betweendifferent configurations and doing small hops and crawling.Being able to successfully evolve these gaits is impressivegiven that one of the tensegrities uses only three rods, whilethe other uses four. However, such simple tensegrities arenot able to achieve efficient rolling motion or complex dy-namical movements mainly due to shape constraints of thestructure used.

Instead of evolving control policies for tensegrities, morerecent work has been done on engineering control algorithmsthat leverage key features of locomotion [17, 2]. There hasalso been recent work involving hand tuning of controls forrolling tensegrity robots by body deformation [16, 8, 21, 4].While this work is able to produce stable smooth dynam-ics, they are not designed to address the oscillatory natureof tensegrities that come up at high speeds, on uneven ter-rain, or upon collisions with other objects that occurs inmany domains. Instead, with our evolutionary approach,these oscillatory complexities of the tensegrity are implicitlyincorporated into the fitness evaluation function generatedfrom the physics simulations, and therefore we are able to

create dynamical control that can incorporate complexitiesof the domain as they arise.

3. TARGET TENSEGRITY PLATFORM

Figure 2: Structure for Tensegrity Robot. This six-roddesign is one of the simplest designs that can behave as a“ball.” It is capable of rolling, changing shapes, and can berobust against failures.

In this paper we show how controls can be evolved on aball shaped tensegrity capable of a large range of movement.To do this we choose as our experimental platform, a 6-rod,24-cable tensegrity as shown in Figure 2. It is chosen since itis one of the simplest tensegrity platforms that can exhibitthe following complex behaviors:

• Many modes of locomotion: They can crawl, “gal-lop” and roll, with rolling being an especially efficientand fast mode of locomotion.

• Robust against failures: They exhibit enough re-dundancy that they can recover from hardware failure.

• Shape changing: They can change shape to “peer”over things, get unstuck or to move sensors located ontensegrity structure.

These “ball” tensegrities can be useful in many domains,especially those in which a tensegrity has to navigate ruggedterrains that can be difficult for wheeled vehicles.

3.1 StructureThe structure of the tensegrity used in this paper is shown

in Figure 2. Rods do not connect directly with other rods,instead, rods are indirectly connected through cables, re-sulting in a continuous tension network as the primary loadtransfer system of the structure. In the orientation shownin Figure 2 (left) one pair of the rods are parallel to x-axis,another pair is parallel to y axis and the last pair is parallelto z-axis. Each end of a rod is connected to the ends of othernon parallel rods via 4 different cables. When the structureis in balance, it is symmetrical and convenient for a rollingmotion. On the other hand, when an external force is ap-plied, it easily deforms and distributes the force to everycomponent of the structure.

In addition to the base tensegrity, we attached a ballshaped payload to the center of the tensegrity via an addi-tional 8 payload cables. The payload represents the essentialparts of the robot, such as computing, sensors, batteries, orother instruments. As opposed to the 24 outer cables, these8 payload cables have constant length and are not activelycontrolled in this work (Figures 1,6).

3.2 ControlsThe tensegrity is controlled by changing the lengths of the

cables. Many hardware implementations do this by using amotor to wind the cable onto a spool that is either interiorto the tensegrity or inside a rod. Other concepts involveusing dynamic cable twisting or elastomers to change thelength of the cable. In this paper we do not consider thehardware implementation, though we do limit our abstractmodel of actuation to reasonable performance characteristicsfor velocity, acceleration, and string elasticity.

The control of the robot is done via sinusoidal control ofthe lengths of the cables. The lengths of the cables changeover time according to a sinusoidal signal, and the param-eters of the signal are the output of the evolutionary al-gorithm. The length of each cable is calculated with theformula:

y(t) = C +A ∗ sin(ωt+ φ) (1)

where,

• C represents the center position of the sine wave.

• A, the amplitude, is the peak deviation of the functionfrom its center position.

• ω, the angular frequency, is how many oscillations oc-cur in a unit time interval

• φ, the phase, specifies where in its cycle the oscillationbegins at t = 0.

By using 24 sinusoidal signals for 24 cables, overall controlof the tensegrity is based on 96 (24 ∗ 4) parameters.

3.3 SimulationOur tensegrity simulator is built on top of the open-source

Bullet Physics Engine [3]. Bullet was chosen because ofits built in support for soft-bodied physics, and has beenused previously in tendon-driven robotics simulators suchas Wittmeier et al’s CALIPER software [23]. The simulatedtensegrity structure has a size of 10 meters for each roddue to the fact that the physics engine is more precise forobjects approximately that size. Cables are represented asnodes with Hooke’s-law-like stiffness between them. There-fore our “cables” are actually somewhat elastic and exert aforce dependent on their length. We keep our model of actu-ation abstract in order to explore the best control solutionsand then drive requirements back into real hardware designrequirements. To enforce additional realism, we prevent thecables being actuated when stretched more than 25%, as anupper limit on the hypothetical motor force. This approachallows us to find the types of control and requirements thatwill be driven into actuation selection.

4. EVOLUTIONARY ALGORITHMSWhile the control parameters of our tensegrity platform

are relatively straightforward, the relationship between theseparameters is highly complex. In this section we explore howwe can use the simulation combined with a fitness evaluationto implement an evolutionary algorithm that can evolve aset of control parameters that leads to the desired behavior.

4.1 Evaluation FunctionWe measure the performance of a simulated tensegrity

based on how far it can travel from a starting location within60 seconds:

f = d(C1, A1, ω1, φ1, · · · , C24, A24, ω24, φ24) , (2)

where, d is the distance travelled, which is a function of the96 parameters of the control policy. Note that the decom-position of the distance function d is not readily obtainablein closed form. Instead it must be computed from observingsimulations or measured from a physical implementation.Also note that our evaluation does not explicitly take anybehavior into account besides distance moved. Tensegritiescan exhibit many different gaits, ranging from hopping torolling, and many different paths, ranging from spirals tostraight lines. However, tensegrities that maximize our fit-ness function tend to roll in fairly straight lines. Deviationsfrom this pattern tend to hurt performance.

4.2 Centralized Evolutionary AlgorithmsIn this paper, we perform both centralized evolution and

multiagent coevolution. In the centralized case, a single con-trol policy is evolved for the entire tensegrity robot. Thiscontrol policy sets the 96 parameters for the sinusoidal con-trollers. The algorithm is a simple evolutionary algorithmdesigned to maximize our fitness function. At the begin-ning of training, a population of n random policies is cre-ated and evaluated based on our fitness function f . Aftereach round of evolution, the worst k policies are removed,and are replaced by mutated versions of the best k policies.Mutation is uniformly random for each parameter. For ex-periments that use crossover, we use a simplest basic singlepoint crossover. For single point crossover algorithm, in ad-dition to mutation, new k policies are assigned to teams oftwo, and for each team, those two policies exchange partof their parameters. The crossover point is a randomly se-lected number between 1 and 96 (number of parameters) andall the parameters after this point are exchanged. In bothcases (crossover and no crossover), as evolution progresses,the population tends to converge to higher performance poli-cies.

4.3 Cooperative Coevolutionary AlgorithmsWhile centralized approaches often produce good results,

evolving a centralized controller can be slow due to the sizeof the search space. If the control parameters are tightlycoupled, then the centralized approach may be the best wecan hope for. However, control of a tensegrity robot is notnecessarily tightly coupled. While changing the length ofa cable will strongly affect neighboring components, it willhave less of an effect on components on the opposite sideof the tensegrity. Therefore decentralized control is possibleand can greatly reduce the search space for each componentin the decentralized controller.

In this paper, we introduce such a decentralized controlleras a cooperative coevolutionary system, using principles de-rived from multiagent systems. In this paradigm each of the24 cables is controlled by an individual agent. The job ofeach agent i is to control the four parameters of the sinusoidcontrolling its cable: Ci, Ai, ωi and φi. To do this, eachagent i will have its own population of control parameters,pi, where each member of the population, pi,j specifies thefour control parameters. Each agent then evolves its popu-

lation to produce good values of control parameters in thecontext of the control choices of the other agents. The goalof these coevolutionary agents is still the same as the cen-tralized evolutionary algorithm: Maximize the global fitnessevaluation, f .

The advantage of this paradigm is that each agent nowonly has to search through four parameters. The difficultyis the value of each agent’s choice of control parameters nowdepends on the choices of the other agents. The exact samechoice may be good or bad, depending on what other agentsare doing. One way to address this is to evaluate every pos-sible team existing at the current generation. In this paper,this is not possible due to the number of possible cooper-ators. We attempt to handle this issue by taking a fixednumber of samples of the population at each generation ofevolution. Between two generations, each agent’s popula-tion is sampled s time and they are put together to forms complete control policies. Each of these control policiesis then evaluated with respect to our global fitness evalu-ation function, f , producing s evaluations. Typically thenumber of samples s will be many times larger than the sizeof the population, therefore each individual member of apopulation will typically be part of multiple control policies.The main issue is how we evaluate a member of a popula-tion pi,j which has participated in multiple control policies,when each control policy has received a different global fit-ness evaluation f .

In this paper, we address this issue in the following threeways:

1. Generational Average - Assign the mean value of theglobal fitness evaluations for control policies in whichthe member participated during this generation.

2. Leniency - Assign the highest value of the global fitnessevaluations for control policies in which the memberparticipated in.

3. Historical Average - Assign the mean value of globalfitness evaluations, averaging across all the generationsthat the member survived.

Taking average and leniency are commonly used methodswith cooperative coevolution [11]. To improve performance,we augment this approach by taking historical averaging.Historical averaging uses all the samples that the membershad been part of, not only the current generation but alsothe ones with previous generations with previous teammates(Algorithm 1). Every surviving agent carries its history tothe new generation and uses that information to calculateits average score.

4.4 Hand-Coded SolutionIn addition to creating control policies through evolution-

ary algorithms, we explore how to hand-code a control solu-tion using the same parameters available to the evolutionarysystem. The goal here is to explore the challenges of hand-coding a solution and to see how well our best effort com-pares to our learned solutions. It turns out that creating acontrol policy by hand using our 96 parameters is extremelydifficult, so we created 8 control groups with 3 cables in eachgroup. These 3 cables form a triangle that have the samelength, making it easier to write a hand-coded controller.Even with this simpler approach, the best achieved solu-tion barely moved. This problem will only get more difficult

Algorithm 1: Cooperative coevolutionary Algorithmwith Historical Average

Data: Population of n elements for each agentfor i=1..15 do

random team ← ∅ ;forall the Populations do

random team ← random agent;endscore = evaluate random team ;forall the agents ∈ random team do

agent.history ← agent.score ;end

endforall the Populations do

forall the agents doagent.fitness = average(agent.history) ;

endorder the population;eliminate last k;copy first k to last k;set score of last k to MIN ;mutate last k;clear history for last k;

end

as we scale the tensegrity robots to more complex versionswith more elements. To improve performance, we reducedthe parameter space by hand coding the amplitudes of eachgroup and making the oscillation frequency the same for allgroups. The results shown later in this paper are for thissecond, better-performing hand-coded solution.

5. EXPERIMENTAL RESULTSIn this section, we present experiments evaluating the per-

formance of our evolution-based methods to control tenseg-rity robots in the physics simulator described in Section 3.3.The goal of our experiments is to evaluate whether evo-lutionary systems can be successfully applied to tensegrityrobots under nominal conditions, and how robust these solu-tions are to limitations in the range of actuation, to actuatornoise and to a physical breakage in a cable of the tensegrity.For the nominal condition case we test the following meth-ods of creating the controller:

• Hand Coded Control policy is developed by hand totry to achieve maximum performance.

• Centralized Evolution A single control policy is learnedfor the entire tensegrity robot.

• Decentralized Evolution Cooperative Coevolution-ary Algorithms (CCEA) approach.

We then test different fitness methods for CCEAs: Aver-age, Leniency, Historical Average. We test the robustness ofour highest performance solution (historical average) in thefollowing ways:

• Actuation Noise We add noise to how far cables areactually moved as compared to how far they are beingrequested to move.

• Cable Failure We test performance when a singlecable in the robot breaks.

• Obstacles We randomly place half sphere obstaclesinto the environment.

All experiments start with a stationary tensegrity roboton the ground. For each experiment, the robots are createdon a flat surface, and after 5 seconds of stabilization time,active control of the cables starts. The agents are given afixed amount of time (60 seconds) to move the robot as faras possible. The evaluation function is the distance betweenthe starting position and the position at the end of the giventime period. The population size in the policy search is setto n = 10 and the selection parameter is set to k = 5. Weperform 10 statistical runs for each type of experiment. Us-ing a t-test we confirm that our conclusions are statisticallysignificant. All our major results are p<0.95.

5.1 Centralized, Decentralized and Hand-Coded

Figure 3: Performance of Control Algorithms. Mul-tiagent coevolution performs significantly better than othermethods since it is able to take advantage of distributed na-ture of tensegrity control.

The first experiment compares three different control poli-cies: Hand-coded, centralized evolution and multiagent co-evolution. Figure 3 shows that both evolution-based ap-proaches can easily outperform the hand coded solution.Looking at the converged policies, the multiagent evolutionapproach provides the best performance by moving 100%more quickly than the single agent and 400% more than ourhand coded agent. Both centralized and decentralized evo-lution are able to achieve smooth rolling motions as shownin Figure 6. Note that while our hand coded tensegrity isnot able to achieve a rolling motion, we are not trying to im-ply that this problem is impossibly complex for non-evolvingalgorithms. In fact there have been several successful algo-rithms to do this [16, 8, 21, 4]. Instead we are illustratingthat it is in fact quite difficult to create these controls, andthat the centralized and multiagent evolutionary algorithmsare creating complex, non-trivial control solutions. In addi-tion a multiagent framework has the potential to be adaptedto many different complex tensegrities with less effort thanhand coding an algorithm for each new tensegrity.

It can be seen that the tensegrity controlled by policiesevolved from coevolution reaches a performance around 900meters in 60 seconds. By observing the behavior, we con-firmed that the movement is established by smooth rolling

motion as illustrated in Figure 6. This rate corresponds tothe tensegrity moving at approximately 28 revolutions perminute.

5.2 Historical Average, Average and Leniency

Figure 4: Evaluation Methods. Using a historical averagereaches best score and it is consistent. Lenient learners havebigger error bars.

The second experiment compares different fitness assign-ment methods for CCEAs. As it can be seen, using a his-torical average performs better than every other method.Moreover, the small error bars signifies that using the histor-ical average consistently provides similar performance. Weare further analyzing historical average as a future research.Looking at the error bars of the lenient learners, it can beseen that standard deviation is high: It also reaches verygood policies in some of the statistical runs, but the averagesuccess is lower.

Figure 5: Sample Size. Taking more samples for each trialimproves stability but takes more time reach better behavior

To make sure that the sample size that we chose doesnot significantly affect the results, we tested the historicalaverage method with different sample size between each gen-eration (s). Figure 5 shows that the sample size affects per-formance when it is too low such as 10, on the other hand,

Figure 6: Tensegrity Dynamics. Tensegrity is able toachieve smooth rolling motion. This rolling is accomplishedsolely by changing the length of the cables. Our learned con-trol policies produce rolling that is also dynamical as thetensegrity does not stop to setup next roll action. This typeof rolling can be fast and highly efficient.

a sample size as high as 1000 decreases the learning speed.Considering this result, we used 50 as the default value forthe rest of the experiments.

5.3 Actuation Noise

Figure 7: Actuation Noise. The best policy can take upto 25% noise, evolving in a noisy environment scores betterin higher noise environments.

To measure the robustness of our evolutionary algorithmagainst noise, we test the multiagent tensegrity robot in anenvironment with different levels of actuation noise. Actu-ation noise is applied at every time step to the sinewavethat the evolutionary algorithm generate to control the ca-bles. At every time step, a random value from a normaldistribution is directly added to the value of the Equation1. To test different levels of noise, we use different envi-ronments where the standard deviation of the noise is setto 1%, 2%, 5%, 10%, 25%, 50%, 100% of the amplitude of thesine wave for each cable.

In this experiment, we test two different policies in ournoisy environment: 1) Policies from a multiagent systemthat had learned in an environment without noise, and 2)Policies that are learned in an environment with the same

amount of noise they are tested in. Figure 7 shows thattensegrities trained both with and without noise can per-form remarkably well when the level of noise is below 15%.This is an impressive result, as it shows that the solutionsgenerated in a non-noisy environment are not highly specificto an exact model of a tensegrity and exact environmentalconditions. Instead the solutions appear highly generaliz-able. Beyond this level of noise performance goes down sig-nificantly. However, while performance is low, a tensegritytrained with a high level of noise can still perform at a base-line level while subjected to high levels of noise, which couldbe very useful in many situations.

Figure 8: Robustness Tests with Obstacles and Bro-ken Link. Coevolutionary Algorithms can overcome bothobstacles and broken link scenarios

5.4 Broken Cable and ObstaclesThe fourth experiment tests the robustness of the struc-

ture and the controller. In our first experiment we removeone of the cables, which decreases controllability and alsodisrupts the balance of the structure. With the cable re-moved, the structure is no longer symmetrical and it cannot keep its ball shape by default. In our second experimentwe place the normal tensegrity in an environment contain-ing randomly placed half sphere obstacles. When we testour best policy trained in a perfect environment in thesetwo conditions, the performance drops to 50% with obsta-cles and it cannot roll with a broken link (Figure 8). On theother hand, if we perform evolution in these conditions, theevolutionary algorithm can still find successful locomotionpolicies for a tensegrity with broken cable, or in an environ-ment with obstacles.

This result shows that under adverse conditions we canevolve a controller that takes advantage of the large rangeof motion inherent in tensegrity robots to effectively main-tain locomotion. Note that this result does not show that theevolved control policy dynamically adapts to problems, sincein this experiment we retrain our policy after the breakage.However, it does show the flexibility of the evolution pro-cess and the ability to pre-evolve controls associated withpotential failure modes.

Figure 9: Tensebot, our Experimental TensegrityRobot Prototype. This 6-rod tensegrity robot is designedto test hardware implementation and shape-changing abili-ties of tensegrities. We are in the process of building 6-rodtensegrity that can roll.

6. HARDWARE ROBOTWith the actuation requirements explored in simulation,

and building on our experience with prior prototype tenseg-rity robots, we will be spending this year researching appro-priate actuation technologies and building a prototype of therolling tensegrity robot discussed in this paper. Our existingprototype tensegrity robot uses position controlled spooled-cable actuation, and we will explore two new approaches:Impedance Controlled (Tension and Position) Spooled Ca-ble actuation, and Twisted Cable Actuation. Our existingprototype robot is already designed for spooled cable actu-ation and we will retrofit it with new sensors and controlsto support Impedance Control. In parallel we will evaluatea novel “twisted cable” actuation approach that we believewill allow for the use of significantly smaller and energy effi-cient motors due to the decoupling of motor torque outputfrom actuator tension output. Finally these two actuatorapproaches will be evaluated for design simplicity, power ef-ficiency, and total system mass, and the best approach willbe used on our new rolling tensegrity robot. This new robotis designed to validate the controls approaches explored hereand to show that these tensegrity robots can be used as land-ing and mobility systems.

7. CONCLUSIONS AND FUTURE WORKTensegrity robotics matched with multiagent evolution-

ary systems have a promising future. The structural prop-erties of tensegrities give them many beneficial properties,while their distributed nature makes them a perfect matchfor multiagent systems. In this paper, we introduce a firststep to this promise. We first show that, in simulation, evo-lutionary algorithms are able to come up with an effectivecontroller that allows a moderately complex tensegrity ballto roll. Then we show how performance can be improved byapplying a multiagent coevolutionary system to this sametensegrity robot. To handle fitness assignment problems incoevolution, we use sampling, introduce a new method basedon the historical average and compare it with average andlenient learners. For future work, we are working on a de-

tailed analysis of this method compared to averaging andleniency.

Not only is the coevolutionary approach able to producea smooth rolling motion for the tensegrity robot, it is ableto do so under a wide range of adverse conditions, includingactuation noise, obstacles and cable breakage. These resultsshow that multiagent evolutionary systems are a strong can-didate for tensegrity control. In addition, the high level ofrobustness may allow our framework now used in simulationto be used on our physical tensegrities now in development.

The multiagent evolutionary system used in this paperrepresents just a glimpse of what may be possible for tenseg-rity control. While the distributed nature of a tensegritymakes it a natural match to the distributed nature of a mul-tiagent system, the multiagent system we use in this paperis actually not as distributed as it could be. While all theagents take independent actions, they all try to maximizethe same global system fitness evaluation function. Theiruse of this global evaluation function can cause agents totake into account too much information and limit their abil-ity to evolve quickly. In contrast, future research may showthat it is possible to use agent-specific evaluation functionsthat are more relevant to an agent’s particular action. Suchchanges could allow coevolving systems to be used for evenmore complex tensegrities and achieve more sophisticatedcontrol behaviors.

AcknowledgmentsThis research was partially supported by the NASA Inno-vative Advanced Concepts (NIAC) Program. Tensebot con-structed with support from Idaho Space Grant Consortium

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