Evolution of Shape-Changing and Self-Repairing

Control for the ATRON Self-Reconfigurable Robot

David Johan ChristensenMaersk Mc-Kinney Moller Institute for Production Technology

University of Southern Denmark, Odense, DenmarkEmail: david@mip.sdu.dk

Abstract—The ATRON self-reconfigurable robotconsists of simple interconnected modules. Modulesmove relative to other modules and as a result changethe shape of the robot. The ATRON modules are diffi-cult to control because of complex motion constraintson the modules. Motion constraints are reduced byusing meta-modules composed of three modules. Ameta-module may emerge from unstructured groups ofmodules if three modules are connected in the rightconfiguration. The meta-module then moves on a sur-face of modules and stop at another position. To attractmoving meta-modules and thereby to specify the shape-changing task of the robot we use attraction-points.In this work we evolve a distributed artificial neuralnetwork controller for the modules. The controller isidentical on every module and controls when a meta-module emerges, how it move and when it stops. Insimulation we demonstrate how this control strategyallows the ATRON robot to shape-change to supportan unstable roof, build a bridge across a gap and toself-repair a broken bone. We conclude that the controlstrategy is able to shape-change and self-repair theATRON robot independent on whether it consists ofdozens, hundreds or thousands of modules.

I. Introduction

Self-reconfigurable robots consist of a number of inter-connected heterogeneous or homogeneous robot modules.Modules have their own processing power and are ableto communicate with other modules and sense the en-vironment. In lattice-based self-reconfigurable robots themodules are rigidly interconnected in a lattice structure.The modules are able to connect to, disconnect from andmove relative to other modules in order to change theconfiguration of modules. The modules are designed togive the self-reconfigurable robot abilities such as shape-change, self-repair and self-assemble. Such abilities mayproduce exceptional robots in terms of flexibility, versatil-ity and robustness.

In this work we consider the ATRON module [8] whichis latticed-based and able to self-reconfigure in 3D. AnATRON module has a limited mobility in a structure ofmodules. Because of complex motion constraints on themodules, moving a module from one lattice position toanother is difficult or may even be impossible. Thereforethe self-reconfiguration of ATRON modules is non-trivial.

We consider shape-changing structures of more than 50ATRON modules. The desired functionality of the robot

Fig. 1. In order to support an unstable roof the structure of 500ATRON modules shape-change, stretching upwards to achieve thefunctionality of a pillar. The process is guided by attractions-pointswhich are shown as small spheres.

system is designed by placing virtual points in space, calledattraction-points. Our goal is to build a controller, that isdistributed, identical on every module and makes the robotchange its shape towards the attraction-points.

To overcome modules’ limited mobility, we use threemodules that cooperate as a single entity, a meta-module,to move across the surface of other modules. The mobilityof such a meta-module is much higher that the mobilityof an individual module.

Attraction-point triggers unstructured groups of passivemodules to form meta-modules which then emerge. Meta-modules move, towards attraction-points, across the sur-face of passive modules. Meta-modules which get stuck orreach an attraction-point stop moving and the modulescomprising the meta-module may at a later time be partof another meta-module. To move meta-modules performmeta-actions which is a sequence of basic module actions.

Knowing its local surrounding a meta-module may cal-culate a subset of its reachable space, which is a graphdefining the possibilities of the meta-module in its currentsituation. Using this graph a meta-module can calculatethe shortest path of meta-actions from its current state(position and orientation) to another state in its local

surrounding. Based on this modules decide when to emergea meta-module, how it should move and when to stops.The part of the modules’ controller that makes thesedecisions are three small artificial neural networks (ANN).The ANN’s takes input calculated from the subset of thereachable space of the meta-module. As outputs one ANNgives a decision on whether to emerge. A second ANNgives as output whether to stop. The third ANN assignsa fitness value to every state in the known subset ofthe reachable space graph. The meta-module will movetowards the fittest state. We evolve the weights of theANN controller by letting the system shape-change andmeasure its performance as a fitness value.

The combination of ATRON modules, meta-modules,attraction-points and evolved artificial neural networkcontrol gives rise to a robot which can change its shapeand self-repair in a large range of scenarios. This slightlycomplex control strategy is the best known solution tothe complex problem of shape-changing and self-repairinglarge structures of ATRON modules.

II. Related Work

Besides the ATRON module, hardware prototypes ofmodules able to self-reconfigure in 3D include the MTRAN[14], 3D-Unit [13], Molecule [10] and I-Cubes [22]. Onemain difference between ATRON and these systems is thecomplexity of the individual module in term of degree offreedom. The ATRON module’s single degree of freedommay make it simple to manufacture but hard to control.

Most prior work, on shape-change of self-reconfigurablerobots, focus is on achieving a particular target shape. Thisis problematic to achieve for systems such as the MTRANand ATRON, because of difficult motion constraints onthe modules. Inspired by Bojinov et al. [3] we avoid thisproblem by trying to achieve a particular functionalityinstead of a particular target shape.

Controlling shape-change of large groups of modulesmakes direct search strategies infeasible because of thecomputational complexity involved. Planning strategiesare often possible on smaller groups of modules, to solvea sub-problem or using heuristic search [10], [21], [24].Distributed control [4], [5], [11], [16] strategies are indepen-dent of the global properties of the structure of modules.This helps to ensure robustness, but distributed controlmay be harder to design than centralized control.

In [1], [6], [12], [17], [18], [21], [23] groups of modules areused as meta-modules to handle the base modules’ motionconstraints. A negative characteristic of meta-modules isthat they increase the granularity of the system. Also theincrease in cost and complexity of a single meta-module,compared to a single module, might be difficult to justifywith the improved mobility.

Prior work on self-repair in self-reconfigurable robotsgenerally involves the detection of module failure, decisionson how to remove a defect module and how to replace itwith a spare module [7], [20]. Alternatively, as in this work,

Fig. 2. Photographs of: (a) A single ATRON module, on the tophemisphere the two male connectors are extended on the bottomhemisphere they are contracted. (b) A structure of seven ATRONmodules connected in the surface-centered cubic lattice structure.

self-repair can emerge as a side effect of the control insteadof having a specialized self-repairing part of the controller[19].

Artificial evolution has previously been used on self-reconfigurable robots to automate the design of control.Østergaard et al. [15] evolved with limited success dis-tributed state-machine based controllers for small struc-tures of 12 to 20 ATRON modules. Similarly evolution wasused on small groups of MTRAN modules to automaticallygenerate locomotion patterns [9]. For the 2D metamorphicsystem genetic programming was used to generate con-trollers for movement of 8 modules to solve tasks such asmoving through a narrow passage [2].

III. The ATRON Self-Reconfigurable Robot

The ATRON module, has a single rotational degree offreedom and is able to self-reconfigure in 3D, see figure2(a). It has a spherical appearance composed of twohemispheres, which the module can actively rotate relativeto each other. The modules connect to neighbour modulesusing its four actuated male and four passive femaleconnectors. The connectors are positioned in 90 degreesintervals on each hemisphere. Using infrared channels themodule is able to communicate with neighbour modulesand sense distance to nearby obstacles or modules. Two”Atmel ATmega128” microcontrollers, one on each hemi-sphere, controls the module. A module weighs 0.850kg andhas a diameter of 110mm. 100 hardware prototypes of theATRON modules exist. A more extensive description ofthe ATRON hardware can be found in [8]. In this work themodules are always connected in a surface-centred cubiclattice structure, see figure 2(b).

Motion constraints on the modules affect their ability toself-reconfigure. The single rotational degree of freedom ofa module makes its ability to move very limited, in factthe module morphology does not allow it to move by itself.One module may move another module by rotating it while

(a) ATRON Meta-module. (b) Meta-action: Turn around corners. (c) Meta-action: Shifting orientation.

(d) Meta-action: Rotation of body-module. (e) Meta-action: Rotation of leg-module.

Fig. 3. Illustrations of the morphology of the ATRON meta-module and its meta-actions. The dark modules comprise the meta-module.The ∗-marked modules in (b) and (c) are required to participate in the corresponding meta-actions.

they are interconnected. Before a module disconnects aneighbour module it must make sure that no moduleswill fall off the structure. When rotating a module musttake into account its limited actuator strength and avoidcollisions. A single module has the strength to rotate oneor two other modules in any direction (worst case is againstgravity).

IV. The ATRON Meta-Module

Motion constraints of the ATRON modules may to someextend be reduced by the use of meta-modules [6]. Inthis work we consider meta-modules composed of threeATRON modules: one centre module (body) is connectedto two other modules (legs), one on each hemisphere, seefigure 3(a). To move meta-modules perform meta-actions,which consist of a sequence of connections, disconnectionsand ±90 degree rotations. The meta-module is able toperform twelve different meta-actions. The meta-actionsfollow three different blueprints which are explained below:

Blueprint 1 (8 meta-actions): Meta-actions followingthis blueprint allow the meta-module to move as a twolegged walker on a flat surface of modules. First, the meta-module connects to a structure-module using a hemisphereof a leg which is not connected to the body. Second,the meta-module is disconnected from all other mod-ules. Third, either the connected leg-module or the body-module makes a ±90 degree rotation, as illustrated infigure 3(e) and 3(d).

Blueprint 2 (2 meta-actions): The ∗-marked modulein figure 3(b) is required to help the meta-module whenperforming this meta-action. The four modules performa sequence of connections, disconnections and rotations,which makes it turn around a ”corner” as illustrated infigure 3(b). A different meta-action following the sameblueprint allows it to turn around a corner in the oppositedirection.

Blueprint 3 (2 meta-actions): The ∗-marked module infigure 3(c) is required to rotate one leg-module towardsthe other leg-module, which then becomes the new body-module of the meta-module. Similarly a meta-action thatrotates the other leg follows this blueprint. The effect ofthese meta-actions are to shift the orientation of the meta-module as illustrated in figure 3(c).

The combination of morphology and meta-actions pro-vides the meta-module with a high ability to move on thesurface of other modules.

V. Attraction-points as Task Specification

We use attraction-points to control the flow of meta-modules from one place to another on the structure ofmodules. Attraction-points are virtual points in space,whose positions are known to the modules. Meta-modulesare attracted by attraction-points and move toward themif possible. Attraction-points are used to specify tasksfor the self-reconfigurable robot. E.g. if the robot is tochange its shape to meet some specifications this couldbe done by providing the robot with a set of attraction-points in the desired shape. Two types of attraction-pointshave been used in this work: inhibiting and non-inhibiting.An inhibiting attraction-point turns off if a module isplaced at its position, then meta-modules are no longerattracted by that point. Non-inhibiting attraction-pointsalways attract meta-modules.

VI. Artificial Neural Network Controller

Modules have to make decisions concerning:

1) When should the module emerge as part of a meta-module?

2) Which meta-actions should the meta-module per-form?

3) When should the meta-module stop?

Decisions are made by three feedforward, 3-layer, sig-moid activation function, artificial neural networks(ANN),

Fig. 4. The illustration shows the reachable-space graph of a meta-module on a structure of modules. The reachable-space defines forany reacheable state of the meta-module which meta-actions it mayperform and the corresponding effect on its state. Small spheresare vertices and lines are edges in the graph. For simplicity in thisillustration only the positions of the centre body-module are used tovisualize the states.

one for answering each of the questions. The controllercalculates at runtime a number of inputs to the ANN’s.The inputs are calculated based on positions of attraction-points and the state of the local surrounding, such aspositions and orientation of nearby modules and obstacles.In subsection VI-A, we explain how the meta-modulescalculate a subset of their reachable-space from which theinputs to the ANN’s are calculated. In subsection VI-B,VI-C and VI-D we explain how the ANN’s are used tocontrol the meta-modules.

A. Reachable-space of Meta-moduleMost of the inputs given to the ANN’s are related to

the reachable-space of a meta-module:

• The reachable-space of a meta-module is a graph,where vertices are legal states(position and orienta-tion) of the meta-module and edges are legal meta-actions which brings the meta-module from one legalstate to another.

Since both the meta-module and the environment arechanging dynamically so will its reachable-space. An ex-ample of a reachable-space of a meta-module on a struc-ture of modules is illustrated in figure 4. Meta-modulescalculate at runtime a small subset of their reachable-space, to produce inputs for the ANN’s: 1) The meta-module builds a map of the local surroundings using neigh-bour to neighbour communication. The communicationrange is limited to six neighbours away. The map containinformations about which positions, in the ATRON lattice,are known to contain passive modules, modules part of ameta-module, obstacles and which positions are empty. 2)The reachable-space subset is calculated in a breadth-firstmanner. Initially the subset only contains one state - theactual state of the meta-module. Iteratively the reachable-space subset is expanded by repeatedly applying rulesto the states in it. Rules correspond to meta-actions, so

in total there are twelve rules one for each meta-action.A rule has a pre-condition which states which positionsrelative to the meta-module should be empty, which shouldcontain passive modules and constraints on the orientationof the meta-module (for some meta-actions). A rule alsohas a post-condition which give the new state of the meta-module relative to the old one. To avoid computationalexplosion, states already seen are not recalculated and afixed number (12) of iterations on the graph are done.This keeps the size of the graph down. Based on 5000test samples there are on average 83 and a maximum of687 vertices in the graph. The relative small size of thegraph enables it to be calculate at runtime on the ATRONmodules.B. Emergence of Meta-module

With a low probability a passive module will attemptto emerge a meta-module. It randomly selects two passiveneighbour modules, one on each hemisphere. It then cal-culates the reachable-space subset of that meta-module.From this it calculates the following inputs to an ANNwhich have 3 neurons in input-layer, 3 neurons in hidden-layer and 1 neuron in output-layer:

• Distance to nearest attraction-point from currentstate of the meta-module.

• Distance to nearest other meta-module from currentstate of the meta-module.

• Biggest known possible reduction in the distancebetween the meta-module and its nearest attraction-point.

The distance is calculated as the sum of the Euclidiandistances for the three modules in the meta-module. If theoutput value of the ANN is greater than 0.5 the meta-module will emerge and the ANN’s for movement andstopping will control the meta-module.C. Movement of Meta-module

When a meta-module has emerged it starts to move,by selecting one of the twelve meta-actions. The selectedmeta-action is then performed and the process is repeated.An ANN with 4 neurons in input-layer, 4 neurons inhidden-layer and 1 neuron in output-layer is used to selectwhich meta-action to perform next. Each state in thereachable-space subset is evaluated separately. We makeextensive use of the shortest path sequence of meta-actions(SPSM) that brings the meta-module from its currentstate to the state being evaluated. The following inputsare given to the ANN for each state:

• Number of meta-actions in the SPSM.• Number of common meta-actions between the current

SPSM and the previous SPSM. The previous SPSMis the latest sequence of meta-actions from which themeta-module performed the first meta-action.

• Shortest distance to another meta-module, measuredfrom a state along the SPSM.

• Reduction in distance between the meta-module andits nearest attraction-point, if it moves to the statebeing evaluated.

The state, which is being evaluated, is assigned a fitnessvalue from the output of the ANN. The state in thereachable-space subset which has the highest fitness valueis selected. And the first meta-action in the correspondingSPSM is then performed by the meta-module. Since thestructure of modules is dynamic and information in themap may be incomplete it happens that the performanceof a meta-action fails. The meta-module then recovers asgood as possible, e.g. if a rotation fails because of collisionthe rotation will be inverted and meta-action cancelled.

D. Stopping of Meta-moduleEach time the meta-module has performed a meta-

action it decides if it is time to stop or perform anothermeta-action. An ANN with 5 neurons in input-layer, 3neurons in hidden-layer and 1 neuron in output-layermakes this decision based on the following inputs:

• Biggest known possible reduction in the distancebetween the meta-module and its nearest attraction-point.

• Distance to nearest attraction-point from currentstate of the meta-module.

• Number of possible connections between the meta-module and its passive neighbours modules.

• Reduction in distance to nearest attraction-point overthe last five meta-actions.

• Number of cancelled meta-actions (e.g. because ofcollision) in the lifetime of the meta-module.

If the output of the ANN is greater than 0.5 themeta-module will stop moving and connect to all passiveneighbour modules.

VII. Evolution of Artificial Neural Network

Controller

Evolution is chosen to optimize the value of the ANN’sweights, since there is no obvious way of training thenetwork and since evolution may be good to exploit coop-eration between meta-modules. The actions of one meta-module may affect other meta-modules in ways which aredifficult to analyze and harder to exploit.

A. Encoding of Artificial Neural NetworksThe topologies of the networks are fixed, only the

weights are optimized by means of evolution. The genomeof each individual is the 50 weights which are directlyencoded as floating points values. Initially the weights haverandom values between -0.5 and 0.5.

B. Genetic AlgorithmA simple genetic algorithm is used. Each generation con-

sist of 100 individuals. The individuals in each generationare evaluated and their fitness calculated. The 3 fittestindividuals are used as elites and directly copied to thenew generation. A child has two parents randomly selectedfrom the group of the 25 fittest individuals. The child isproduced by using a randomized 12-point crossover anda mutation rate of 5%. When mutating a gene it is withequal likelihood replaced with a new random value or asmall random value added to or subtracted from the gene.

Fig. 5. The graphs show the average and highest fitness for eachgeneration, when evolving the weights of the artificial neural networkcontroller for the ATRON modules.

C. Fitness Evaluation

To evaluate the individuals they perform two randomlygenerated tasks. A task is to shape-change a randomstructure of 50 modules into another random structurespecified by 50 inhibiting attraction-points, placed withinthe ATRON lattice. The individuals in a generation are allevaluated on the same random tasks, but from generationto generation new random tasks are generated. The initialand target shape of the modules are not far apart, onaverage 45% of the modules are initially placed at anattraction-point. A task is terminated if there within300 timesteps has been no decrease in Euclidian distancebetween the modules and the attraction-points. In thesimulator a 90 degree rotation takes 10 timesteps. Thefitness of an individual is calculated as the average fitnessfrom each of the two tasks. The fitness from a task iscalculated as the relative change in distance between thestructure of modules and the attraction-points: fitness =(Dstart −Dend)/Dstart. Distance between the structure ofmodules and the attraction-points is measured as the sumof Euclidian distances between a module and its nearestattraction-point.

A number of evolutionary experiments were performedbefore reaching the details described above. The finalcontroller, used for experiments in this work, was obtainedfrom a evolutionary run for which the fitness graph isshown in figure 5. The noise in the fitness evaluationindicates that some tasks are harder to solve than other.

VIII. Experiments

In this section we demonstrate how shape-change andself-repair behaviours may be achieved using attraction-points and the evolved artificial neural network controller.The purposes of the experiments are to: 1) validate thecontrol strategy presented in this paper, 2) demonstratepossible future applications of self-reconfigurable robots.

A. Experiment: Scalability

The ANN controller was evolved using tasks containing50 modules. To investigate how the controller scaled toshape-changing structures of more modules we measuredthe controller’s performance as it performed a series of

Fig. 6. The graphs show how the relative change in distance of anevolved and an alternative hand-coded controller scale from 50 to1200 modules in the structure. Each point in the graphs is calculatedas the average of 10 tasks. Calculated from the entire interval, theevolved controller has a 95% confidence interval for the mean of0.325 to 0.345 and a standard deviation of 0.0787. The alternativecontroller has a 95% confidence interval for the mean of 0.237 to 0.260and a standard deviation of 0.0875. The evolved controller performssignificantly better than the alternative controller.

tasks. Tasks were of the same random type as used whenevolving the controller, but the number of attraction-points and modules were varied from 50 to 1200 in stepsof 50 modules. The graph in figure 6 indicate that therelative change in distance, when performing a task, doesnot decline as a function of the number of modules inthe structure. Therefore the experiment indicates that theevolved controller scales up to at least 1200 modules.

For comparison the equivalent graph of an alternativecontroller is also shown in figure 6. This alternative con-troller is hand-coded based on its reachable-space subsetand does not use ANN’s. The alternative controller:

• Emerge, if it is able to reduce its distance to thenearest attraction-point.

• Move, along the shortest path of meta-actions, to-wards the state that minimize its distance to anattraction-point.

• Stop, if it no longer is able to reduce its distance tothe nearest attraction-point.

The experiments indicate that the evolved controllerperforms significantly better than the alternative con-troller.B. Experiment: Support Unstable Roof

In earth quake or cave environments it might be de-sirable to have systems which can support an unstableroof. In this experiment a random structure of 500 modulesinitially lay on a floor. A roof is positioned at the height of26 modules above the floor. The target functionality is thesame as that of a pillar. To achieve this functionality 117inhibiting attraction-points are placed in a column shape.As the robot change-shape upwards the attraction-pointsof lower positions will be inhibited by the modules at theirpositions. The result of this simulated roof supportingexperiment is shown in figure 1.C. Experiment: Bridge Gap

In a range of scenarios it may be useful to have asystem which can build a bridge across a gap. In this

Fig. 7. A structure of 1000 ATRON modules build a bridge acrossa gap. A single non-inhibiting attraction-point is used to guide themodules shape-change.

experiment 1000 ATRON modules are initially placed in arandom structure. A single non-inhibiting attraction-pointis placed as shown in figure 7. The shape of the ATRONrobot stretches towards the attraction-point, effectivelybuilding a bridge across the gap. The ATRON simulatordoes not support physics. During this experiment longthin arms of ATRON modules are build, which most likelywould break off in a real-world gravity environment. Thisproblem could be reduced by adding more attraction-points to guide the shape-change.

D. Experiment: Self-Repairing Bone

A future miniaturization of modules would open upfor new possible applications, e.g. smart material whichcould self-repair. This experiment demonstrate the useof miniature ATRON modules in a self-repair scenario.Initially, using a CAD model, 3426 ATRON modules areassembled in the form of a bone, see figure 8. A totalof 1663 inhibiting attraction-points are placed at thesame positions as ATRON modules which is connectedto eight neighbours. This leaves the surface of the bonefree of attraction-points. At timestep 20, 114 modules areremoved which damage the strength of the bone. Since theremoved modules no longer inhibit the attraction-pointsthis triggers the emergence of meta-modules. After 1000timesteps the modules have rearranged themselves, thebone is self-repaired and its strength largely recovered.

IX. Conclusion and Future Work

In this paper we have described a distributed shape-change and self-repair control strategy for the ATRONrobot. A key ingredient in the control strategy is the mod-ules’ continuous calculation of a subset of their reachable-

Fig. 8. Self-repair of a bone build from 3426 ATRON modules: Attimestep 0, there is no activity. At timestep 20, the bone breaks. Attimestep 1000, modules have rearranged themselves to self-repair thebone.

space graph. On the basis of this graph we evolved an arti-ficial neural network controller for the modules. The con-troller controls the emergence, movement and stopping ofmeta-modules composed of three ATRON modules. Tasksof the robot are specified using attraction-points whichtrigger meta-modules to emerge and move towards them.The combination of meta-modules and evolved artificialneural network controller are shown to be able to deal withthe difficult motion constraints of the ATRON modules.The control strategy allows the robot to change its shapeto meet some desired functionality. In simulation we haveverified that the control strategy scales to shape-changeand self-repair scenarios with several thousands of modulesin the robot. Future work includes the transference of theevolved controller to the physical ATRON modules.

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