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Self-assembling Mobile Linkageswith Passive and Active Modules

Carrick Detweiler∗, Marsette Vona†, Yeoreum Yoon, Seung-kook Yun§, Daniela Rus¶

Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of Technology, Cambridge, Massachusetts, USA∗carrick@mit.edu,†vona@mit.edu,§yunsk@mit.edu,¶rus@csail.mit.edu

Abstract— We explore the concept of self-assembling robotsystems consisting of simple passive structural modules plusactive robotic modules. In particular, we consider a space of2- and 3-DOF robots with rotating grippers which attach topassive structural bars. The resulting systems range from apassive truss with one independent active climbing module tofully self-reconfiguring dynamic structures comprised of activemodules and passive struts. We describe hardware experimentswith two robotic modules interacting with fixed and free bars,and algorithms for self-assembly and mobility in larger-scalesimulated systems.

I. INTRODUCTION

SELF-reconfiguring robots are modular robot systems thatare physically connected and capable of making different

geometric structures. Most current research in this field isfocused on homogeneous systems in which all the modulesare identical. In this paper we explore the concept of self-assembling robot systems consisting of passive structuralmodules plus active robotic modules.

We study a special class of heterogeneous self-reconfiguringrobots we call active linkages. The robots in this class arecomprised of two types of modules: passive structural barswhich may either be fixed in the world or free to moveindividually, and mobile active 2 and 3 degree of freedommodules (figures 3 and 9, respectively) with rotating gripperswhich may pick up or climb on the passive modules, organizeand hold them in a desired shape, and actively move themfor self-assembly, self-reconfiguration, or self-repair purposes.The passive modules can be passed around by the activemodules and coordinated to form the skeleton of a largeclass of truss and linkage geometries. For example, Figures 1and 2 show a simulation of a self-assembling active towerbelonging to this class. So far we have manually fabricatedthe passive bars or used existing structures, but we predict thatthe absolute simplicity in form and function of this class ofpassive module will ultimately enable on-demand manufacturein-situ from elements present (or intentionally placed) in thelocal environment of the deployed system.

A long-term application of these systems is in-space struc-ture construction. The modules will pack tightly in a space-craft, yet they will be able to self-assemble, self-reconfigure,self-repair, and adapt their collective morphology, and func-tion, to perform a variety of tasks—some known in advance(pre-launch) and some dynamic (post-launch). The modulescan act both as effectors to assemble/repair/service other space

Fig. 1. Simulation of a tower with 75 active and 60 passive modules acting asa hybrid serial-parallel hyper-redundant active structure. This example showsa possible self-inspection capability—a camera mounted on the tower topcould be aimed to inspect lower parts of the tower. Active modules, drawn asdark segments, have rotating grippers (not drawn) at their extremities. Passivestructural bar modules are drawn as light segments.

structures and as active orbiting structures themselves. Otherapplications include terrestrial construction of increasinglymore capable structures such as dynamic scaffolds and mov-able towers for construction tasks.

Challenges in building such structures span the entire spec-trum from issues related to designing simple and robust activemodules to problems of control and planning. Control forthese systems is challenging because their c-space has dynamictopology, and in the general case they are highly under-constrained (hyper-redundant) systems with a continuum ofsolutions. Similarly, planning is challenging due to the largenumber of degrees of freedom that have to be coordinated forhigh-level tasks.

In this paper we also examine some control and coordinationissues that arise when building and using self-assemblinglinkages with passive and active modules. We describe acontinuum of possibilities that covers the spectrum frompassive trusses with active modules that can traverse themall the way to active linkages that can self-assemble, self-inspect, self-repair, and move. We present a hardware imple-mentation of a modular 3-DOF robot called Shady3D, and theconcept of Multi-Shady which instantiates the idea of mobileactive structures composed from many modules. We presentour hardware and control algorithms for Shady3D, simulatedcontrol algorithms for Multi-Shady, and hardware experiments

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Fig. 2. Snapshots from a simulation showing the construction of a two-legged walking structure (top row, rightmost) starting from a “packed” configurationof active and passive modules (top row, leftmost); a walker structure locomoting on a truss segment (middle row); and a walker structure performing concaveand convex transitions, walking up a tower, and reconfiguring into a new structural block of the tower (bottom row).

that show how two 3-DOF Shady3Ds and a rigid bar can self-assemble as a 6-DOF modular manipulator.

II. RELATED WORK

The idea of robots which self-assemble (and/or self-replicate) using elements from the environment is not new,for example see Chirikjian et al’s paper on lunar-surface self-assembly [1] and references therein. In this paper we explorethe particular idea of separating the system into active modulesand passive bars, with an emphasis on the possibility only pro-ducing the latter—much simpler—units from the environment.

Our proposed systems and algorithms are further related toprior work in the fields of self-reconfiguring robots, hyper-redundant robots, variable-geometry truss robots, and trussclimbing robots.

A. Self-Reconfiguring Robots

Of all the self-reconfiguring modular robots which havebeen previously reported, our current work seems most closelyallied with systems based on rotary DOF and mechanicalconnection mechanisms, for example: Murata, Kurokawa, etal’s “3D Fracta” [2]; Kotay and Rus’ “Molecule” [3]–[5];Unsal, Kiliccote, and Khosla’s bi-partite “I-Cubes” [6] system;Duff, Yim, et al’s PolyBot [7]; and Lund, Beck, Dalgaard, Støyet al’s ATRON [8], [9].

A major difference in our present work is that we areproposing modular systems with only some modules contain-ing active DOF—the rest serve as passive structural elements.In contrast, all of the above referenced systems are eitherhomogeneous (all modules identical and actuated) or areheterogeneous but still require actuation in all modules.

B. Hyper-Redundant Robots

Research in the field of hyper-redundant robots has mainlyexplored non-reconfiguring systems with high DOF andfixed kinematic topology, typically open chains. Both planarsystems—e.g. Burdick and Chirikjian’s “snakey” (which isalso a variable geometry truss, see below) [10], [11]; Green-field, Rizzi, Choset et al’s modular snake [12]—and full spatialmechanisms, e.g. Suthakorn and Chirikjian’s binary-actuation

manipulator [13]; Wolf, Choset, et al’s “Schmoopie” [14]—have been explored. The planar systems typically have one(effective) kinematic DOF per link, and the spatial systemsmay have two or more. Sometimes the links are internallyparallel mechanisms, an arrangement which has been called“hybrid serial-parallel” [13], [15], [16].

C. Variable Geometry Truss and Truss Climbing Robots

Variable geometry trusses (VGTs), can be viewed as ageneralization of the serial-chain hyper-redundant systemsto more general kinematic topologies. Both fixed-topologysystems like the NASA/DOE “SERS DM” [17] and manually-reconfigurable systems—notably Hamlin, Sanderson, et al’sTETROBOT [15]—have been considered. Also related arerobotic systems which assemble static trusses, for example,Everest, Shen, et al’s SOLAR [18], and Howe and Gib-son’s “Trigon” system [19]. Such self-assembling and self-reconfiguring truss systems are a promising direction forrobotic assembly of large structures in space—for example,see Doggett’s overview of automatic structural assembly forNASA [20].

Several truss climbing robots have been explored by othergroups, e.g. Staritz et al’s “Skyworker” [21], Amano et al’shandrail-gripping robot for firefighting [22], Ripin et al’s poleclimbing robot [23], Nechba, Xu, Brown et al’s “mobile spacemanipulator SM2” [24], Kotay and Rus’ “Inchworm” [25], andAlmonacid et al’s parallel mechanism for climbing on pipe-like structures [26].

Our proposed systems can act as self-reconfiguring/self-assembling modular VGTs (section V), and our Shady3D robot(section IV) shows how the same module designs can also beapplied to truss-climbing.

III. ABSTRACT MODEL

We consider an abstract continuum of modular linkagerobots with varying functionality. The simple end of the con-tinuum is a fixed linkage with one active climbing unit, and thecomplex end is a self-assembling/self-reconfiguring variable-geometry linkage composed of active and passive robot mod-ules. Examples of intermediate points along the continuuminclude fixed linkages with multiple independent climbingunits and manually-assembled variable-geometry linkages.

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By selecting a point along the continuum, a designer canmatch system function (and cost) to the requirements of aspecific application. As a further aid to system design, wepropose unified models for robot modules which allow re-use of basic electromechanical designs and kinematic controlalgorithms in implementations at all points on the continuum.

A. Generic Module Models

It is likely impractical to specify a single hardware designwhich applies to all modular linkage applications, so insteadwe propose abstract module models which can be scaled,adapted, and specialized to yield hardware appropriate forclasses of applications. This allows us to re-use not onlythe basic electromechanical layout, but also kinematic controlalgorithms and user-interface software.

We propose two abstract module models: passive units,which are simple rigid bars; and active units incorporatingseveral rotary DOF and grippers.

1) Passive Module Model: The passive modules are simplystraight rigid bars. Their cross-section, length, and materialproperties are application-dependent, and in some applicationsthese attributes may vary among modules. Individual passivemodules may either be mobile or fixed in the world. Weusually depict passive modules as light-colored line segments,as shown in Figure 3.

2) Active Module Model: Active modules contain severalactuated DOF and grippers for attaching passive modules. In2D we have focused on a module with two rotating grippers,as shown in Figure 3. In 3D we add a rotational DOF in themiddle of the module, as shown in Figure 9.

Such a module can hold two passive modules in arbitraryrelative orientations (figure 3, middle), and it can also loco-mote independently along a fixed truss by alternately grippingand swinging (figure 3, bottom). In 2D we model the activeand passive modules as occupying separate parallel planes. Weassume that the grippers are designed to retract when open sothat they may move over passive modules without collision.

Fig. 3. A 2D active module concept (top) with two independently rotatinggrippers which can connect to passive modules (middle, drawn as lightsegments). Such a module can locomote independently along a fixed trussby alternately gripping and swinging (bottom).

IV. Shady3D: AN ACTIVE MODULE IMPLEMENTATION

Shady3D [27], [28] is capable of autonomously graspingpassive bars, grasping other Shady3D modules, and movingon 3D trusses. It moves by grasping a truss element and usingits rotating degrees of freedom to pivot about the graspingpoint. The robot is a 3D extension of the two-dimensionalShady window shading robot [29], [30].

Shady3D, shown in figure 4, is composed of two rotatinggrippers linked by a two-part arm. Each gripper can grasp andrelease a truss bar by closing and opening its paddles. Thegrippers are connected to the arm by rotating joints (rotationalrange ±100◦), enabling them to align with truss bars in variousorientations. The The two sides of the arm are connected by athird rotating joint which controls the relative angle betweenthe directions of the two grippers. Shady3D has five degrees offreedom: three rotational degrees of freedom for locomotion,actuated by MicroMo 1724TR00SR DC micromotor combinedwith a 66:1 gearhead; and two degrees of freedom for gripperopening and closing, actuated by Sanyo NA4S mini gearmo-tors with 298:1 gearhead. The robot includes proprioceptiveand environmental sensors, on-board computation, custom-built motor control boards, and on-board power providedby four 3.7V 750mAh Polymer Li-ion batteries. The robot’sdimensions are 250mm × 80mm × 133mm and its weightis 1.34kg. All the structural parts for Shady3D are rapidprototyped in plastic or consist of PCB boards.

A. Grippers

In order to achieve reliable movement, the grippers mustachieve a firm hold on the grasping surface to avoid slippageand falling off. Thus, reliability is the main design consid-eration for the gripper. Other important design goals includecompliance and error tolerance.

The gripper firmly envelops a truss element with a 3/4insquare cross section, preventing wobbling. Rubber pads on thecontact surface of the gripper paddles prevent slippage.

Several features are implemented to accomplish compliancefor misalignment and tilt. Four detector switches are locatedon the gripper paddles and are used in the grasping procedure.If the gripper is not aligned with the truss, one or two ofthe switches in diagonal position will be pressed before theothers. Based on this information, the gripper joint is rotatedto resolve the misalignment. Compliance for tilt caused bygravity is accomplished mechanically with a slope along theedges of the housing and slopes in the gripper paddles. Whenthe gripper paddles are closed, the truss is guided and pulledto the contact surface by the slopes, as shown in figure 5. Thegripper paddles fully retract allowing translation and rotationover the truss surface without collision.

B. Sensing

Shady3D incorporates sensors to estimate its own configura-tion, to detect the the truss bars, and to cope with misalignmenterror. The three joint motors have 512 counts/rev encoderswhich are used for controlling the joint to reach a desiredangle. A potentiometer connected to one of the gripper paddle

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Fig. 4. A hardware implementation of the 3D active module concept shown in figure 9. At left the three rotary DOF are indicated. At right two Shady3Dprototypes are shown attached to a fixed truss.

(a) (b)

(c) (d)

(e) (f)

Fig. 5. Shady3D grip compliance. Slopes in the gripper housing, marked withthe red arrow in (b), guide the gripper along the edge of the truss. Slopes inthe paddles, highlighted in (e), help the gripper pull the truss and compensatefor the gap indicated in (d) between the contact surface and the truss.

shafts senses the state of each gripper. Four detector switchesare incorporated in each gripper for misalignment detection,as described above. These switches can be used to detect bothhorizontal and vertical misalignment.

C. Electronics and Control

Shady3D’s electronics system consists of three layers: low-level motor control boards, a mid-level on-board Robostixcontrol board, and an off-board workstation connected via awireless BlueTooth link for high-level control and planning.

Sensor information is transferred from the low-level motorcontrollers to the workstation. The five motor controllers

collect information from the sensors and send this informationto the Robostix microcontroller, which organizes the dataand forwards it to the workstation, where a control programevaluates the state of the robot.

The control commands flow the other direction, from theworkstation to the Robostix, and from there to the motorcontrollers. Nested control loops of increasing bandwidth areclosed at the workstation, at the Robostix, and within the motorcontrollers.

The robot’s basic motion primitives are as follows:• Open Gripper. This motion opens the paddles of the

designated gripper. The gripper paddles are fully retractedbehind the contact surface of the gripper housing toprevent collision while the gripper moves over a truss.The average time for this operation is 20.8 sec.

• Close Gripper. This motion ensures a reliable grasp ona truss. A major challenge is the correction of grippermisalignment. Failure detection and recovery is done asdescribed above. The average time for completing thisoperation is 24.0 sec.

• Joint Rotation. The gripper joints provide locomotioncapabilities within a plane, and the middle joint rotationenables the robot to swap motion planes. Each jointincludes a limit switch for position reference. The averagetime for completing a 90 degree rotation is 14.4 sec.

D. Experimental Characterization

Experiments with Shady3D hardware were performed on acustom-designed truss (figure 4, right) constructed from 3/4insquare aluminum tubes. The truss is a rectilinear 3D structureincluding a main square horizontal frame with a vertical framebuilt inside. The vertical frame is located so that an individualShady3D robot can move from the horizontal frame to thevertical frame with a single step. This truss has 54 differentgrip positions for a robot module starting from a particularinitial pose.

We have tested hundreds of single step and multiple stepnavigation for Shady3D within this environment. Single stepmotions were tested for various situations as follows:

• straight movement in horizontal and vertical planes• transitions between bars of differing orientations in hor-

izontal and vertical planes• transition between horizontal and vertical planes

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• multi-step navigation with vertical and horizontal stepsTable I summarizes the results for the trials we recorded forevaluation purposes. Most failures occurred during transitionsbetween trusses in a vertical plane. Except for the case wherethe mechanical malfunction of one gripper switch caused afailure, the original cause for these failures was the sag inthe anchor joint and consequent downward tilt of the robotbody. Though such errors were overcome in most cases, thisproblem needs to be addressed for more robust locomotion.

V. MultiShady: SELF-ASSEMBLY OF ACTIVE LINKAGES

Multiple Shady robots can connect to one another usingpassive bars to form a larger active structure. The robotsbecome smart joints in the self-assembled structure: they canactuate the structure to travel, bend, twist, and self-reconfigure.

We have developed self-assembly algorithms for creatingmeta-modules out of Shady3D units and bars. These meta-modules can perform linear translations and rotations ona substrate of modules. Thus, many of the self-assemblyand self-reconfiguration algorithms previously developed forcubic lattice module systems can be instantiated onto thesestructures.

The space of Shady3D structures we can generate from suchmeta-modules consists of objects that can be decomposed intoblocks. In this section we show how to create the block metamodule and how to control the translation and rotation of thismodule.

Figure 6 through 8 show several snapshots from simulationsfor three types of algorithmic behaviors: meta-module build-ing, moving, and rotating. Each algorithm is sketched below.

A. Meta-module Self-Assembly

Figure 6 shows the block meta-module self-assembly.Twelve active modules and eight passive bars are employedto build a three-dimensional cube-like block. The algorithmworks as follows:

• Two active modules form a six-degree-of-freedom manip-ulator by connecting to each other using a passive bar.Eight active modules form four such manipulators.

• The four 6-DOF manipulators move to the base locationof the block and pick up four remaining active modulesholding passive bars. Thus, each 6-DOF manipulatorbecomes a structure consisting of three active modulesand two passive bars.

• The four structures formed in the previous stage arrangethemselves in the desired poses. Then, they connect totheir neighbors to complete the tower structure.

B. Meta-module Locomotion

Figure 7 demonstrates the block moving procedure. Thestructure can be moved in steps of its own size. Since the meta-module is symmetric in three dimensions, it can be translatedby one step in any direction given the appropriate scaffold. Themeta-module can also be rotated by 90 degrees, as described inthe next section. These capabilities allow structures to move on

Fig. 6. Four snapshots of the tower building simulation. Shady3D modulesare drawn as an elongated U-shape with light and dark halves; free bars andthe grid are drawn as straight segments.

the ground and meta-modules to move on a grid of other meta-modules for self-assembly and self-reconfiguration purposes.

The meta-module locomotion algorithm consists of thefollowing steps:

• The upper part of the block is tilted toward the directionin which it moves. For this, two legs in diagonal positionare rotated so that all gripper joints in the middle of legshave parallel joint vectors.

• The legs of the block are moved to their desired positionon the next grid cell. One leg is moved at a time tomaximize the stability of the structure during the process.

• After all legs are moved, gripper joints in the middle ofthe legs are rotated synchronously to recover the originalshape of the block.

Fig. 7. Four snapshots of the tower moving simulation.

C. Meta-module rotation

Figure 8 shows a simulation where the block is rotated by90◦. The rotation is divided into two stages. The algorithm is

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Type Attempted Successful Success Rate Failure Modalitystraight, horiz. plane 60 60 100.0%transition, horiz. plane 17 15 88.2% joint motor failure; incomplete grip

straight, vert. plane, horiz. dir. 30 28 93.3% excessive current in gripper motor;larger gripper misalignment

straight, vert. plane, vert. dir. 32 32 100.0%

transition, vert. plane 21 17 81.0% gripper switch malfunction; excess cur-rent in gripper motor; incomplete grip

horiz. to vert. transition 16 16 100.0%Total 176 168 95.5%

TABLE ISUMMARY OF SHADY3D SINGLE-STEP MOTION EXPERIMENTS.

as follows:• The top face of the block is rotated by 30◦ with respect

to the grid by cooperatively rotating the joints of modulesin the legs.

• Each leg, one at a time, is relocated at the intermediateposition. This relocation allows the block to rotate theremaining 60◦.

• The top face of the tower is rotated further by 60◦ tocomplete the 90◦ rotation.

• Each leg, one at a time, is moved to the final position,restoring the original shape of the tower.

Fig. 8. Four snapshots of the tower rotating simulation.

D. Hierarchical Control

Structures consisting of many active robotic modules andpassive bars may constitute complex very high-DOF hyper-redundant systems. The many DOF support a wide range ofmovement and capabilities, such as the system’s ability toself-inspect. We propose a hierarchical control methodology,dividing the total set of active and passive modules into groupsforming meta-modules1, and we design particular controllersand planners for these smaller groups. There may be manyinstances of the same type of group, so the total number ofdistinct group control algorithms may be much lower than

1The block in the previous section is one instance of a meta-module thatcan be created from active and passive modules.

the total number of group instances. We also implementcontrollers and planners which operate at the highest level, andwhich consider the aforementioned groups to be monolithicmeta-modules, thus forming a hierarchy of control.

As the scale of the systems we explore increases, wepredict that it will likely be useful to extend this hierarchyto additional levels; i.e. to form groups within groups, etc., ateach level designing controllers and planners which operateon meta-modules of the lower-level.

Meta-modules in self-reconfiguring robots have previouslybeen explored [31]–[34], but mostly in the context of topo-logical reconfiguration and structural shape-changing. We ex-tend the concept to also include kinematic/geometric linkagecontrol without change of topology, and we generalize to ahierarchy of module-group controllers which may each haveseveral different operational modes, as described next.

As an example of hierarchical control, figure 2 and 1 showthe simulated construction and operation of a reconfigurablemobile tower in a vertical plane. The groups, in this case, arecomposed of five active modules (dark segments) and fourpassive modules (light segments). We have developed a set ofseven separate controllers for such groups which can

• assemble the group from a starting “packed” configura-tion into a two-legged walking structure

• locomote the walking structure with a statically stable gaitalong a fixed truss segment from the site of the walker’screation to the base of a tower-in-progress

• make a concave transition from walking on the segmentto walking up the side of the tower

• walk up the side of the tower• make a convex transition from walking up the tower to

standing on top of the tower• reconfigure from the walker shape to an inverted-U shape

trapezoidal tower structural block• tilt, as a tower block, to the left or rightUsing these group controllers, we can direct the simulated

construction of an arbitrary-height tower. Figure 1 shows a15-block tower containing 75 active modules and 60 passivemodules.

Once such a tower is assembled, we can apply a high-levelcontroller to command the blocks to collectively perform atask. We have explored high-level controllers which utilizethe block-tilting group controller to make the tower a hybridserial-parallel [13], [15], [16] hyper-redundant [10], [12], [14]active structure, allowing it to bend and move like a tentacle.

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A possible application is tower-self inspection: a cameramounted on the tower top could be positioned to inspect lowersections (figure 1). We have implemented a damped-least-squares (DLS) inverse kinematics high-level control algorithm,following [35], which allows the user to interactively drag thetower towards a goal configuration.

VI. SELF-ASSEMBLY OF A 6-DOF MODULARMANIPULATOR

A 6-DOF manipulator can execute arbitrary motion in3D and is also a component of the Shady3D meta-moduleformation described above. In this section we describe hard-ware experiments that enable two Shady3D modules to self-assemble as a 6-DOF manipulator with the help of a passivebar.

Figure 9 (top) shows that the direct connection of twoShady3D modules gives only 5-DOF because the axes of twogripper rotation joints lie on the same line. This problem canbe solved by introducing a passive bar as shown in the bottomof the figure.

Fig. 9. (top) A 5-DOF manipulator obtained by directly connecting twoShady3Ds; (bottom) A 6-DOF manipulator incorporating a passive bar.

We have developed and implemented a distributed algorithmfor the self-assembly and forward kinematic control of a 6-DOF manipulator using two 3-DOF Shady3D modules anda passive bar with embedded LEDs. The algorithm worksas follows. Given a specified position for the passive barwithin the Shady3D experimental environment, each Shady3Dmodule positions itself optimally so as to be able to reachthe bar. In the first step of the algorithm each Shady3Dmodule moves independently and in parallel to reach andgrasp the bar. See Figures 10(a, b, c) for snapshots from theexecution of this step. The bar is detected using the LEDsensors within the Shady3D grippers. Upon grasping the bar,the Shady3D modules signal to each other to coordinate thecompletion of the grasping step and the self-assembly of a

6-DOF manipulator. Finally, one of the modules releases itsgrasp of the environment.

The 6-DOF manipulator is controlled using forward kine-matics by providing joint angles as input. The two modulesare controlled independently and in parallel to demonstratethe movement of the arm (see Figures 10 (d, e, f).) Anadditional bar is manually presented to the free gripper ofthe 6-DOF manipulator, grasped, transported, and dropped at aspecified location (see Figure 10 (g, h, i).) We have performedthis experiment 10 times in a row during the course of onehour. Each experiment consisted of 9 joint movements and 5grasping/release operations and it takes about 4 minutes. Allthe control steps succeeded for all the experiments. However,due to a hardware failure at the end of the 7th experiment oneof the gripper motors had to be replaced.

An important component of this self-assembly process isdetecting the passive bar and grabbing it. Many methods canbe used for this purpose. We embedded IR LEDs that can bedetected by sensors added to the robot grippers as shown infigure 11. One LED is located at each side of the bar, whichcontains a battery to power them. The robot module has anIR sensor on each gripper. Using this system, the robot cansense the bar from up to 50cm.

Fig. 11. The passive bar with embedded IR LEDs and batteries.

Controlling the arm is challenging because of the distributednature of the arm’s linkage. We use a numeric inverse kine-matics method again based on DLS, as follows:

• get target displacement relative to the current configura-tion

• clamping: divide the displacement into small steps inwhich a Jacobian linearization is valid

• for each step compute angle updates by DLS• coordinate actuation of robot modules

This method is efficient and accurate provided the arm isnot close to a singular configuration. For the self-assembled6-DOF arm, singularities occur when the arm linkage is linearand when all four gripper points are located in the same plane.To handle such configurations we use a modified version ofDLS in which we clamp position and orientation separately,in order to minimize position errors near singularities. Thisvariable clamping method trades off position and orientationerrors.

We confirm usefulness of the method by implementing theinverse kinematics on the system so that two robots forms a6-DOF manipulator and the end-effector moves along x,y andz axis with ±100mm displacement.

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(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Fig. 10. Implementation of self-assembly of 6-DOF modular arm and an example of moving a bar. (a) Robots in the approach position. (b) Swinging inwardsto find the bar. (c) Grasping each side of the bar. (d) A 6-DOF manipulator, composed of two modules and a passive bar, connected at a single location. (e)The base module has rotated the other. (f) The manipulator stretched to its maximum height. (g) Gripping a manually given bar to be moved. (h) The bar ismoved to the dropping position. (i) The manipulator has dropped the bar.

VII. CONCLUSION

In this paper we discussed the long-term concept of self-assembling robot systems consisting of simple passive struc-tural modules, possibly manufactured on-demand and/or com-posed from elements present in the environment, plus activerobotic modules. Incorporating environmental parts in this wayextends our current notion of modular robots. The passivecomponents may be much easier to fabricate in-situ (or evento intentionally deploy) than the active modules. The activemodules can be thought of as robotic joints that enable thestructures formed this way to be dynamic in novel ways. Suchstructures can move in place by bending and twisting to inspectthemselves, they can self-repair, and they can self-reconfigure.

We have described a proof of concept implementation wherethe active module type is a 2- or 3-DOF linear structurewith grippers at both ends and the passive modules are rigidbars. We showed how a variety of linkage structures canbe self-assembled from these two basic module types insimulation, and we showed results of hardware experimentsfor an active module climbing on a passive 3D truss. Linkage

structures incorporating many active modules can be hyper-redundant robots with a large number of degrees of freedom,and we described a hierarchical method for controlling thesestructures. Finally, we gave an example of a physical structurethat can be self-assembled: a 6-DOF manipulator made of 2robot modules and one passive bar.

We believe that modular robots that integrate environmentalcomponents via self-assembly can lead to new robot capa-bilities. For example, even the simple case of a linear chainstructure of robot modules and bars suggests the possibility ofrapidly configuring modular manipulators with varying lengthand therefore workspace. This paper presents some small firststeps in the direction of building modular robots that canaugment their structures with passive bars. Much work remainsto be done to design better hardware modules with this kind ofcapability as well as the supporting distributed planning andcontrol algorithms.

ACKNOWLEDGMENT

This research was done in the Distributed Robotics Labora-tory at CSAIL, MIT. Support for this work has been provided

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in part by Intel, NSF IIS-0426838, and MURI ARO W911NF-0510219. We are very grateful for this support. We are alsograteful to the members of DRL for insightful discussions andfeedback.

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