2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) Besançon, France, July 8-11, 2014

Hinged-Tetro: A Self-reconfigurable Module for Nested Reconfiguration

Vincent Kee, Nicolas Rojas, Mohan Rajesh Elara, and Ricardo Sosa

Abstract— Nested reconfiguration is an emerging research Examples include versatile amphibious robots capable of area in modular robotics. Such a novel design concept utilizes intra-reconfiguration between terrestrial and aquatic gait individual robots with distinctive reconfiguration characteristics mechanisms [1], metamorphic robotic hands capable of intra- (intra-reconfigurability) capable of combining with other ho- mogeneous/heterogeneous robots (inter-reconfigurability). The reconfigurable palm topologies [2], and reconfigurable walk- objective of this approach is to generate more complex mor- ing mechanisms that produce a wide variety of gait cycles phologies for performing specific tasks that are far from the [3]. Intra-reconfiguration for sensing enables a robot to adapt capabilities of a single module or to respond to programmable its sensor configuration to the environment or task at hand. assembly requirements. The two-level reconfiguration process To this end, evolutionary design techniques for perceptual in nested reconfigurable robotic system implies several technical challenges in hardware design, planning algorithms, and control intra-reconfigurability [4], [5] and strategies for recognizing strategies. In this paper, we discuss the theory, concept, and and eliminating corrupted sensory have been proposed [6]. initial mechanical design of Hinged-Tetro, a self-reconfigurable Finally, intra-reconfiguration for computing allows robots module conceived for the study of nested reconfiguration. to reconfigure its control in response to environmental/task Hinged-Tetro is a mobile robot that uses the principle of demands [7], [8], [9]. hinged dissection of polyominoes to transform itself into any of the seven one-sided tetrominoes, the pieces, in a Inter-reconfigurability has gained widespread popularity in straightforward way. The robot can also combine with other the robotics community due to the possibility of assembling modules for shaping complex structures or giving rise to a robot a variety of specialized robots and complex structures using a with new capabilities. Some preliminary experiments of intra- standard set of components. Numerous inter-reconfigurable reconfigurability with an implemented prototype are presented. robots have been developed for a variety of potential ap- plications ranging from surveillance to space exploration I. INTRODUCTION and using different schemes for module docking and un- Reconfigurability is a valuable design strategy in robotics docking, and all types of reconfiguration —manual, semi- that has been studied since the 1980s. It typically falls manual, and self. Relevant examples include CEBOT, Poly- into two broad classes: intra-reconfigurability and inter- Bot, Crystalline, M-TRAN, ATRON, Molecube, CKBot, and reconfigurability. An intra-reconfigurable robot can be many others. For a complete review of inter-reconfigurable viewed as a collection of components (sensors, actuators, robotics, its history, concept, and most important results, the mechanical parts, power sources, controllers, etc.) acting interested reader is referred to [10], [11], [12]. as a single entity while having the ability to change, for Given this picture of the reconfigurable robotics field, we instance, its structure, mobility, or principal activity without consider the next step in the area is to integrate the advan- requiring any external assembly or disassembly. In contrast, tages of the intra-reconfigurability and inter-reconfigurability an inter-reconfigurable robot consists of a congregation of concepts. We call this consolidated approach: nested recon- modular homogenous or heterogeneous components capable figuration. A nested reconfigurable robotic system can be of forming a variety of morphologies through an ongoing defined as a set of modular robots with individual reconfig- attachment and detachment process. uration characteristics (intra-reconfigurability) that combine Intra-reconfigurability has been generally centered on with other homogeneous/heterogeneous robot modules (inter- functional modules, namely motion, sensing, and control. reconfigurability). The objective of this system is to generate Intra-reconfiguration for motion allows robots the flexibility more complex morphologies for performing specifictasks of traversing over a variety of terrains and spaces (land, that are far from the capabilities of a single unit or to respond air, and water) as well as a series of manipulation skills. to programmable assembly requirements. The distinction between intra- and inter-reconfigurability Vincent Kee is with the Electrical Engineering and Computer Science has been framed previously as assembly and disassembly Department, Massachusetts Institute of Technology, 77 Massachusetts Ave, at macro- and micro- scales, wherein the individual robotic Cambridge, MA 02139 (email: [email protected]) Nicolas Rojas was with the SUTD-MIT International Design Center, module maintains its morphology as constant when assem- Singapore University of Technology and Design. He is now with the De- bled in an aggregate structure [13]. The concept of nested partment of Mechanical Engineering and Materials Science, Yale University, reconfiguration explicitly considers the ability of the modular New Haven, CT, USA (email: [email protected]) Mohan Rajesh Elara and Ricardo Sosa are with the Engineering components at the atomic level to internally transform their Product Development Pillar, Singapore University of Technology and morphology without splitting. This can be seen in fact as Design, 20 Dover Drive Singapore 138682 (email: {rajeshelara, ri- a generalization of the self-deformation principle used in cardo sosa}@sutd.edu.sg). This work was supported by the SUTD-MIT International Design Center tensegrity-based cellular robots [14]. under grants IDG31200110 and IDD41200105. In this paper, we discuss the theory, concept, and initial

978-1-4799-5736-1/14/$31.00 ©2014 IEEE 1539 II. POLYOMINOES Polyominoes, sometimes called n-ominoes or super- dominoes, are plane geometric figures formed by joining one or more equal (cells) edge to edge. An example of a , a 16-omino, is presented in Fig. 1(a: top). Since its perimeter (24 units) is not equal to that of its minimal bounding box (20 units), this shape corresponds to a non- convex polyomino. Sets of joined squares with at least one couple of cells connected only at their corners [Fig. 1(a: bottom-left)] or with edges that do not perfectly match to each other, are not considered polyominoes. Observe that polyomino regions may be hollow, the first polyomino with a hole is the depicted in Fig. 1(a: bottom-right) —a polyomino of seven squares. (a) Polyominoes can be seen as a generalization of the —the two equal squares joined edge to edge used in the I eponymous board game— to a set of multiple squares. The word polyomino is attributed to Solomon Golomb [15], [16]; L who seems to be the first mathematician to treat the subject Z O seriously, a passion that started during his graduate studies in Harvard [17]. Polyominoes are familiar in popular culture because they have been used as entertainment since, at least, the eighteenth century. Classical examples of such S practical assembly games include the rectangular puzzles J T Jags and Hooks (1785) and Sectional Checkerboard (1880) [18]. Since the 1950s, several authors have discussed the prob- (b) lem of estimating the number t(n) of polyominoes composed of n squares [17]. Currently, the best known bound is Fig. 1. (a): An example of a polyonimo composed of 16 squares — n n i.e., a 16-omino (top). A set of joined squares that is not a polyomino. In 3.9856

1540 TABLE I THE NUMBER OF n-OMINOES FOR n ≤ 8

One- Name n Free Fixed sided Monomino 1 111 Domino 2 112 Triomino 3 226 4 5 7 19 5 12 18 63 6 35 60 216 Heptomino 7 108 196 760 8 369 704 2725 Fig. 2. Examples of hinged dissections. Kelland’s proof of the Pythagorean theorem by a hinged rearrangement (top). Dudeney’s hinged dissection of an equilateral triangle into a (bottom). another figure [23], [24]. For example, any two simple polygons in the plane —i.e., polygons with non-intersecting in the case of tetrominoes, for instance, I corresponds to a sides— of equal area can be dissected by straight line cuts rectangle, O to a square, and T to an octagon, theorem 1 into a finite number of congruent polygonal figures which implies that there exists at least one hinged dissection of can be rearranged without overlapping to form the other polygons that can be rotated into any n-omino for a given polygon [25], a result known as the Wallace-Bolyai-Gerwien n. In fact, in [29], the authors propose an elegant hinged theorem [26]. Some popular geometric dissections include dissection of polyominoes and prove that: the Tangram —the dissection invented in ancient China, the Hindu problem —the Greek cross dissection into Theorem 2 (Demaine et al., 2005) A cycle of 2 n right five pieces to form a square [27], and the Bhaskara’s proof isosceles triangles, joined at their base vertices, can be of the Pythagorean theorem [28]. rotated into any n-omino. Now, let us suppose that instead of allowing the smaller figures in a dissection to be rearranged arbitrarily, the pieces Although theorem 2 gives us the appropriate foundation to are pin-jointed at their vertices. This special subclass of develop a self-reconfigurable robot module able to transform dissections are called hinged dissections [29]. In 1864, the itself into any of the seven one-sided tetrominoes; for me- British mathematician and physicist Phillip Kelland pre- chanical simplicity reasons (e.g. number of joints, process of sented what seems to be the first published hinged dissection transformation), we are interested in the natural hinged dis- [24], a proof by rearrangement of the Pythagorean theorem sections of polyominoes. A natural dissection is the cutting of [Fig. 2(top)]. For many years, a problem that aroused the a n-omino into some of its constituent squares. When all of interest of several mathematicians was determining if there them are cut using n−1 hinges, the corresponding dissection is always a hinged dissection between two simple polygons, is called a maximum natural dissection. An example of a that is, if there exists a collection of geometric shapes non-maximum natural dissection of polyominoes is depicted hinged at their vertices that can be folded in the plane in Fig. 3(a: left). In this instance, three stacked identical continuously without self-intersection to form both polygons. squares dissected by only one hinge can be rotated into the Fig. 2(bottom) shows a classical example of this problem, two one-side triominoes [Fig. 3(a: right)]. Such dissection is the hinged dissection of an equilateral triangle into a square called the L-hinged dissection of triominoes —the L stands by Henry Dudeney [30]; see [29]. Recently, in a remarkable for the position on the hinge from a top view of the three work, Abbott et al. [31] generalized the hinged dissection stacked identical squares. For the case of tetrominoes, a problem of two polygons and constructively proved that possible option of maximum natural dissection is the LRL- actually any finite collection of polygons of equal area hinged dissection presented in Fig. 3(b: right). However, all has a common hinged dissection. The following theorem the one-side tetrominoes cannot be obtained by rotations of summarizes this result: this hinged dissection:

Theorem 1 (Abbott et al., 2012) Any finite set of polygons Lemma 3 The LRL-hinged dissection of four identical of equal area have a common hinged dissection that can fold squares cannot be rotated into all one-sided tetrominoes. continuously without intersection between the polygons. For two target polygons with vertices drawn on a rational grid, Proof: First, according to the notation of Fig. 3(b: the number of required pieces is pseudopolynomial, as is the right), let us consider some unfeasible relative locations of running time of the algorithm to compute the common hinged squares 1 and 3. For example, given that the hinges joining dissection. them to square 2 are in opposite corners, it is not possible that square 1 and 3 share an edge after a rotation, of both Since any polyomino can be associated to a polygon — or one of them, respect to square 2. In general, if we trace

1541 1 3 2 1 3 3 2 1 1 2 4 4 2 1 3 3 2

(a) 4 4 1 2 3 3 2 1 1 1 1

2 2 2 Fig. 4. In all these cases of permutations for labeling a T-tetromino using the set {1, 2, 3, 4}, the feasible locations of square 4 respect to square 3 3 3 3 (in dark gray) do not match the required position (in dark orange) when a LRL-hinged dissection is used. 4 4 4

(b) tetrominoes. Fig. 3. (a): The L-hinged dissection of three stacked identical squares Proof: Four stacked identical squares can be dissected (left) can be rotated into the two one-side triominoes (right). The dark gray indicates that square 1 is rotated (+180◦) respect to square 2 in by three hinges in 8 different ways, namely, LLL, LLR, LRL, order to obtain the second triomino. (b): Maximum natural dissections of LRR, RLL, RLR, RRL, and RRR, where the sequence of L tetrominoes. The LLL-hinged dissection (left), the LLR-hinged dissection and R letters indicates the position of the hinges from up to (center), and the LRL-hinged dissection (right). The LRL-hinged dissection cannot be rotated into all one-sided tetrominoes (Lemma 3). down at a top view of the set of squares. Sequences RLR, RRL, and RRR are mirror reflections of sequences LLL, LLR, and LRL, respectively. Sequences LRR and RLL can ◦ two lines —one vertical and another horizontal— dividing be achieved by rotating sequences LLR and RRL by 180 , square 2 into four equal parts and splitting the Euclidean respectively. Therefore, up to congruence, four stacked iden- plane into six regions (including the lines itself), there is no tical squares can be dissected by three hinges in 3 different option that after any combination of rotations, squares 1 and ways, namely, LLL, LLR, and LRL. By lemma 3, it is known 3 lie at consecutive regions. that a LRL-hinged dissection of four identical squares cannot Now, suppose that the LRL-hinged dissection can be ro- be rotated into all one-sided tetrominoes. Finally, Table II tated into the T-tetromino [Fig. 1(b)]. Since for any tetromino presents feasible sequences of transformations from the I- there are 24 different ways of labeling the constituent squares tetromino to all the one-sided tetrominoes using the LLL- aR using the set {1, 2, 3, 4}, this implies that at least one of and LLR-hinged dissections. In such table, b indicates a b a such permutations for the T-tetromino can be achieved with rotation of square respect to square . the LRL-hinged dissection. However, all permutations but Up to the authors’ knowledge, the LLR-hinged dissection the four cases presented in Fig. 4 cannot be assembled with was presented for the first time in [29], where the authors such hinged dissection either because two hinged squares also show that five identical squares cannot be hinged to be are not successive in the permutation —i.e., edge to edge— rotated into all pentominoes. Theorem 4 closes the circle for or because square 1 and 3 lie at consecutive regions when hinged dissections of tetrominoes. This result gives us the square 2 is divided into four equal parts by two lines. The appropriate geometries for developing a self-reconfigurable remaining four cases cannot be arranged because the feasible robot module able to transform itself into any of the seven locations of square 4 with respect to square 3 do not match one-sided tetrominoes. We call this robot Hinged-Tetro. Al- the required position in all cases [Fig. 4]. This exhausts though any of the two types of hinged dissections (LLL and all cases for assembling a T-tetromino using a LRL-hinged LLR) can be used for the intra-reconfiguration purposes, it dissection. Thus, our assumption is contradicted. will be shown that for some inter-reconfigurability operations Other possible options of maximum natural dissection —i.e. combinations of two or more Hinged-Tetros— both ge- for tetrominoes are the LLL- and LLR-hinged dissections ometries are needed. Next, we present the mechanical design presented in Fig. 3(b: left and center). In contrast to the of the proposed robot module. Details about other aspects, LRL-hinged dissection previously discussed, all the one-side such as controller design, inter-communication systems, and tetrominoes can be obtained by rotations of these hinged perception sensors, are out of the scope of the present report dissections. In fact, it can be shown that: and are discussed elsewhere.

IV. DESIGN OF HINGED-TETRO Theorem 4 The LLL- and LLR-hinged dissections of four identical squares are the unique maximum natural dissec- A nested reconfigurable robotic system is a set of modular tions, up to congruence, that can be rotated into all one-sided robots with individual reconfiguration characteristics that

1542 TABLE II TRANSFORMATION OF THE LLL- AND LLR-HINGED DISSECTIONS INTO ALL ONE-SIDED TETROMINOES

Hinged dissection OTZSL J

1 1 1 2 1 1 2 4 1 2 4 2 1 2 3 2 2 4 3 3 3 4 3 4 4 3 3 2 ◦ 2 ◦ 2 ◦ 2 ◦ 2 ◦ 3 ◦ 1) R1 = +180 1) R3 = −90 1) R3 = −90 1) R3 = −90 1) R1 = +180 1) R4 = −180 3 ◦ 3 ◦ 3 ◦ 2 ◦ 2) R4 = −180 2) R4 = −90 2) R4 = −180 2) R1 = +180 2 ◦ 4 3) R1 = +180 (LLL)

1 1 2 1 2 4 1 1 1 2 1 2 3 3 2 3 2 4 3 2 3 4 4 3 4 4

3 2 ◦ 2 ◦ 2 ◦ 2 ◦ 2 ◦ 2 ◦ 1) R3 = −180 1) R3 = −180 1) R1 = +180 1) R1 = +180 1) R1 = +180 1) R1 = +180 3 ◦ 3 ◦ 2 ◦ 2 ◦ 2) R4 = +180 2) R4 = +180 2) R3 = −90 2) R3 = −90 4 2 ◦ 3 ◦ 3) R1 =+90 3) R4 = +180 (LLR) combine to form, for instance, a more complex robot mech- Fig. 5(left and right). From Table II, it can be observed anism suitable for performing specific tasks that are far from that block 2 never rotates during an intra-reconfiguration the capabilities of a single robot module. The robot modules operation, therefore this unit is considered the system’s in a nested reconfiguration framework can independently anchor. Accordingly, all heavier robot subsystems such as modify, for example, their structure, mobility, or principal the drive system and electronics are concentrated in block 2 activity to tackle an emerging situation in the environment [Fig. 5(right-top)]. The mechanical design of Hinged-Tetro or to respond to the requirements of a morphogenesis oper- can be divided into three main parts: structure, mobility unit ation —the shaping of new morphologies. The fundamental and revolute joints, and docking system. Next each of them characteristics of a nested reconfigurable robot module are: is briefly discussed. i) autonomy of transformation and 2D/3D locomotion, ii) no A. Structure access to centralized control, iii) defined intra-reconfiguration scenarios, iv) established local sensing and communication During inter-reconfiguration operations, a nested reconfig- tools, and v) determined docking systems and protocols. urable system based on Hinged-Tetros can be considered a Following these guidelines, we propose a research robot mobile architecture because the modules are not limited to platform for the study of nested reconfiguration. reaching specific points in the their working envelope — the Euclidean plane in such case. In contrast, during intra- Hinged-Tetro is a mobile self-reconfigurable robot module reconfiguration operations, a single Hinged-Tetro behaves as based on the theory of hinged dissection of polyominoes a lattice architecture because the system docks at particular (section III) that is able to transform itself into any of points of the square grid defined by the robot module. The the one-sided tetrominoes. The geometry of Hinged-Tetro is interested reader is addressed to [10] for a proper discussion highly useful for research in nested reconfiguration because about architectural groups in modular self-reconfigurable the robot can easily rearrange its own blocks to change robotic systems. its structure (intra-reconfiguration) and also combine with The cohabitation of mobile and lattice architectures in other Hinged-Tetros to form, for instance, more complex Hinged-Tetro-based systems has to be considered into the morphologies to accomplish tasks that a single system could design of the robot module structure because the complexity not tackle on its own (inter-reconfiguration). of reconfiguration control completely varies in each situa- The design of the proposed robot module focuses on tion. In the intra-reconfiguration case, the module can be simplicity in order to facilitate mass production in the controlled using a finite-state machine approach using a future. Thus, Hinged-Tetro’s design is modular as it is an minimal number of sensors or even in open loop. In the assembly with easily interchangeable shared components. inter-reconfiguration case, the robot needs some degree of This characteristic allows the Hinged-Tetro to be readily intelligence and perception in order to combine with other configured either as a LLL-hinged dissection or as a LLR- modules. hinged dissection. Fig. 5(center) presents a complete CAD The Hinged-Tetro’s body consists of four cubes (10cm of a fully-functional Hinged-Tetro in LLR configuration. each in the current design) connected by three revolute joints Exploded views of the constituent blocks are presented in [Fig. 5(center)]. The cubic shape of each block allows an

1543 Fig. 5. Design of a fully-functional Hinged-Tetro in LLR configuration (center). The modular design of the robot can be observed in the exploded views of the constituent blocks (left and right). Since block 2 does not rotate during any intra-reconfiguration operation, the unit is used as the system’s anchor and concentrates the heavier subsystems (right-top). See text for details. easy intra-reconfiguration process while providing enough C. Docking system space to allocate appropriate sensors for inter-reconfiguration Mechanical docking systems have been shown to be faster, purposes. Each wall of the cubes is 5mm thick and hollow stronger, and more reliable than connectors based on magnets with internal ribbing to minimize weight while maintaining [11], [32]. Thus, for both intra-reconfiguration and inter- strength. The blocks have a modular design, allowing many reconfiguration operations, Hinged-Tetro utilizes a simple parts to be reused in the system. but robust electromechanical mechanism based on gendered connectors. The male connector consists of three arms spaced 120◦ apart, similar to the blades of a mechanical fan. B. Mobility unit and revolute joints The center shaft of this connector is directly attached to a positional servomotor and the ends of its blades are filleted Free movement of Hinged-Tetro in the Euclidean plane to ease the docking in conditions where systems are not well is required for inter-reconfiguration processes regardless the aligned. Once two compatible faces mate, the male connector robot’s shape (e.g., I-tetromino, L-tetromino). To accomplish depresses a limit switch located behind the female connector this, Hinged-Tetro employs a holonomic drive system using to stop joint rotation. The connection finishes with a rotation four omni-wheels located on block 2 [Fig. 5(right-top)]. of approximately 60◦ of the male connector, thus locking the During intra-reconfiguration, the wheels lock to avoid the two systems in place. The connection is kept secure as the movement of block 2 while all the other ones rearrange positional servomotor holds the docking mechanism in the their positions. Blocks 1 [Fig. 5(left-top)], 3 [Fig. 5(right- locked position as long as the robot is powered on. Details bottom)], and 4 [Fig. 5(left-bottom)] rest on one metal ball of the proposed docking system can be observed in Fig. 5. caster to facilitate movement during inter-reconfiguration Figure 6(left) presents the design of Hinged-Tetro in its locomotion and intra-reconfiguration operations. seven intra-reconfiguration shapes. An instance of inter- Hinged-Tetro has three revolute joints that connect the reconfiguration is depicted in Fig. 6(right). This morphology constituent blocks in a chain formation for performing the is called the fork formation. It corresponds to the 16-omino intra-reconfiguration operations. The single-axis rotation pro- presented in Fig. 1(a: top). This formation can be made using vided by each joint allows its adjacent blocks to rotate with four I-tetrominoes, two O-tetrominoes and two I-tetrominoes, a range of motion of up to 180◦, as required by the lattice or one L-tetromino, one J-tetromino, one I-tetromino, and architecture resulting from the transformation operation be- one O-tetromino. In this last case, corresponding to the tween different tetromino shapes (see Table II). Each joint system shown in Fig. 6(right), all Hinged-Tetros but the is designed as a Butt/Mortise hinge. Block 2 works as frame module in the I-tetromino shape use the LLR-hinged dissec- —i.e., the motor is docked to it— for the rotation of blocks tion. LLL- and LLR-hinged dissections are needed in this 1 and 3. This last block works as frame for the rotation of combination to avoid the collision of some joints. The fork block 4. formation, useful for manipulation tasks, is an example of

1544 Fig. 6. Hinged-Tetro in its seven intra-reconfiguration shapes (left). An example of inter-reconfiguration, the fork formation for manipulation tasks (right). Such morphology can be made using three Hinged-Tetros in LLR configuration (L-, J-, and O-tetrominoes) and one Hinged-Tetro in LLL configuration (I-tetromino). generating new morphologies in order to perform objectives that are far from the capabilities of a single unit.

V. P ROTOTYPE AND EXPERIMENTS Figure 7 shows a prototype of the robot module design presented in section IV, implemented for testing the basic operations of intra-reconfiguration of Hinged-Tetro —i.e.,se- quence of transformation and rotation/docking of blocks. In the prototype, most components were selected commercially- off-the-shelf while the remaining parts were fabricated on entry-level 3D printers with ABS plastic and using minimal lathe operations. Given the prototype’s objective, the mo- bility unit was not considered —the system was replaced with a plastic base to keep block 2 at the same level as the other blocks. In the presented version, each revolute joint of Hinged-Tetro is powered by a continuous rotation servo with a stall torque of 15 kg-cm. Regarding the docking system, the center shaft of each male connector was attached to a micro servo with a stall torque of 1.3 kg-cm. Finally, the control system, located in block 2, was implemented in an ATmega328 microprocessor with 32 KB of memory running at 16 MHz on an Arduino Uno microcontroller Fig. 7. Prototype of Hinged-Tetro for testing the basic operations of intra- board. Communication with the computer was established reconfiguration. A transformation into all one-sided tetrominoes, following via UART TTL (5V) serial communication through a USB the sequence S → I → O → T → L → J → Z → S, can be observed tether that also provides power for the module. in the accompanying video. For performing the intra-reconfiguration operations, the presented prototype of Hinged-Tetro utilizes a finite-state O → T → L → J → Z → S machine of seven states, one per each of the one-sided , where the letter indicates the tetrominoes. An example of the required movements for the type of tetromino. The obtained results validate the proposed transition between states can be observed in Table II. In design and open the door for the next steps in our approach the tests, Hinged-Tetro receives triggering commands from that now focus on the autonomous inter-reconfiguration of a operator on a computer, then proceeds with the required multiple Hinged-Tetros. transition by checking the status of limit switches and send- VI. CONCLUSION ing signals to the appropriate servos. All transformations are programmed to prevent crashes between blocks regardless The idea of nested reconfiguration has been introduced and the current state of Hinged-Tetro. The accompanying video discussed. This concept integrates the two major approaches shows the transformation of the prototype into all its intra- in reconfigurable robotics: intra-reconfigurability and inter- reconfiguration shapes following the sequence S → I → reconfigurability. A nested reconfigurable robotic system is

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