Hinged-Tetro: a Self-Reconfigurable Module for Nested Reconfiguration
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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 Tetris 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 squares (cells) edge to edge. An example of a polyomino, 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 heptomino depicted in Fig. 1(a: bottom-right) —a polyomino of seven squares. (a) Polyominoes can be seen as a generalization of the domino —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 puzzles 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 <t(n) < 4.6496 [19]. This counting considers general, shapes formed by at least one couple of squares connected only fixed polyominoes, known as lattice animals in statistical at their corners are not considered polyominoes (bottom-left).Thefirst polyomino with a hole, an heptomino (bottom-right). (b): The seven one- physics. In such polyominoes only translation movements sided tetrominoes and their corresponding names. are assumed, so two fixed polyominoes are different if they do not have the same orientation. Polyominoes that can be translated and rotated but not reflected are called one-sided polyominoes. Those that can be picked up and flipped are n mechanical design of Hinged-Tetro, a self-reconfigurable called free polyominoes. The number of free -ominoes, r(n) module conceived for the study of nested reconfiguration. say , is less than or equal to the number of one-sided n s(n) Hinged-Tetro is a mobile self-reconfigurable robot module -ominoes, say . In fact, it can be easily shown that t(n) ≤ r(n) ≤ s(n) ≤ t(n) based on the theory of hinged dissection of polyominoes that 8 [20]. For instance, there is able to transform itself into any of the one-sided tetromi- are one free, one one-sided, and two fixed dominoes (2- noes, the Tetris pieces. The robot is of interest for research ominoes), two free, two one-sided, and six fixed triominoes in nested reconfiguration because it can easily change its (3-ominoes), and five free, seven one-sided, and nineteen structure and also combine with other modules to form new fixed tetrominoes (4-ominoes). Table I shows the number morphologies to accomplish, for instance, manipulation tasks