We consider the theoretical model of Crystalline robots, which have been introduced and prototyped by the robotics community. These robots consist of independently manipulable unit-square atoms that can extend contract arms on each side and attach detach from neighbors. These operations suffice to reconfigure between any two given (connected) shapes. The worstcase number of sequential moves required to transform one connected configuration to another is known to be ( n). However, in principle, atoms can all move simultaneously. We develop a parallel algorithm for reconfiguration that runs in only O(logn) parallel steps, although the total number of operations increases slightly to ( n logn). The result is the first (theoretically) almost-instantaneous universally reconfigurable robot built from simple units.
A linear-time parallel algorithm for reconfiguring within the bounding box of source and target is given in @cite_5 . The total number of individual moves is also linear. No restrictions are made concerning physical properties of the robots. For example, @math strength is required, since modules can carry towers and push large masses during certain operations.
@cite_5
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We present a complete, local, and parallel reconfiguration algorithm for metamorphic robots made up of Telecubes, six degree of freedom cube shaped modules currently being developed at PARC. We show that by using 2 spl times 2 spl times 2 meta-modules we can achieve completeness of reconfiguration space using only local rules. Furthermore, this reconfiguration can be done in place and massively in parallel with many simultaneous module movements. Finally we present a loose quadratic upper bound on the total number of module movements required by the algorithm. In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2×2×2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2) parallel steps [8,10,4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations. A self-reconfigurable (SR) robot is one composed of many small modules that autonomously act to change the shape and structure of the robot. In this paper we consider a general class of SR robot modules that have rectilinear shape that can be adjusted between fixed dimensions, can transmit forces to their neighbors, and can apply additional forces of unit maximum magnitude to their neighbors. We present a kinodynamically optimal algorithm for general reconfiguration between any two distinct, 2D connected configurations of n SR robot modules. The algorithm uses a third dimension as workspace during reconfiguration. This entire movement is achieved within O( √ n) movement time in the worst case, which is the asymptotically optimal time bound. The only prior reconfiguration algorithm achieving this time bound was restricted to linearly arrayed start and finish configurations (known as the “x-axis to y-axis problem”). All other prior work on SR robots assumed a constant velocity bound on module movement and so required at least time linear in n to do the reconfiguration. In this paper we propose a novel algorithm that, given a source robot S and a target robot T, reconfigures S into T. Both S and T are robots composed of n atoms arranged in 2x2x2 meta-modules. The reconfiguration involves a total of O(n) atomic operations (expand, contract, attach, detach) and is performed in O(n) parallel steps. This improves on previous reconfiguration algorithms [D. Rus, M. Vona, Crystalline robots: Self-reconfiguration with compressible unit modules, Autonomous Robots 10 (1) (2001) 107-124; S. Vassilvitskii, M. Yim, J. Suh, A complete, local and parallel reconfiguration algorithm for cube style modular robots, in: Proc. of the IEEE Intl. Conf. on Robotics and Automation, 2002, pp. 117-122; Z. Butler, D. Rus, Distributed planning and control for modular robots with unit-compressible modules, Intl. J. Robotics Res. 22 (9) (2003) 699-715, doi:10.1177 02783649030229002], which require O(n^2) parallel steps. Our algorithm is in-place; that is, the reconfiguration takes place within the union of the bounding boxes of the source and target robots. We show that the algorithm can also be implemented in a synchronous, distributed fashion.