## A Grammatical Approach to Self-Organizing Robotic Systems

### BibTeX

@MISC{_agrammatical,

author = {},

title = {A Grammatical Approach to Self-Organizing Robotic Systems},

year = {}

}

### OpenURL

### Abstract

Abstract — In this paper we define a class of graph grammars that can be used to model and direct concurrent robotic selfassembly and similar self-organizing processes. We give several detailed examples of the formalism and then focus on the problem of synthesizing a grammar so that it generates a given, prespecified assembly. In particular, to generate an acyclic graph we synthesize a binary grammar (rules involve at most two parts), and for a general graph we synthesize a ternary grammar (rules involve at most three parts). In both cases, we characterize the number of concurrent steps required to achieve the assembly. We also show a general result that implies that no binary grammar can generate a unique stable assembly. We conclude the paper with a discussion of how graph grammars can be used to direct the self-assembly of robotic parts. I.

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Citation Context ...conformations are complimentary. If they do attach, their conformations change (mechanically for example), thereby determining in what future interactions the components may partake. As in other work =-=[2]-=-, [3], we consider the conformation of a part or robot as corresponding to a discrete symbol, and we Eric Klavins ∗ Robert Ghrist † David Lipsky † ∗Electrical Engineering † Mathematics University of W... |

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Citation Context ...stable set in this paper (Definition 3.8), the identification of “unique” assemblies has been explored [20]. There is also other work on supplying assembling robots with state information [21], [22], =-=[23]-=-, although not in a graph-theoretic context, and also initial work by other groups [24], [25] on building a self-assembling robot similar to that described in the introduction to this paper. A. Rules ... |

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Citation Context ... ˙xi(xj − xi) ||xj − xi|| (xj − xi) is a damped nonlinear spring, with spring potential U, modeling the latching mechanism. We suppose that U has a minimum at ||xi − xj|| = R as before. In other work =-=[34]-=- we describe how such a mechanism would work using capillary forces or with robots [4], [5]. 12sX. DISCUSSION We have defined a class of graph grammars that describe self-organizing robotic systems. W... |

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Citation Context ... then, two trajectories as we have defined them could really be representatives of the same behavior. In this section, we relate the interleaved semantics with a concurrent or partial order semantics =-=[30]-=-. Concurrency allows us to reason more naturally about the number of steps required to assemble a structure with a given graph grammar. The definition we give is similar to that found in the Petri Net... |

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Citation Context ... capsids in simulation [9]. The addition of simple processing to each part, similar in capability to that assumed in the present paper, is considered in models of the assembly of the T4 bacteriophage =-=[10]-=-. Self assembly as a graph process has been described by Klavins [3], although the graph grammar formalism is new to this paper, and a rule synthesis procedure for trees was given that is somewhat mor... |

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Citation Context ...ce to mechanical system synthesis. Graph grammars come in many flavors. The variety we use in this paper is called Graph Rewriting Systems on Induced Subgraphs (IGRS), investigated by Litovsky et al. =-=[16]-=- (The requirement that rules are applied on induced subgraphs is equivalent to our requirement in Definition 3.2 that witnesses be monomorphisms). Our results about the reachable and stable sets being... |

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Citation Context ...examples (above) of covers of a graph (below). The cover on the left is a 3-fold cover; that on the right is 2-fold. describe geometry, such as tilings of the plane [27]; Distributed self-replication =-=[28]-=-; and Grammars for directing distributed tasks in cooperative control of vehicle swarms [29]. V. TOPOLOGICAL PROPERTIES OF GRAPH GRAMMARS It is intuitively clear that a grammar containing only binary ... |

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Citation Context ...o that of processes as described by Reisig [12] and our notion of concurrent equivalence is directly related to Abrams’ and Ghrist’s work on State Complexes [13]. Graph grammars were introduced [14], =-=[15]-=- more than two decades ago and have been used to describe a broad array of systems, from data structure maintenance to mechanical system synthesis. Graph grammars come in many flavors. The variety we ... |

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Citation Context ...particular, we suppose that the components themselves are (very) simple robots, whose capabilities we will specify in the body of this work. Our starting point is the idea of conformational switching =-=[1]-=-: Each component (robot, molecule, particle, etc.) exists in one of several conformations or shapes. When two components come into close proximity, they attach or not based on whether their conformati... |

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Citation Context ...tivation for the theory presented in this paper is a robotic testbed under construction at the University of Washington wherein “programmable parts” execute local rules to form global assemblies [4], =-=[5]-=-. Figure 1 shows a photograph of several programmable parts. On each edge of a part is a magnetic latching mechanism and an infrared (IR) transceiver. Each part is controlled by an on-board microcontr... |

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Citation Context ...hybridization of complimentary strands of DNA) upon random collisions. Somewhat similar to 2sthe stable set in this paper (Definition 3.8), the identification of “unique” assemblies has been explored =-=[20]-=-. There is also other work on supplying assembling robots with state information [21], [22], [23], although not in a graph-theoretic context, and also initial work by other groups [24], [25] on buildi... |

2 | Grammatical self assembly for planar tiles
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Citation Context ... f c e d c f e b d c b Fig. 7. Two examples (above) of covers of a graph (below). The cover on the left is a 3-fold cover; that on the right is 2-fold. describe geometry, such as tilings of the plane =-=[27]-=-; Distributed self-replication [28]; and Grammars for directing distributed tasks in cooperative control of vehicle swarms [29]. V. TOPOLOGICAL PROPERTIES OF GRAPH GRAMMARS It is intuitively clear tha... |

1 |
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Citation Context ... on the right is 2-fold. describe geometry, such as tilings of the plane [27]; Distributed self-replication [28]; and Grammars for directing distributed tasks in cooperative control of vehicle swarms =-=[29]-=-. V. TOPOLOGICAL PROPERTIES OF GRAPH GRAMMARS It is intuitively clear that a grammar containing only binary rules cannot distinguish between a cycle of length 2N, and two identical cycles of length N ... |