We address the problem of reconfiguration planning for a metamorphic robotic system composed of a large number of hexagonal mobile robots. Our objective is to develop an algorithm to plan the concurrent movement of individual robots over a lattice composed of identical robots, from an initial configuration I to a goal configuration G, when G contains one or more obstacles. The contribution of this paper is a deterministic motion planning algorithm to envelop multiple obstacles in an admissible set of goal configurations while eliminating the risk of module collision or deadlock. We developed a discrete event simulator to test our algorithms, and every admissible G tested was filled successfully. We include a full proof of correctness and analysis of our algorithm.

An algorithm for electing a leader in an asynchronous network with dynamically changing communication topology is presented. The algorithm ensures that, no matter what pattern of topology changes occur, if topology changes cease, then eventually every connected component contains a unique leader. The algorithm combines ideas from the temporally ordered routing algorithm (TORA) for mobile ad hoc networks (Park and Corson, 1997) with a wave algorithm (Tel, 2000), all within the framework of a height-based mechanism for reversing the logical direction of communication links (Gafni and Bertsekas, 1981). It is proved that in certain well-behaved situations, a new leader is not elected unnecessarily.

This paper presents algorithms to plan the concurrent and collision-free movement of n hexagonal metamorphic robots (modules) over a contiguous surface in a hexagonal grid. The problem is complicated by the fact that the surface may include "non-concurrently traversable" segments, where narrow passages between surface cells may result in module collision, regardless of the space separating moving modules. We present a new algorithm to identify unoccupied cells that, when filled with modules, form bridges to span all non-concurrently traversable segments of the surface. Our bridging algorithms have the added benefit of reducing the overall traversal time for a given surface. Additionally, we show that four modules are sufficient to bridge any contiguous non-concurrently traversable segment, allowing concurrent module movement with minimal inter-module spacing. Finally, we present the results of simulating our algorithms using a discrete event simulator.

The problem addressed is the distributed reconfiguration of a system of hexagonal metamorphic robots (modules) from an initial straight chain to a goal configuration that satisfies a simple admissibility condition. Our reconfiguration strategy depends on finding a contiguous path of cells that spans the goal configuration and over which modules can move concurrently without collision or deadlock, called an admissible substrate path. A subset of modules first occupy the admissible substrate path, which is then traversed by other modules to fill in the remainder of the goal. We present a two-phase reconfiguration strategy, beginning with a centralized preprocessing phase that finds and heuristically ranks all admissible substrate paths in the goal configuration, according to which path is likely to result in fast parallel reconfiguration. We prove the correctness of our path-finding algorithm and demonstrate its effectiveness through simulation. The second phase of reconfiguration is accomplished by a deterministic, distributed algorithm that uses little or no intermodule message passing.

The problem addressed is reconfiguration planning for a metamorphic robotic system composed of any number of hexagonal robots when a single obstacle with multiple indentations or "pockets" is embedded in the goal environment. We extend our earlier work on filling a single pocket in an obstacle to the case where the obstacle surface may contain multiple pockets. The planning phase of our algorithm first determines whether the obstacle pockets provide sufficient clearance for module movement, i.e., whether the obstacle is "admissible". In this paper, we present algorithms that sequentially order individual pockets and order module placement inside each pocket. These algorithms ensure that every cell in each pocket is filled and that module deadlock and collision do not occur during reconfiguration. This paper also provides a complete overview of the planning stage that is executed prior to reconfiguration and presents a distributed reconfiguration schema for filling more than one obstacle pocket concurrently, followed by the envelopment of the entire obstacle. Lastly, we present examples of obstacles with multiple pockets that were successfully filled using our distributed reconfiguration simulator.

The problem addressed is the distributed reconfiguration of the metamorphic robot system composed of any number of two dimensional robots (modules). The initial configuration we consider is a straight chain of modules, while the goal configuration satisfies a simple admissibility condition. Our reconfiguration strategy depends on finding a contiguous path of cells, called a substrate path that spans the goal configuration. Modules fill in this substrate path and then move along the path to fill in the remainder of the goal without collision or deadlock. In this paper, we address the problem of reconfiguration when a single obstacle is embedded in the goal environment. We introduce a classification for traversable surfaces, which allows for coherence in defining admissibility characteristics for various objects in the hexagonal grid. We present algorithms to 1) determine if an obstacle embedded in the goal fulfills a simple admissibility requirement, 2) include an admissible obstacle in a substrate path, and 3) accomplish distributed reconfiguration.

The problem addressed is the distributed reconfiguration of a metamorphic robot system composed of any number of two dimensional robots (modules) front specific initial to specific goal configurations. The initial configuration we consider is a straight chain of modules, while the goal configuration satisfies a simple admissibility condition. Reconfiguration of the modules depends on finding a contiguous path of cells, called a substrate path, that spans the goal configuration. Modules fill in this substrate path and then move along the path to fill in the remainder of the goal without collision or deadlock. In this paper, we examine the problem of finding the substrate path most likely to result in fast parallel reconfiguration, drawing on results from our previous papers (2000, 2001). Admissible goal configurations are represented as directed acyclic graphs (DAGs). We present a combination graph traversal-weighting algorithm that traverses all paths in the rooted DAG and use this algorithm to determine the best substrate path. We extend our definition of admissible substrate paths to consider admissible obstacle surfaces for reconfiguration when obstacles are present in the environment.

The problem addressed is the distributed reconfiguration of a metamorphic robotic system composed of an arbitrary number of two-dimensional hexagonal robots (modules) from specific initial to specific goal configurations. The initial configuration considered is a straight chain of robotic modules, while the goal configurations considered satisfy a more general "admissibility" condition. A centralized algorithm is described for determining whether an arbitrary goal configuration is admissible. We prove this algorithm correctly identifies admissible goal configurations and finds a "substrate path" within the goal configuration, along which the modules can move to reach their positions in the goal. A second result of the paper is a distributed algorithm for reconfiguring a straight chain into an admissible goal configuration. Different heuristics are proposed to improve the performance of the reconfiguration algorithm and simulation results demonstrate the use of these heuristics.

The problem we address is the distributed reconfiguration of a metamorphic robotic system composed of any number of two dimensional hexagonal modules from specific initial to specific goal configurations. We present a distributed algorithm for reconfiguring a straight chain of hexagonal modules at one location to any intersecting straight chain configuration at some other location in the plane. We prove our algorithm is correct, and show that it is either optimal or asymptotically optimal in the number of moves and asymptotically optimal in the time required for parallel reconfiguration. We then consider the distributed reconfiguration of straight chains of modules to a more general class of goal configurations.