Jennifer E. Walter

An asynchronous leader election algorithm for dynamic networks

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 [16] with a wave algorithm [21], all within the framework of a height-based mechanism for reversing the logical direction of communication links [6]. It is proved that in certain well-behaved situations, a new leader is not elected unnecessarily.

Distributed reconfiguration of metamorphic robot chains

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.

Algorithms for fast concurrent reconfiguration of hexagonal metamorphic robots

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.

Choosing good paths for fast distributed reconfiguration of hexagonal metamorphic robots

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.

Deterministic distributed algorithm for self-reconfiguration of modular robots from arbitrary to straight chain configurations

The problem addressed is the reconfiguration of a system of hexagonal metamorphic robots from an initial arbitrary shape configuration I, to a straight chain goal configuration, G. This is the first time a fully distributed deterministic algorithm has been written to achieve the parallel reconfiguration of a system of homogeneous modules from an initial arbitrary shape to a straight chain goal configuration. The contribution of this paper is an algorithm that uses no pre-processing or message passing to accomplish reconfiguration. The algorithm eliminates the possibility of module collision by assuming modules have the capability to detect another module at a distance of one cell away on each of their six sides. The algorithm is successful as long as: the system starts in an initial configuration that satisfies admissibility requirements, the goal cells are known to all modules, and if every module is equipped with sensors to determine if the cell adjacent to and in the same direction as a neighboring empty cell is occupied. A discrete-event simulator tests the algorithm.

Distributed reconfiguration of hexagonal metamorphic robots in two dimensions

The problem addressed in the distributed reconfiguration of a metamorphic robotic system composed of any number of two dimensional hexagonal modules from specific initial to specific goal configurations. The initial configuration considered is a straight chain of 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. The main 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.

Using a pocket-filling strategy for distributed reconfiguration of a system of hexagonal metamorphic robots in an obstacle-cluttered environment

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.

Enveloping obstacles with hexagonal metamorphic robots

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.

Layering algorithm for collision-free traversal using hexagonal self-reconfigurable metamorphic robots

This paper presents an algorithm that deterministically plans the simultaneous, collision-free movement of n hexagonal metamorphic robots (modules) over any contiguous surface composed of modules in a hexagonal grid. A planning stage algorithm identifies narrow passages between surface cells where moving modules will come into contact. After identifying all narrow passages on a surface, our algorithm identifies the cells that can be used to build temporary structures across the entrance to each narrow passage using 1, 2, or 3 modules. The algorithm does not use intermodule message passing at any stage of the traversal, making it suitable for modules with limited communication capabilities. The algorithm maintains optimal spacing between moving modules throughout the traversal. Our current algorithm is an improvement over previous bridging algorithms because the bridging cells are situated such that when they are filled with modules, they do not form narrow passages (pockets) on the surface. In this paper, we also propose a multi-layered technique for finding longer bridges. We discuss the complexity and performance of our algorithms and give an example of the results of simulating them using a discrete event simulator.