System Model: Physical Module Constraints: 1)A module must have a minimum of two adjacent free sides in order to move. 2) A module must have an adjacent obstacle cell or neighboring module to rotate around. 3)Modules cannot carry, push, or pull other modules, i.e., a module is only allowed to move itself. 4)Modules are deformable and move by a combination of rotation and changing joint angles, either clockwise (CW) or counter-clockwise (CCW). Algorithm Module Constraints: 1)Modules move in synchronous rounds. 2)Only one module tries to move into a particular cell in each round. 3)Modules have local information and a map of the initial state of the plane. 4)Two moving modules are separated by two free cells. Bridging Algorithm for Hexagonal Self-Reconfigurable Metamorphic Robots SSSSS Illustration of module movement over a substrate (obstacle or stationary module). Plamen Ivanov Faculty Mentor: Jennifer Walter Department of Computer Science, Vassar College General Problem Statement: The overall goal of this system of robots is to take an initial configuration (cyan) of modules, reorganize them into a straight chain in order to traverse a surface (red) then reassemble them into a goal configuration (green). This will be accomplished using two phases: a centralized planning phase followed by a reconfiguration phase. Both phases are executed without any message passing between the modules. The algorithm presented here deals with the traversal phase of the reconfiguration. Identifying the Main Bridge Cases The main bridge cases are identified by looking at the immediate neighbors of the bridge identifier cells. The four cases shown above cover all possible cases for narrow pocket entrances. Metamorphic Robots: A system of metamorphic robots is a cluster or grouping of robot modules, in which each robot is identical in size, shape, mobility and computational capabilities to each other robot. This allows for the system to reassemble into different shapes in order to accomplish different tasks or serve different functions. Typically, these systems use regular symmetry to densely fill a plane (cubes, hexagons, etc). Results: The algorithm described here provides a deterministic traversal planner for any contiguous hexagonal surface. It correctly identifies and classifies all possible 1 or 2 module bridge cases and successfully guides the modules across the surface. References: D. Little and J. Walter. “Using Hexagonal Metamorphic Robots to Form Temporary Bridges.” In Proc. of IEEE Intl. Conf. on Intelligent Robots and Systems, pages , J. Walter and D. Little. “Bridging gaps in traversal surfaces with hexagonal metamorphic robots.” In Proc. of the 10 th Intl. Conf. on Robotics and Remote Systems for Hazardous Environments, Gainesville, FL, Mar , Research supported by NSF grant IIS My Problem Blocking simple and complex non-concurrently traversable pockets by building a temporary bridge structure consisting of 1 or 2 modules to ensure a collision free motion planner. Future Work: Expanding the algorithm to work on pockets openings that are wider than 2 cells and constructing bridges with more than two modules will create a more efficient motion planner by reducing the time necessary to traverse a surface. Future work on the motion planner in general will include working with real modules and more realistic scenarios. Such scenarios include: module fault tolerance, limited global knowledge, asynchronous movement and changing environment. Identifying Bridge Sub-Cases Only LEFT and RIGHT bridge cases have sub-cases. These sub-cases depend on the number of perimeter cells that are located inside the pocket and on its layout. We have proven that we can recognize and classify all possible cases. To the sides are listed all RIGHT sub- cases. The LEFT sub-cases are a mirror image of the RIGHT sub-cases. Bridge Cells There are three types of bridge cells: Bridge, TempSupport and Support. The role of the Bridge cell is to block the entrance to the narrow pocket. In some cases a module cannot reach a bridge cell before the other modules start going through the pocket, so it needs the TempSupport to move over. Once the Bridge is in place the TempSupport needs to move to a location in which it would be able to rejoin the rest of the modules, preserving the optimal intermodule spacing of two free cells between moving modules. SINGLE BASICLEFTRIGHT Bridge Cell Obstacle Cell Free Cell Bridge Identifier Cell Free or Obstacle Cell Pattern for All BASIC CasesPattern for All SINGLE Cases Patterns for LONG (perimeter length > 4) RIGHT Cases Patterns for SHORT (perimeter length <= 4) RIGHT Cases Pockets The figures on the left and right represent typical surface formations. These “Pockets” can have either simple or complicated layout. Due to the motion constraints of the modules, whenever a Pocket has an entrance that is only two cells wide the modules cannot traverse the entrance. To avoid a collision between modules, we stop the first modules that reach a “narrow” pocket and build a bridge to block the pocket. Simple Pocket Complex Pocket Finding the Narrow Pockets Our algorithm uses a single virtual module to traverse the surface and map and number its perimeter cells. Once the perimeter cells have been numbered in ascending order, the algorithm looks for pairs of cells that are in contact but have numbers that differ by more than one. The pairs that are not included in the range of another pair are the ones that mark a narrow pocket entrance. We call them bridge identifiers. A hexagonal surface with initial module positions (cyan) and goal cells (green) Modules in movement (blue), Bridges (pink) and Bridge Identifiers (yellow) cells shown. Initial Configuration Goal Configuration Non-concurrently traversable