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					                                                                               Bridging Algorithm for
                                                                 Hexagonal Self-Reconfigurable Metamorphic Robots
                                                                                                             Plamen Ivanov Faculty Mentor: Jennifer Walter
                                                                                                                   Department of Computer Science, Vassar College
Metamorphic Robots:                                                                                                                                                                                                      Results:
A system of metamorphic robots is a cluster or grouping of                                                                                                                                                               The algorithm described here provides a deterministic traversal
robot modules, in which each robot is identical in size, shape,                                                                   My Problem                                                                             planner for any contiguous hexagonal surface. It correctly
mobility and computational capabilities to each other robot.                 Blocking simple and complex non-concurrently traversable pockets by building a temporary bridge structure                                   identifies and classifies all possible 1 or 2 module bridge cases
This allows for the system to reassemble into different shapes in                              consisting of 1 or 2 modules to ensure a collision free motion planner.                                                   and successfully guides the modules across the surface.
order to accomplish different tasks or serve different functions.
Typically, these systems use regular symmetry to densely fill a
plane (cubes, hexagons, etc).                                                                Bridge Cell       Obstacle Cell       Free Cell         Free or Obstacle Cell        Bridge Identifier Cell

                                                                                                                                       Pockets
                                                                                                                The figures on the left and right represent typical surface
                S               S   S      S         S                                                          formations. These “Pockets” can have either simple or
            Illustration of module movement over a substrate                                                    complicated layout. Due to the motion constraints of the
                      (obstacle or stationary module).                                                          modules, whenever a Pocket has an entrance that is only
                                                                                                                two cells wide the modules cannot traverse the entrance.
General Problem Statement:                                                                                      To avoid a collision between modules, we stop the first
The overall goal of this system of robots is to take an initial                                                 modules that reach a “narrow” pocket and build a bridge
configuration (cyan) of modules, reorganize them into a straight                                                to block the pocket.
chain in order to traverse a surface (red) then reassemble them
into a goal configuration (green). This will be accomplished                         Simple Pocket
                                                                                                                        Finding the Narrow Pockets
                                                                                                                                                                                                                              A hexagonal surface with initial module positions (cyan) and goal cells (green)
using two phases: a centralized planning phase followed by a                                                    Our algorithm uses a single virtual module to traverse the
reconfiguration phase. Both phases are executed without any                                                     surface and map and number its perimeter cells. Once the
                                                                                                                perimeter cells have been numbered in ascending order,                 Complex Pocket
message passing between the modules. The algorithm presented
here deals with the traversal phase of the reconfiguration.                                                     the algorithm looks for pairs of cells that are in contact
        Initial Configuration
                                                                                                                but have numbers that differ by more than one. The pairs
                                                       Goal Configuration                                       that are not included in the range of another pair are the
                                                                            Pattern for All BASIC Cases         ones that mark a narrow pocket entrance. We call them                     Pattern for All SINGLE Cases
                                                                                                                bridge identifiers.
 Non-concurrently
 traversable
                                                                                                                   Identifying the Main Bridge Cases

System Model:                                                                   Patterns for SHORT
                                                                              (perimeter length <= 4)
                                                                                                                                                                                                Patterns for LONG
                                                                                                                                                                                          (perimeter length > 4) RIGHT
Physical Module Constraints:                                                       RIGHT Cases                                                                                                         Cases

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
                                                                                                           SINGLE              BASIC                LEFT                     RIGHT                                       Modules in movement (blue), Bridges (pink) and Bridge Identifiers (yellow) cells shown.

module to rotate around.                                                                                   The main bridge cases are identified by looking at the immediate
3)Modules cannot carry, push, or pull other modules, i.e., a                                               neighbors of the bridge identifier cells. The four cases shown above                                          Future Work:
module is only allowed to move itself.                                                                     cover all possible cases for narrow pocket entrances.                                                         Expanding the algorithm to work on pockets openings that are
4)Modules are deformable and move by a combination of                                                                                                                                                                    wider than 2 cells and constructing bridges with more than two
                                                                                                                                                                                                                         modules will create a more efficient motion planner by reducing
rotation and changing joint angles, either clockwise (CW) or                                                           Identifying Bridge Sub-Cases                                                                      the time necessary to traverse a surface. Future work on the
counter-clockwise (CCW).
                                                                                                                                                                                                                         motion planner in general will include working with real
                                                                                                           Only LEFT and RIGHT bridge cases have sub-cases. These sub-cases
                                                                                                                                                                                                                         modules and more realistic scenarios. Such scenarios include:
                                                                                                           depend on the number of perimeter cells that are located inside the
                                                                                                                                                                                                                         module fault tolerance, limited global knowledge, asynchronous
                                                                                                           pocket and on its layout. We have proven that we can recognize and
                                                                                                                                                                                                                         movement and changing environment.
                                                                                                           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.
                                                                                                                                                                                                                         References:
                                                                                                                                                                                                                         D. Little and J. Walter. “Using Hexagonal Metamorphic Robots to Form
                                                                                                                                   Bridge Cells                                                                          Temporary Bridges.” In Proc. of IEEE Intl. Conf. on Intelligent Robots
                                                                                                           There are three types of bridge cells: Bridge, TempSupport and                                                and Systems, pages 2652-2657, 2005.
Algorithm Module Constraints:
                                                                                                           Support. The role of the Bridge cell is to block the entrance to the
1)Modules move in synchronous rounds.                                                                                                                                                                                    J. Walter and D. Little. “Bridging gaps in traversal surfaces with
                                                                                                           narrow pocket. In some cases a module cannot reach a bridge cell
2)Only one module tries to move into a particular cell in each                                                                                                                                                           hexagonal metamorphic robots.” In Proc. of the 10th Intl. Conf. on
                                                                                                           before the other modules start going through the pocket, so it needs
round.                                                                                                                                                                                                                   Robotics and Remote Systems for Hazardous Environments, Gainesville,
                                                                                                           the TempSupport to move over. Once the Bridge is in place the                                                 FL, Mar. 28-31, 2004.
3)Modules have local information and a map of the initial state
                                                                                                           TempSupport needs to move to a location in which it would be able to
of the plane.
                                                                                                           rejoin the rest of the modules, preserving the optimal intermodule
4)Two moving modules are separated by two free cells.
                                                                                                           spacing of two free cells between moving modules.
                                                                                                                                                                                                                                         Research supported by NSF grant IIS-
                                                                                                                                                                                                                                         0712911.

				
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