Exploration of Finite 2D Square Grid by a Metamorphic Robotic System

Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid

“…The proposed algorithms slice the field into planes and the MRS visits the cells of each plane by sweeping each row or column of the plane. Thus, the proposed algorithms are extensions of the search algorithms by Doi et al in a finite 2D cubic grid [7].…”

“…By adding the above rules to the algorithm, the MRS can start the search. In the case of two modules, we show that there is a cell which cannot be visited by the MRS. Doi et al showed that in the 2D square grid two modules equipped with a common compass can move straight to one of the eight directions (north, south, east, west, northeast, northwest, southeast, and southwest) when they observe no wall [7]. By the same discussion, the MRS of two modules equipped with a common compass in 3D cubic grid can move straight to one direction, and the possible moving directions are eight diagonal directions in addition to those eight directions on planes perpendicular to x, y, or z axis when they can observe no wall.…”

“…Doi et al pointed out that the oblivious modules can use the shape of the MRS as global memory and the MRS can solve more complicated problem as the number of modules increases. They investigated search in a finite 2D square grid, that requires the MRS to find a target cell in a finite rectangle field [7]. Each module does not know the position of the target cell or the initial configuration of the MRS.…”

“…We demonstrate that three modules are necessary and sufficient when the modules are equipped with a common compass and five modules are necessary and sufficient when the modules are not equipped with a common compass. The numbers of sufficient modules in the 3D cubic grid are the same as those in the 2D square grid [7] because the MRS has more states in the 3D cubic grid than in the 2D square grid. For the intermediate case with a common vertical axis, we demonstrate that four modules are necessary and sufficient.…”

Exploring the Outer Boundary of a Simple Polygon

“…The robot has to inspect an unknown environment based only on what it has seen so far and to return to the starting point. This problem has important applications [4]- [6], such as rescuing human beings in disaster area, exploring damaged nuclear base and so on.…”