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, The task is parallelized as many positions can be filled at the same time. The modular robot drawn in red detects a section of line merge made by the internal hole

, 61 of messages for four topologically different representations on three different scales. The number of messages remains linear and similar across all representations, Three classes of target structure: Power Button, Letter C and Bumpy respective representations

. .. , Relative number of available docking positions over the percentage of construction. It shows parallelism of the method by having as many docking positions as possible at the same time. The thick lines represent the standard deviation in a certain construction percentage, p.63

, 65 4.14 Locomotive example made by 61,780 Catoms constructed using the distributed 3D self-assembly algorithm. The self-assembly can be done without any position being blocked during the construction, Some examples of modular robots configurations that express if the center position (colored module) can be docked or not. Modules in green represent positions that can be docked with the surrounding modules

. .. , 69 4.17 Number of available docking position during the progression of 3D selfassembly. Multilayer Algorithm presents a peak of efficiency at a regular phase in the construction

, Comparing the number of time steps required to build a cube and a hollow version of a cube

, 74 4.23 Number of time steps needed to self-assembly a hollow sphere composed of 3.889 modules

, Messages required for the self-assembly of a sphere in a solid and hollow version

, Messages required for the self-assembly of a cylinder in a solid and hollow version

, Messages required for the self-assembly of a cylinder in a solid and hollow version

, Pyramidal object used for evaluation of self-assembly algorithm that is made of 42.744 modules

. .. , 78 4.30 Number of available docking position during the progression of 3D selfassembly for the Locomotive 3D. Multilayer algorithm presents a peak of efficiency at a regular phase in the construction, Messages used during the execution of the self-assembly planning algorithm for the pyramidal object

B. , Diameter bounds by the numer of vertices in the network graph for difference LMR network. S-Lattice and H-Lattice stands for Square and Hexagonal lattices, which are two-dimensional lattices. SC-Lattice stands for 3D Simple Cubic Lattice. The terms "LB" and "UB" respectively stand for "lower bound" and "upper bound"

, ) of 3D Catoms and its decomposition into horizontal layers with color gradient from the center of the ball

, Table comparing different types of hardware specification for modular robot

, Coordinate of all possible neighbors in FCC lattice for Catoms3D, p.17

. .. , 18 3.1 Summary of encoding scene methods for Programmable Matter, p.33

. .. Robots-planning-algorithm-overview, 49 4.2 Total number of time steps for the self-assembly with two spheres of the same scale. The solid version contains 5931 modules and in its hollow version 3889 modules

F. Besançon,