Self-reconfiguration of shape-shifting modular robots with triangular structure

In this paper, we present a reconfiguration algorithm for shape-shifting modular robots with triangular structure. The is derived from novel description of the configuration space based on extended binary trees. Extended trees representing same are grouped into equivalence classes, which allows one-to-one correspondence between and its mathematical representation. Reconfiguration then accomplished by successive construction goal configuration, realized moving individual modules along surface robot building up tree populating unoccupied indices in ascending order new modules. capable solving self-reconfiguration problem structure O(n2) steps demonstrated two examples. We discuss limits proposed methods, regarding constraints implementation lack efficient collision avoidance, outline possible resolutions.