Gait design by graph coloring for robots that have legs on their faces

This paper proposes a gait design method for robots that have legs on their faces. The method is based on a graph coloring problem in the theory of graphs. Representing a structure of a robot as a graph on a sphere, it is shown that the number of phases of movements needed for a leg is given as a minimum chromatic number of that graph. Also the allocation of an initial phase for each leg is given by a specific coloring pattern. For the demonstration of an actual hardware construction, we show a 12 legged square prismatic robot in which all the legs are driven by a row of gears.