Motion of minimal configurations of a modular robot: Sinusoidal, lateral rolling and lateral shift

Complex modular robots can be constructed by means of simple modules. There is no geometric superior size to the total number of modules that can be added. The number of possible configurations growth exponentially. However, an inferior limit exists: the minimum number of modules needed to achieve the locomotion. In this paper, three minimal configurations has been developed using only two and three one-degree-of-freedom modules. The simplest one is pitch-pitch (PP) configuration, composed of two modules, which can move in a straight line, forward or backward, at different speeds. The second one is the pitch-yaw-pitch (PYP), with one more module that moves in the yaw axis. In this case, three new kinds of motion can be achieved: 2D sinusoidal motion, lateral shift and lateral rolling. All these gaits are controlled by sinusoidal waves using different amplitudes and phases. Finally, the third configuration is a three-modules star, that can be moved in three directions as well as rotated parallel to the ground.