Controlling the Locomotion of Spherical Robots or Why BB-8 Works

Abstract

Spherical robots have a wide range of self-propulsion mechanisms. Of particular interest in this paper are propulsion systems where wheels are placed in contact with the inner surface of the spherical shell of the robot. Here, locomotion is achieved by a combination of the actions of the motors along with the rolling constraints at the point of contact of the shell with the ground surface. We ask and seek the answer to the following question using elementary arguments: What is the minimal number of actuations needed to completely prescribe the motion of the robot for the two distinct cases where it is rolling and sliding on a surface? We find that two points of actuation are all that is needed provided some simple geometric conditions are satisfied. Our analysis is then applied to the BB-8 robot to show how locomotion is achieved in this robot.