Stability of steady motions of a mobile robot with roller-carrying wheels and a displaced centre of mass

The motion of a mobile three-wheel robotic vehicle on a horizontal surface is investigated. Passive rollers are fastened along the rim of each wheel, enabling each wheel not only to roll in the usual manner, but also to move perpendicular to its plane. Each of these wheels, as well as the ordinary wheels, is equipped with one drive, which rotates the wheel about its axis. The vehicle equipped with roller-carrying wheels can move in any direction with any orientation. The motion of the robot on a horizontal surface is studied in the case where the centre of mass of the robot deviates from the geometric centre of the triangular platform, and there is no slip at the points of contact of the rollers with the supporting surface. In the case of free motion of the robot, an additional first integral is pointed out and the exact solution found is analysed. An equation for specifying steady motions, under which a constant voltage is supplied to the DC motors that drive the wheels, is constructed. The stability of the rectilinear motion of the robot is investigated.