Dynamics of a Mobile Robot with Three Ball-Wheels

A mathematical model is developed for a mobile robot with three ball-wheels. The resulting model turns out to be a Chaplygin system, which allows the dynamics equations and the kinematic constraints to be integrated separately. The system is driven by six actuators: one actuator connected to one roller of each wheel, and three more actuators controlling the orientation of the ball-carriers with respect to the platform. Analysis of the mathematical model of this system using the holonomy matrix yields conditions under which the system can be rendered holonomic. Holonomy can be achieved by keeping the ball-carriers in pure translational motion. Therefore, the control of the system can be simplified by imposing constraints on the ball-carriers that prevent them from changing their orientation with respect to an inertial frame. KEY WORDS—mobile robot, ball-wheel, nonholonomic constraints, holonomy matrix, Chaplygin system