Dynamical Modelling and Positioning Control Simulation of a Spherical Robot Driven by Three Omnidirectional Wheels

In this paper, we concerned on the dynamical modelling and the position control problem for a novel spherical robot which was driven by three omnidirectional wheels. We first introduce the mechanism of our spherical robot. And then considering the noholonomic constraints of the shell contacting with the omnidirectional wheels and the shell contacting with the ground, we developed a nonlinear dynamical model for the system by use of Chaplygin equation. With the model, we suggested that the robot was an under-actuated system which consists of six independent velocities and three driving-torque inputs. By linearized the position variables of the shell, we designed a controller to regulate the position of the system according to the Theorem of Partial Feedback Linearization. Numerical simulations were exploited to show the effectiveness of our controller.