Control of a spherical robot: Path following based on nonholonomic kinematics and dynamics

This paper presents the controller design for the path following of a spherical mobile robot, BHQ-1. Firstly, a desired velocity for the reference path is deduced from the kinematic model, which cannot be transformed into the classic chained form. Secondly, a necessary torque for the desired velocity is obtained based on the dynamic model. As to the kinematics, a one-dimensional function is selected to measure the two-directional tracking error, and the velocity of rolling forward is reasonably assumed to be constant; therefore the multiple-input multiple-output (MIMO) system is transformed into a single-input single-output (SISO) system. As to the dynamics, both exact dynamics and inexact dynamics with modeling error as well as bounded unknown disturbance are taken into account, based on which a proportional-derivative (PD) controller and a sliding mode controller with adaptive parameters are proposed respectively. Finally, convergence analysis and simulation results are provided to validate these controllers.