Control of a Spherical Robot: Path Following Based on Nonholonomic Kinematics and Dynamics

Abstract

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.