Stabilization of the Extended Nonholonomic Double Integrator Via Logic-Based Hybrid Control

Abstract

This paper derives a hybrid control law for an extended nonholonomic double integrator (ENDI) that captures the dynamics of a wheeled robot subject to force and torque inputs. A simple logic-based hybrid controller is proposed which yields global stability and convergence of the closed-loop system to an arbitrarily small neighborhood of the origin. This is achieved by mapping the state-space into a two dimensional closed positive quadrant space and dividing it into three overlapping regions where, for each region, a feedback law is conveniently designed. Convergence and stability of the closed-loop hybrid system are analyzed theoretically. An application is made to the control of a wheeled mobile robot of the unicycle-type. Simulation results are presented that illustrate the performance of the hybrid control law.