State Estimation and Output Feedback Control of Nonholonomic Mobile Systems Using Time-Scale Transformation

Abstract

In this paper, we propose an optical measurement system for a nonholonomic wheeled robot, and develop a state estimation method and a measurement-output feedback controller. Since the kinematic model of such a wheeled mobile robot is expressed as a driftless nonlinear state equation, there arises a difficulty in observer design that the observability depends on control inputs. This matter is settled by transforming the time-scale of the state equation to a new one, which represents the trajectory of the mobile robot. Then we construct a nonlinear observer which achieves local exponential estimation-error convergence and allows us to specify its rate, where the design method is based on “the extended Luenberger observer (Zeitz)”. Finally, we apply a control strategy for a class of driftless systems based on “time-state control form (Sampei et al.)” to the position control problem by combining it with the observer to form an output feedback controller. Some results of numerical simulations are also presented.