Linear Observer‐Based Active Disturbance Rejection Control of the Omnidirectional Mobile Robot

Abstract

Abstract This article describes the design of a linear observer‐linear controller‐based robust output feedback scheme for output reference trajectory tracking tasks in an omnidirectional mobile robot. The unknown, possibly state‐dependent, additive nonlinearities influencing the input‐output tracking error dynamics are modeled as an absolutely bounded, additive, unknown “time‐varying disturbance” input signal. This procedure simplifies the system tracking error description to that of three independent chains of second order integrators with, known, position‐dependent control gains. These simplified systems are additively perturbed by the unknown, smooth, time‐varying signal which is proven to be trivially observable. Generalized proportional integral ( GPI ) observers, are shown to naturally estimate, in an arbitrarily close manner, the unknown perturbation input of the simplified system and a certain number of its time derivatives. This information is used to advantage on the linear, observer‐based, feedback controller design via a simple cancellation effort. The results are implemented on a laboratory prototype of an omnidirectional mobile robot.