Real-time linear control of the omnidirectional mobile robot

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 nonlinearity influencing the input-output tracking error dynamics, is 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, while additively being perturbed by the unknown, smooth, time-varying signal which is proven to be trivially observable. The total state-dependent uncertain input is assumed to be locally approximated by an arbitrary element of, a, fixed, sufficiently high degree family of Taylor polynomials for which a linear observer with a corresponding self-updating internal model may be readily designed. Generalized Proportional Integral (GPI) observers, which are the dual counterpart of GPI controllers (see [1]), are shown to naturally estimate, in a arbitrarily close manner, the unknown perturbation input of the simplified system and a certain number of its time derivatives, thanks to its embedded, internal time-polynomial model of the unknown, state-dependent, perturbation input. 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 in a trajectory tracking problem.