Real-time linear control of the omnidirectional mobile robot

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 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 cancelation effort. The results are implemented on a laboratory prototype in a trajectory tracking problem.

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

“…This cancelation is achieved via smoothed versions of the observer generated variables,ˆ( )ξ js j t z = 1 , j = x, y, f and the use of the estimated tracking error velocities ê2x, ê2y and ê2f, also in their smoothed versions, ê2xs, ê2ys and ê2fs. The controller is then given by, 15) with K1 = diag(k1x, k1y, k1f), K0 = diag(k0x, k0y, k0f) and…”

“…The closed loop system is obtained from the substitution of the observer-based feedback controller (15), into the simplified tracking error dynamics expression (14). One obtains ˆwhich, thanks to the performance of the high gain GPI observer, converges to a small neighborhood of zero quite fast.…”

“…In fact, the efficiency of the scheme is successfully tested in real‐time experiments on a laboratory prototype of a mobile robot where unknown viscous frictions, Coulomb frictions, dead zones, and backlash phenomena are present. In preliminary results had been presented including an odometry‐based localization system and considering substantially simpler trajectories.…”

PSO-based optimized neural network PID control approach for a four wheeled omnidirectional mobile robot

“…In [8], the output feedback control structure with a linear controller and observer was used for tracking tasks of a TW-OMR. Disturbances on the system considered as additive uncertainty terms with the control action provide to the wheels.…”

Predictive Control of Mobile Robot Using Kinematic and Dynamic Models

“…On the other hand, a mechanical design process and an independent PID wheel controllers have been introduced in [10] for the omnidirectional mobile platform, whereas in [11] a method of generating near-optimal trajectories for an omnidirectional robot is proposed; this method provided an efficient method of path planning and allowed a large number of possible scenarios to be explored in real time. Authors of [12] presented a PI feedback control method for an omnidirectional mobile platform which is equipped with three lateral orthogonal-wheel assemblies.…”