The trajectory tracking task in a wheeled mobile robot (WMR) is solved by proposing a three-level hierarchical controller that considers the mathematical model of the mechanical structure (differential drive WMR), actuators (DC motors), and power stage (DC/DC Buck power converters). The highest hierarchical level is a kinematic control for the mechanical structure; the medium level includes two controllers based on differential flatness for the actuators; and the lowest hierarchical level consists of two average controllers also based on differential flatness for the power stage. In order to experimentally validate the feasibility of the proposed control scheme, the hierarchical controller is implemented via a Σ-Δ-modulator in a differential drive WMR prototype that we have built. Such an implementation is achieved by using MATLAB-Simulink and the real-time interface ControlDesk together with a DS1104 board. The experimental results show the effectiveness and robustness of the proposed control scheme.

This paper presents a hierarchical controller that carries out the angular velocity trajectory tracking task for a DC motor driven by a DC/DC Buck converter. The high level control is related to the DC motor and the low level control is dedicated to the DC/DC Buck converter; both controls are designed via differential flatness. The high level control provides a desired voltage profile for the DC motor to achieve the tracking of a desired angular velocity trajectory. Then, a low level control is designed to ensure that the output voltage of the DC/DC Buck converter tracks the voltage profile imposed by the high level control. In order to experimentally verify the hierarchical controller performance, a DS1104 electronic board from dSPACE and Matlab-Simulink are used. The switched implementation of the hierarchical average controller is accomplished by means of pulse width modulation. Experimental results of the hierarchical controller for the velocity trajectory tracking task show good performance and robustness against the uncertainties associated with different system parameters.

A mathematical model of a new "full-bridge Buck inverter-DC motor" system is developed and experimentally validated. First, using circuit theory and the mathematical model of a DC motor, the dynamic behavior of the system under study is deduced. Later, the steady-state, stability, controllability, and flatness properties of the deduced model are described. The flatness property, associated with the mathematical model, is then exploited so that all system variables and the input can be differentially parameterized in terms of the flat output, which is determined by the angular velocity. Then, when a desired trajectory is proposed for the flat output, the input signal is calculated offline and is introduced into the system. In consequence, the validation of the mathematical model for constant and time-varying duty cycles is possible. Such a validation of this mathematical model is tackled from two directions: (1) by circuit simulation through the SimPowerSystems toolbox of Matlab-Simulink and (2) via a prototype of the system built by using Matlab-Simulink and a DS1104 board. The good similarities between the circuit simulation and the experimental results allow satisfactorily validating the mathematical model.

This paper reports a solution for trajectory tracking control of a differential drive wheeled mobile robot (WMR) based on a hierarchical approach. The general design and construction of the WMR are described. The hierarchical controller proposed has two components: a high-level control and a low-level control. The high-level control law is based on an input-output linearization scheme for the robot kinematic model, which provides the desired angular velocity profiles that the WMR has to track in order to achieve the desired position (x∗, y∗) and orientation (φ∗). Then, a low-level control law, based on a proportional integral (PI) approach, is designed to control the velocity of the WMR wheels to ensure those tracking features. Regarding the trajectories, this paper provides the solution or the following cases: (1) time-varying parametric trajectories such as straight lines and parabolas and (2) smooth curves fitted by cubic splines which are generated by the desired data points {(x1∗, y1∗),..., (xn∗, yn∗)}. A straightforward algorithm is developed for constructing the cubic splines. Finally, this paper includes an experimental validation of the proposed technique by employing a DS1104 dSPACE electronic board along with MATLAB/Simulink software.

In this paper, we present a controller to solve the path-tracking task in a wheeled mobile robot. We show that a linear PD controller, driven by the tracking error, can be used to generate the desired profiles to be tracked by the motor velocities by means of two linear inner proportional-integral loops. We formally prove that an ultimate bound exists which can be rendered small by a suitable selection of the controller gains. This is the first time that such a result is presented in the literature when considering, simultaneously, both the kinematic and the dynamic models of the wheeled mobile robot.