Controlling the differential mobile robot with system uncertainty: Constraint-following and the adaptive robust method

Abstract

We aim to control the differential mobile robot system to follow a class of pre-specified constraints sufficiently closely in the presence of system uncertainties. The mass and the moment of inertia of the differential mobile robot are considered as the uncertain parameters, which are (possibly) fast time-varying. In the first step, based on Udwadia and Kalaba’s approach, an adaptive robust control scheme is proposed to deal with the system uncertainties. The adaptive law is of leakage type, which can adjust itself based on the tracking error. Using this adaptive robust control scheme, we can obtain the desired armature currents of the two direct current (DC) motors, which are not the real control inputs. In the second step, taking the motor dynamics into account, a Lyapunov Minimax approach for the required actual control inputs (i.e., the input voltages of the two DC motors) is proposed to generate the desired armature currents. This two-step control methodology guarantees uniform boundedness and uniform ultimate boundedness, and renders the system to follow a class of pre-specified constraints approximately.