Toward Position-Only Time-Delayed Control for Uncertain Euler–Lagrange Systems: Experiments on Wheeled Mobile Robots

This letter addresses the various practical design issues of a continuous-time time-delayed control (TDC) and proposes a new controller to make the TDC more suitable and applicable for real-life systems. While TDC has been renowned for its robust performance and simplicity in form, it requires state-derivatives feedback which may not be available explicitly in practice; and multiple numerical differentiations of the noisy state data deteriorate performance by invoking measurement error. In this letter, position-only time-delayed control (POTDC) has been proposed for a class of Euler-Lagrange systems which encompasses a large class of practical systems such as robotic manipulators and unmanned mobile robots. Contrary to the conventional TDC, the proposed POTDC eliminates explicit requirement of velocity and acceleration feedbacks and uses only position information of present and past instances to estimate the velocity and acceleration terms. It thus alleviates the measurement error arising from a numerical computation of state-derivatives. Moreover, based on the Razumikhin theorem, continuous-time stability is rigorously analyzed with consideration of the time-delay element in POTDC, which indeed establishes a selection criterion for the sampling interval and provides the designer a range of sampling intervals for same choice of controller gains. This allows POTDC to be suitable for systems which specifically operate with high sampling intervals due to application requirement. Accordingly, experimental validations of POTDC are provided in comparison with TDC under various sampling intervals, using a wheeled mobile robot.