Interval Barrier Lyapunov Function and Its Application to Wheeled Mobile Robot

Since the classical barrier Lyapunov function (BLF) suffers from the restriction on the availability of constrained signals, this work proposes the concept of the interval BLF through introducing the nonlinear interval observer (NIO) technology. Specifically, the velocity-constrained tracking control design of the wheeled mobile robot (WMR) is studied without the linear velocity measurement. To accomplish the constraint objective on the unmeasured linear velocity, the NIO is developed to estimate the upper and lower boundaries of that. Through tactfully using these boundaries and designing the interval BLF, the tracking control scheme is developed for the WMR to accomplish the velocity constraint objective for both the linear and angular velocities. Finally, the proposed control scheme is demonstrated through numerical validation.