Safe prescribed time controller for wheeled mobile robots by using control barrier functions as a safety filter

In this paper, we design a prescribed time controller to achieve a desired trajectory within a user-defined time, ensuring that the error dynamics converge to the equilibrium point at this time. Subsequently, a proportional controller is utilized to maintain the system's errors at the equilibrium point beyond the prescribed time. Additionally, we introduce a control barrier function (CBF) as a safety filter to guarantee that the system remains within a safe zone, avoiding collisions with predefined unsafe areas along the trajectory. To validate the proposed control methodology, we conducted a series of simulations across various scenarios. The results demonstrate the scheme's capability to reach the equilibrium point regardless of initial conditions and user-defined prescribed time, while consistently maintaining safety within the defined set space.