Prescribed-Time Safety Control for Unknown Systems and Its Application to Robotic Manipulator

In this paper, the concept of prescribed-time safety is introduced in the case that initial states are not in a safe set, which requires that the trajectories of systems visit a safe set within the prescribed time and then remain in the safe set. In contrast to safety-critical applications that require trajectories to always be in the safe set, prescribed-time safety control presents a greater challenge due to the introduction of a convergence time constraint. This paper presents a method to ensure prescribed-time safety for robotic systems. First, the prescribed-time control barrier function (PTCBF) is proposed for systems with relative degree of one, and it is extended to prescribed-time high order control barrier function (PTHOCBF) for systems with arbitrary relative degrees. Then, quadratic programming (QP) subject to PTCBF condition is constructed to solve control input. However, the proposed method cannot guarantee safety for systems with uncertain models. To address this limitation, a prescribed-time sliding mode disturbance observer (PTSMDO) is proposed to estimate the uncertainty. The estimated error is close to 0 before the time that states stay in the safe set. Based on the observed value of the uncertainty, the control input is solved by QP. Finally, the effectiveness of the proposed method is verified by a simulation and a physical experiment on Franka Emika robot. Note to Practitioners-This paper is motivated by the challenge encountered in robotic systems, which necessitate the control of the system's state to reach a predefined safe set and subsequently carry out tasks within this safe set in various practical applications, particularly in the realm of robot motion planning. In comparison to existing methods such as finite-time CBF and fixed-time CBF, the proposed prescribed-time CBF approach in this paper offers the advantage of allowing users to preselect the arrival time. Additionally, given that robot systems are typically subject to uncertainties stemming from parameter errors and external disturbances, this paper also introduces a method to the issue of prescribed-time safety for robot systems featuring uncertain models. The uncertain term within the model can be accurately estimated prior to the moment when the state arrives at the safe set, employing the proposed disturbance observer. Subsequently, the prescribed-time CBF is integrated with the estimation results to construct QP for control input. The simulation and experiment conducted on the Franka Emika robot verify that the proposed method is feasible.