Prescribed-Time Safety Filter for a 7-DOF Robot Manipulator: Experiment and Design

Abstract

In this research effort, we formulate a prescribed-time safety filter (PTSf) for the case of a redundant manipulator performing a fixed-duration task. This formulation, which is based on a quadratic programming approach, yields a filter that is capable of avoiding multiple obstacles in a minimally invasive manner with bounded joint torques, while simultaneously allowing the nominal controller to converge to positions located on the boundary of the safe set by the end of the fixed-duration task. To demonstrate the efficacy of the proposed method, we performed a series of simulations and experiments on Baxter, a seven-DOF collaborative robot manipulator. In these simulations and experiments, Baxter must follow a 6-s parabolic trajectory as closely as possible while navigating around a large spherical obstacle blocking its path and place an object precisely on the surface of a table without overshoot by the end of the 6 s. The results of our simulations and experiments demonstrated the ability of the PTSf to enforce safety throughout the 6-s task, while allowing the robot manipulator to make contact with the table and thus achieve the desired goal position by the end of the task. Furthermore, when compared with the exponential safety filter (ESf), which is the state-of-the-art in current literature, our proposed method yielded consistently lower joint jerks. Thus, for tasks with a fixed duration, the proposed PTSf offers performance benefits over the exponential filters currently present in literature.