A New Perspective on Projection-to-State Safety and Its Application to Robotic Arms

Projection-to-state safety (PSSf) is a special case of input-to-state safety (ISSf), which uses projections to create a low-dimensional representation of the uncertainties and allows quantifying the impact of the projected disturbance on the safety guarantees in a low-dimensional space. In this paper, rather than reasoning PSSf as a characterization of safety in terms of projected uncertainties, we interpret it as a property of the original dynamical system that is guaranteed by ISSf of the projected dynamical system. This new perspective allows for simplifying controller synthesis via projected dynamical systems and quantifying the impact of uncertainties on the safety of the original dynamical systems. Moreover, we extend the results of PSSf to deal with high relative degree constraints via a coordination transformation strategy, which makes it also applicable to some high-order systems. To exhibit the efficacy of the new perspective, a robotic arm application, and its corresponding numerical results are provided for validation.