The objective of the presented research is to design barrier function inspired algorithms that enable safe shared autonomy for humans and autonomous systems teams. While always guaranteeing safety, the autonomy should be reactive to humans’ cognitive state to enhance collaboration among them. In chapter 3 we present our preliminary research, where we solved the problems of guaranteeing the execution of robotic tasks over long time horizons, and building valid discontinuous high-order control barrier function candidates for piecewise continuous systems. Additionally, we also develop a Matlab-Simulink testing platform using Microsoft Flight Simulator for high-quality visualization. This simulator will soon enable us to test our theoretical findings with human in the loop experiments, as explained in the proposed work in chapter 4. Lastly, we also aim to develop the theory to build high-order nonsmooth but continuous control barrier functions, as it is still an open question within the barrier function literature.