  Safe stabilization is a significant challenge for quadrotors, which involves
reaching a goal position while avoiding obstacles. Most of the existing
solutions for this problem rely on optimization-based methods, demanding
substantial onboard computational resources. This paper introduces a novel
approach to address this issue and provides a solution that offers fast
computational capabilities tailored for onboard execution. Drawing inspiration
from Sontag's universal formula, we propose an analytical control strategy that
incorporates the conditions of control Lyapunov functions (CLFs) and control
barrier functions (CBFs), effectively avoiding the need for solving
optimization problems onboard. Moreover, we extend our approach by
incorporating the concepts of input-to-state stability (ISS) and input-to-state
safety (ISSf), enhancing the universal formula's capacity to effectively manage
disturbances. Furthermore, we present a projection-based approach to ensure
that the universal formula remains effective even when faced with control input
constraints. The basic idea of this approach is to project the control input
derived from the universal formula onto the closest point within the control
input domain. Through comprehensive simulations and experimental results, we
validate the efficacy and highlight the advantages of our methodology.
