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.

翻译：四旋翼飞行器的安全稳定控制是一个重要挑战，其目标是在避障的同时到达目标位置。现有解决方案大多依赖基于优化的方法，需要大量机载计算资源。本文提出了一种新颖方法来解决该问题，并提供了适用于机载执行的快速计算解决方案。受Sontag通用公式启发，我们提出了一种融合控制李雅普诺夫函数（CLF）与控制屏障函数（CBF）条件的解析控制策略，有效避免了机载求解优化问题的需求。此外，我们通过引入输入-状态稳定性（ISS）与输入-状态安全性（ISSf）概念拓展了该方法，增强了通用公式应对扰动的能力。进一步地，我们提出了一种基于投影的方法，确保通用公式在面临控制输入约束时仍能保持有效性。该方法的核心思想是将通用公式导出的控制输入投影至控制输入域内最近点。通过全面的仿真与实验结果，我们验证了所提方法的有效性并突出了其优势。