Collision avoidance is a problem largely studied in robotics, particularly in unmanned aerial vehicle (UAV) applications. Among the main challenges in this area are hardware limitations, the need for rapid response, and the uncertainty associated with obstacle detection. Artificial potential functions (APOFs) are a prominent method to address these challenges. However, existing solutions lack assurances regarding closed-loop stability and may result in chattering effects. Motivated by this, we propose a control method for static obstacle avoidance based on multiple artificial potential functions (MAPOFs). We derive tuning conditions on the control parameters that ensure the stability of the final position. The stability proof is established by analyzing the closed-loop system using tools from hybrid systems theory. Furthermore, we validate the performance of the MAPOF control through simulations, showcasing its effectiveness in avoiding static obstacles.

翻译：避障问题是机器人学中广泛研究的课题，尤其在无人机应用领域。该领域的主要挑战包括硬件限制、快速响应需求以及与障碍物检测相关的不确定性。人工势函数是应对这些挑战的重要方法。然而，现有解决方案缺乏对闭环稳定性的保证，并可能导致抖振现象。受此启发，我们提出一种基于多重人工势函数的静态避障控制方法。我们推导了控制参数的调节条件，以确保最终位置的稳定性。通过运用混杂系统理论工具分析闭环系统，建立了稳定性证明。此外，我们通过仿真验证了多重人工势函数控制的性能，展示了其在静态避障中的有效性。