Control barrier functions (CBFs) provide a simple yet effective way for safe control synthesis. Recently, work has been done using differentiable optimization based methods to systematically construct CBFs for static obstacle avoidance tasks between geometric shapes. In this work, we extend the application of differentiable optimization based CBFs to perform dynamic obstacle avoidance tasks. We show that by using the time-varying CBF (TVCBF) formulation, we can perform obstacle avoidance for dynamic geometric obstacles. Additionally, we show how to alter the TVCBF constraint to consider measurement noise and actuation limits. To demonstrate the efficacy of our proposed approach, we first compare its performance with a model predictive control based method on a simulated dynamic obstacle avoidance task with non-ellipsoidal obstacles. Then, we demonstrate the performance of our proposed approach in experimental studies using a 7-degree-of-freedom Franka Research 3 robotic manipulator.

翻译：控制障碍函数（CBFs）为安全控制综合提供了一种简单而有效的方法。近期，已有研究利用基于可微优化的方法，系统性地构建针对几何形状间静态避障任务的CBFs。本文中，我们将基于可微优化的CBFs扩展至动态避障任务。我们表明，通过采用时变控制障碍函数（TVCBF）框架，可实现动态几何障碍物的避障。此外，我们还展示了如何调整TVCBF约束以考虑测量噪声和执行机构限制。为验证所提方法的有效性，我们首先在非椭球障碍物的仿真动态避障任务中，将其性能与基于模型预测控制的方法进行对比。随后，我们通过使用七自由度Franka Research 3型机器人操纵器的实验研究，展示了所提方法的实际性能。