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，已有工作利用基于可微优化的方法系统性地构建用于几何形状间静态障碍物规避任务的CBFs。在本研究中，我们将基于可微优化的CBFs应用扩展到动态障碍物规避任务。我们证明，通过采用时变CBF（TVCBF）公式，能够实现针对动态几何障碍物的规避。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器限制。为验证所提方法的有效性，我们首先在包含非椭球障碍物的仿真动态障碍物规避任务中，将其性能与基于模型预测控制的方法进行比较。随后，我们通过使用7自由度Franka Research 3型机器人操作臂的实验研究，展示了所提方法的性能。