Control barrier functions (CBFs) provide a simple yet effective way for safe control synthesis. Recently, work has been done using differentiable optimization (diffOpt) based methods to systematically construct CBFs for static obstacle avoidance tasks between geometric shapes. In this work, we extend the application of diffOpt 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 extend 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 and a circular CBF based method on a simulated dynamic obstacle avoidance task. 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（CBF）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，系统性地构建用于几何形状间静态避障任务的控制障碍函数。本研究将可微优化控制障碍函数的应用拓展至动态避障任务，证明了通过采用时变控制障碍函数（TVCBF）框架，可实现针对动态几何障碍物的规避。此外，我们进一步展示了如何在考虑测量噪声与执行机构限制的条件下扩展时变控制障碍函数约束。为验证所提方法的有效性，首先在动态避障仿真任务中，将其与基于模型预测控制的方法及基于圆形控制障碍函数的方法进行性能对比；随后，在七自由度Franka Research 3型机械臂的实验研究中验证了所提方法的实际效果。