Differentiable optimization based time-varying control barrier functions for dynamic obstacle avoidance

Abstract

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 propose a novel pipeline for diffOpt CBFs to perform dynamic obstacle avoidance tasks while considering measurement noise and actuation limits. 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 enable 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.