Comparative Analysis of Energy Transfers and Performance in Safety-Critical Control Using Control Barrier Functions

Abstract

Control barrier functions (CBFs) are used in safety-critical control strategies, implementing a modification of a nominal control action to achieve invariance of a subset of the state space representing safe operating conditions. In this paper we perform a comparative study involving existing safety-critical CBF designs, including energy-based CBFs and Exponential CBFs. The analysis, performed both theoretically and on a benchmark obstacle avoidance task, provides insights into how these CBFs affect energy transfers and the overall performance of the closed-loop system, highlighting benefits and limitations of each approach. To validate our analysis, we conduct software simulations on a 3R planar robot and a 7-DoF robotic manipulator, complemented by experimental evaluations on a physical robotic platform.