Safety-Critical Control on Lie Groups Using Energy-Augmented Zeroing Control Barrier Functions

TL;DR

This paper develops safety-critical control methods on Lie groups using Zeroing Control Barrier Functions, enabling obstacle avoidance and energy safety in mechanical systems with theoretical validation and simulations.

Contribution

Introduces two classes of ZCBFs on Lie groups for obstacle avoidance and energy safety, with theoretical validation and practical simulations.

Findings

Effective obstacle avoidance demonstrated in simulations

Energy safety constraints successfully enforced

Method applicable to various mechanical systems

Abstract

We study safety-critical control on fully actuated mechanical systems by means of Zeroing Control Barrier Functions (ZCBFs) defined on Lie Groups. Specifically, we introduce and theoretically validate two classes of ZCBFs. The first enforces kinematic constraints, suitable for implementing obstacle avoidance algorithms. The second enforces kinetic energy limits along prescribed inertial-frame translational and rotational directions, relevant for ensuring safe physical interaction. Numerical simulations involving slit traversal and safe landing scenarios are presented to validate the effectiveness and versatility of the proposed methodology.