Optimization-free Smooth Control Barrier Function for Polygonal Collision Avoidance

TL;DR

This paper introduces an optimization-free, smooth control barrier function approach for polygonal collision avoidance that is computationally efficient, nonconservative, and applicable to various multi-vehicle and robotic systems.

Contribution

It proposes a novel smooth CBF method that avoids optimization, using Boolean logic and log-sum-exp approximation, extending to multi-vehicle and robotic applications.

Findings

The method is computationally efficient and nonconservative.

Successfully applied to distributed collision avoidance of vehicles.

Extended to control a container crane avoiding moving obstacles.

Abstract

Polygonal collision avoidance (PCA) is short for the problem of collision avoidance between two polygons (i.e., polytopes in planar) that own their dynamic equations. This problem suffers the inherent difficulty in dealing with non-smooth boundaries and recently optimization-defined metrics, such as signed distance field (SDF) and its variants, have been proposed as control barrier functions (CBFs) to tackle PCA problems. In contrast, we propose an optimization-free smooth CBF method in this paper, which is computationally efficient and proved to be nonconservative. It is achieved by three main steps: a lower bound of SDF is expressed as a nested Boolean logic composition first, then its smooth approximation is established by applying the latest log-sum-exp method, after which a specified CBF-based safety filter is proposed to address this class of problems. To illustrate its wide applications, the optimization-free smooth CBF method is extended to solve distributed collision avoidance of two underactuated nonholonomic vehicles and drive an underactuated container crane to avoid a moving obstacle respectively, for which numerical simulations are also performed.