Collision Avoidance for Elliptical Agents with Control Barrier Function Utilizing Supporting Lines

TL;DR

This paper introduces a collision avoidance approach for elliptical agents using control barrier functions and supporting lines, ensuring accurate distance measurement and non-conservative evasive maneuvers in 2D space.

Contribution

It formulates a novel separation condition for elliptical agents using supporting lines and maximizes signed distance to match actual distance, enabling effective collision avoidance.

Findings

Validated in simulations showing effective collision avoidance

Supports non-conservative evasive maneuvers

Provides a new formulation for elliptical agent separation

Abstract

This paper presents a collision avoidance method for elliptical agents traveling in a two-dimensional space. We first formulate a separation condition for two elliptical agents utilizing a signed distance from a supporting line of an agent to the other agent, which renders a positive value if two ellipses are separated by the line. Because this signed distance could yield a shorter length than the actual distance between two ellipses, the supporting line is rotated so that the signed distance from the line to the other ellipse is maximized. We prove that this maximization problem renders the signed distance equivalent to the actual distance between two ellipses, hence not causing the conservative evasive motion. Then, we propose the collision avoidance method utilizing novel control barrier functions incorporating a gradient-based update law of a supporting line. The validity of the proposed methods is evaluated in the simulations.