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This paper presents a collision avoidance method for elliptical agentstraveling in a two-dimensional space. We first formulate a separation conditionfor two elliptical agents utilizing a signed distance from a supporting line ofan agent to the other agent, which renders a positive value if two ellipses areseparated by the line. Because this signed distance could yield a shorterlength than the actual distance between two ellipses, the supporting line isrotated so that the signed distance from the line to the other ellipse ismaximized. We prove that this maximization problem renders the signed distanceequivalent to the actual distance between two ellipses, hence not causing theconservative evasive motion. Then, we propose the collision avoidance methodutilizing novel control barrier functions incorporating a gradient-based updatelaw of a supporting line. The validity of the proposed methods is evaluated inthe simulations.

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