  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.
