This paper deals with the problem of collision avoidance amongst autonomous vehicles that can be represented by the unicycle model on a 2D plane. The control strategy is inspired by the way animals navigate, relying only on line-of-sight (LOS) angle and time-to-collision (TTC) as feedback, made available by the on-board gimbaled monocular camera. The novelty of this work is in the proposed avoidance strategy that achieves collision avoidance without the measurement of distance, including the guarantees supported by Lyapunov-based analysis. Additionally, the proposed solution does not require an underlying logic that decides to avert or not the collision, therefore relaxing the conservatism of previous results. The proposed framework is also suitable for evading collisions in a scenario with multiple obstacles. Simulation results validate the collision avoidance law and illustrate its application to multiple obstacles.