# Why reciprocal velocity obstacle generates oscillation free navigation compared to VO

I am tryin to understand this paper about "reciprocal velocity obstacles for real-time multi-agent navigation" and to compare it with the original Velocity Obstacle approach.

I can not understand the proof to why this approach produces oscillation-free velocities.

Also Lemma 4 (Convexity) is:

Could somebody explain Lemma 4 to me and how it is significant?