I have been working with the Velocity Obstacles concept. Recently, I came across a probabilistic extension of this and couldn't understand the inner workings.
Source: Recursive Probabilistic Velocity Obstacles for Reflective Navigation http://www.morpha.de/download/publications/FAW_ASER03_Kluge.pdf
What does the equation at the bottom and the top mean? Vij is the relative velocity of agent i to agent j. ri & ci and rj & cj are their respective radius and centers.
Update: What does inf(ri + rj) and sup(ri + rj) mean? Does it mean that I should define a function that goes from 1 to 0 from inf to sup? And if not, then how do I calculate the value of PCC at any given point?