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

Shape Uncertainty Formulation

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?

  • $\begingroup$ The notation $PCC_{ij} : \Bbb R^2 \to [0,1]$ means "$PCC_{ij}$ is a function from $\Bbb R^2$ (real ordered pairs) to the interval $[0,1]$." $\endgroup$
    – apnorton
    Oct 24, 2014 at 3:36
  • $\begingroup$ Inf and sup are terms that deal with limits. The bottom equation seems to treat at least one of those symbols as a random variable, but I'd have to dig deeper to find where it's defined. $\endgroup$
    – apnorton
    Oct 24, 2014 at 3:38


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