free motions of round robots on metric graphs
445KbAbstractIn this thesis, we study the path connectivity problem of configuration spaces of two robots that move without collisions on a connected metric graph. The robots are modelled as metric balls of positive radii. In other words, we wish to find the number of path connected components of such a configuration space. Finding a solution to this problem will help us hermes kelly 32 replica
to understand which configurations can be reached from any chosen configuration. In order to solve the above problem, we show that any collision free motion of two robots can be replaced by a finite sequence of elementary motions. As a corollary, we reduce the path connectivity problem for a 2 dimensional configuration space to the same problem for a simple 1 dimensional subgraph (the configuration skeleton) of the space.