  Motion planning in modified environments is a challenging task, as it
  compounds the innate difficulty of the motion planning problem with a
changing
  environment. This renders some algorithmic methods such as probabilistic
  roadmaps less viable, as nodes and edges may become invalid as a result of
these
  changes.
  In this paper, we present a method of transforming any configuration
  space graph, such as a roadmap, to a dynamic data structure capable of
updating
  the validity of its nodes and edges in response to discrete changes in
obstacle positions.
  We use methods from computational geometry to compute 3D swept volume
  approximations of configuration space points and curves to achieve 10-40
  percent faster updates and up to 60 percent faster motion planning queries
than previous algorithms while requiring a
  significantly shorter pre-processing phase, requiring minutes instead of
  hours needed by the competing method to achieve somewhat similar update
times.
