LaValle Planning Algorithms Ch 4


  • (110) Lots of discussion of sets & topology, manifolds, groups
  • 2 topo spaces may have same fundamental group even if they are homomorphic
  • A robot w/n DOF is usually describable by an n-dim manifold, called the configuration space (C-space)
  • C-space transforms dealing w/models  & transforms to computing a path traversing a manifold
  • (129) Use of open set for free regions in manifold makes finding shortest paths impossible, although it is possible to get arbitrarily close to it
  • (131) Many problems are NP-hard, the dimension of C-space is unbounded (?)
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