  We define an admissibility condition for abstractions expressed using angelic
semantics and show that these conditions allow us to accelerate planning while
preserving the ability to find the optimal motion plan. We then derive
admissible abstractions for two motion planning domains with continuous state.
We extract upper and lower bounds on the cost of concrete motion plans using
local metric and topological properties of the problem domain. These bounds
guide the search for a plan while maintaining performance guarantees. We show
that abstraction can dramatically reduce the complexity of search relative to a
direct motion planner. Using our abstractions, we find near-optimal motion
plans in planning problems involving $10^{13}$ states without using a separate
task planner.
